51: Does Recycling Actually Conserve or Preserve Things? (MacBride)
Samantha MacBride
#scholarly, #argument, #systemanalysis, #logos, #ethos, #kairos, #cognitivebias, #currentevents, #research, #science
""217" " by grotos is licensed under CC BY 2.0 (cropped)
There are a series of assumptions behind the familiar assertion that recycling saves resources and energy, and in so doing, protects the environment . These assumptions are in the motto, “ recycling saves trees .” With recycling – one assumes – used materials stand in for raw materials. This way, recycled content cuts down on the need to extract (conservation), which in turn prevents some of the environmental damage from extraction that would be taking place without recycling (preservation).
Conservation and preservation are distinct, though linked, ideas. Historians of North American environmentalism distinguish the Conservation Movement , which focused on the responsible management of materials to sustain production and economic growth, from the Preservation Movement , which stressed the protection of wilderness. 1 Both movements have been rightly critiqued for failing to consider questions of power and equity in people’s health, dignity, and livelihoods. 2 Still, the distinction between conserving resources for use in production, and preserving complex ecosystems (which include people in human settlements), is useful for a question I now pose about recycling. Does recycling, in the way it is practiced today, actually conserve or preserve things that matter?
To answer “yes” requires that a set of assumptions hold true. When we say recycling saves trees, we start by assuming that the paper in the recycling bin goes to a plant to be sorted and baled. Plant managers find buyers for the bales, which are shipped off to a manufacturer. We assume that this manufacturer, individually or as part of a larger industry sector, is weighing the options between using virgin input (wood pulp) or secondary input (recycled paper). When it costs less to use recycled paper as an input, the manufacturer is going to use the secondary material to make things. So far, so good.
But to save trees, much less forests, more has to happen. When the decision is made to use recycled input, the virgin alternative ought to be conserved in a way that preserves ecosystems and people. Preservation isn’t achieved if the virgin stock is directed into a new product that hasn’t existed before; or if it is conserved technically for later use, and then harvested and utilized when economic growth makes for favorable conditions to ramp up production. It’s not enough to simply offer up recycled paper on a commodity market to be grabbed when price signals are favorable. It doesn’t do to merely measure increases in recycled content of various products on the market. Nor is it sufficient to theorize that recycling may have slowed a sectoral growth rate that would have proceeded, all things being equal, faster in an imaginary world in which there was no recycling at all. To save trees in a way that matters ecologically and socially means something more. It means that forests, including forest ecosystems and surrounding livelihoods in all of their complexity, are actually protected in today’s world.
Theoretically, there is no reason why recycling couldn’t deliver on such protection, were it integrated into a system of monitoring that followed through on promises. Such a system would need to identify limits on rates of extraction in accordance with their ecosystemic threat; include long term planning for stabilization of some extractive industries, and phase-out of others; and ensure maximum protection of future lands and ecosystems from development. Under such a system, extractive industries would need to demonstrate to what degree recycled inputs substituted for virgin sources in their sectors annually, and also that their sectors were not encroaching with new development in terrains that matter to people and other living things.
Empirically, there is no question that at certain times, for certain periods, recycling may have conserved virgin resources to some degree; and even that recycling may play a role in localized resource policies, such as boosting timber plantations that spare virgin forests as sources in papermaking. In fact, portions of the assumption of conservation, can be and regularly are dragged out for theoretical and/or empirical testing within the disciplines of resource economics, materials flow analysis, and life cycle analysis. There is much scholarship that asks whether recycling has resulted in, or could theoretically result in, less net extraction or harvest. 3 Such inquiries are interesting in their own right, and to the extent that they tell us something about tradeoffs that manufacturers make between virgin and recycled inputs, they inform an understanding of what recycling could, under ideal circumstances, achieve in terms of actual conservation — which would be a precondition for, but not a guarantee of, actual preservation.
We are on shaky ground, however, if we take these assumptions for granted. I trace my concern on this matter to the work of William Stanley Jevons. 4 In the 19th century, technological improvements in mining and combustion were greatly improving the efficiency of using coal as fuel. Noting these developments, Jevons argued that, rather than conserve coal, improvements in efficiency, and a subsequent drop in coal price, would paradoxically lead to an increased demand for coal.
The Jevons Paradox. Public Domain.
Now known as Jevons’ Paradox, this perspective observes that when you increase efficiency in production and consumption, you may well see an increase in overall extraction . 5 Massive amounts of scholarship have followed the Jevons’ Paradox, most around energy efficiency. 6 In the materials realm, recycling can be thought of as a form of efficiency (getting more out of the same input). 7 There is a growing body of work tracing the effects of recycling on extraction of virgin materials, in particular in the area of metals. 8 Scholars ask questions about conservation of metals in part because the data on their trade is more available than for other materials. It’s more organized. It’s more harmonized among different nations, given the nature of these economies. Both the economy of metals and as well as the material properties of metals make them relatively easy to be recycled over and over again and be reintroduced back into production, especially in comparison the heterogeneous range of synthetic polymers we call plastics. Yet we see growing rates of metals extraction taking place alongside growing recycling rates, worldwide. We can speculate about what those growth rates would have been had recycling not existed, but it would be hard to argue that global production systems are using less virgin raw material as a result of metals recycling, much less that metal recycling is preserving lands from mining. 9
"French waste lines" by Charos Pix is licensed under CC BY-NC-SA 2.0
The caveats and careful measurements in the specialized literatures above suggest that recycling can conserve resources temporarily in some cases, almost always absent considerations of preservation. Such nuances fall away, however, as recycling becomes idealized and abstracted as an ethical, “earth-saving” end unto itself. Under-examined assumptions of conservation and preservation run deep through recycling discourse, and are also core to the notion that reuse will cut down on the flow of materials and energy from cradle to grave. Each time reuse and recycling are affirmed in the waste hierarchy, there is a hazy sense that somewhere, by someone, some sort of accounting is going on to ensure that overall, recycling is delivering protection of things that matter. I would wager that many in the media, in environmental education, and even in environmentally focused NGOs hold this position. This is how recycling would, actually and not just in theory, “save the planet.” But is there really any coordinating body who is conducting such accounting? No. 10 And is recycling actually preserving ecosystems and livelihoods, or achieving real-world “dematerialization” (the technical term for less use of raw materials overall)? Not in any systematic way. 11
Oil, Gas, and Plastics
So far I’ve used the examples of forest products and metals. I have done so because of the historical potency of the motto “recycling saves trees”, and the relatively developed scholarship around steel, aluminum, and other metals. In reality, much more is going on around forestry, or the mining and metals trade, than is taken into account when one simply looks at recycling. But at least we have some data to inform questions. If we examine the plastics industry and the role of plastics recycling, we find that similar assumptions abound, with particular complications, and little information. How can we evaluate the assumption that plastic recycling reduces the need to extract fossil fuels; or the separate but related claim that manufacturing with recycled inputs uses less energy, meaning lower fuel use economy-wide, meaning diminished carbon emissions?
It is well known that only a small percentage of global fossil fuel extraction is used directly in plastics production. 12 So even recycling every shred of plastic would not, on its own, diminish the need to drill at current rates by much. Looking specifically at the U.S., the situation is no different. Let’s say we build up domestic plastic recycling capacity in the U.S., as many are calling for in the wake of China’s imports restrictions. What would the effect be of repatriating that tonnage, and feeding it back into domestic production, on domestic fossil fuel extraction – to make plastics, or to generate electricity?
It may surprise you to learn that the U.S. Energy Information Administration (EIA) “is unable to determine the specific amounts or origin of the feedstocks that are actually used to manufacture plastics in the United States.” 13
The reason hints at the constantly fluctuating conditions of virgin raw material sourcing that I’ve alluded to above, and data limitations that I’ll elaborate below. The EIA writes:
Because the petrochemical industry has a high degree of flexibility in the feedstock it consumes and because EIA does not collect detailed data on this aspect of industrial consumption, it is not possible for EIA to identify the actual amounts and origin of the materials used as inputs by industry to manufacture plastics. 14
Let’s pivot back to the day-to-day understanding of recycling, in which it is it is axiomatic to assert that plastic recycling saves oil and gas resources . 15 On a ton-for-ton basis, in a hypothetical scenario in which recycled materials actually substitute for fossil fuels, and lead to a concomitant net decrease in extraction or fuel combustion, such claims hold. But without data on “actual amounts and origin of materials used as inputs,” it is not possible to evaluate the actual effect of plastics recycling on conserving such inputs. This would be the precondition to assessing what role, if any, plastics recycling has on actual preservation of things that matter in the U.S. (such as coastal communities , Indigenous peoples’ lands, and/or arctic wildlife refuges ).
Frequent assumptions are being made among well-intentioned members of the media, environmental organizations, and concerned individuals that actual, current recycling efforts are part of real world protection. In more specialized discussions around Zero Waste and Circular Economy, there is a rolling process of coming to terms with hints that assumptions of conservation and preservation don’t hold. If, for example, we are dismayed to learn that plastics are “downcycled,” our dismay betrays a faith in the assumption of preservation in the background. If only plastic bottles could be produced in a closed-loop fashion , we reason, then we would be able to conserve at least some of the resources that would otherwise be extracted. Presumably, such conservation is needed for ecosystemic preservation, not just to boost the economic fortunes of the plastics industry.
Now let’s turn to the huge, multinational firms in the petrochemical industry that drill for the precursor materials for plastics at the beginning of the production chain. Let’s say more Americans recycled their plastics, and this resulted in an influx of more recycled plastic onto the market. Even with robust closed loops achieved, does anyone really think that the executives at one of these multinationals would get to the point of saying, “well, you know, it’s good that the need for input materials is being met by recycled plastic, and that means that this year we can scale back production a bit. We don’t need to open up a new offshore platform. It isn’t required to meet society’s needs after all!”
Ultimately, this would have to be the scenario in which more and more recycling of plastics actually preserved things that matter ecologically and socially. Yet very little of the empirical work needed to trace materials flows exists in the area of plastics recycling, in part because of a dearth of data. 16 And in the area of plastics waste we have perhaps the most egregious misuse of claims that recycling is going to address problems related to pollution and climate change. The industry, and affiliated academic researchers, carry out life-cycle analyses that are impeccable in their methodological approach to quantifying different energy and material requirements associated with primary and secondary flows of plastics. 17
None to my knowledge, however, answer the question of what more plastics recycling would do to diminish overall ecosystem withdrawals of fossil fuels. Does tar-sands extraction slow as a result? How about pipeline construction? Perhaps, with improved plastics recycling, we don’t need a Northeast U.S. expansion of storage capacity for hydrofractured natural gas. Not yet? Well, then, what are the plans for the scaleback?
Ideological Implications
These are both empirical and ideological questions. 18 They are ideological because a general optimism about recycling as earth-saving has become internalized in the thought processes of children and adults genuinely concerned about preservation. In everyday speak, assumptions of conservation and preservation swirl in a distant, misty background. In order to preserve optimism, can-doism, and a solutions oriented outlook it is easier not to look into these depths. In fact, critique of recycling’s earth-saving claims falls harshly on concerned ears, leaving bewilderment and a sense of betrayal. Sometimes, it is met with a binary response: either recycling is part of an overall process of saving resources and saving energy and by extension it’s saving the planet, or it’s a waste of time and it’s a sham and a lie.
I would urge all who are interested in this kind of thing to move away from binaries. The alternative is uncertain and less morally satisfying. It requires taking multiple perspectives, and wading through material complexity, power relations, institutional arrangements, and ideological maneuvering around recycling, asking again and again how, or even if, this or that initiative — often proudly and cheerfully announced by a consortium of producers — preserves things that matter. It also means looking at how recycling actually takes place in any particular place and time, not just under modelled conditions. Some of this work involves redirecting outrage. So, for example, if recycling plants are unable to sell recycled plastics because of market slumps, it is less morally shocking than a reflection of market conditions that they will landfill them instead? When people ask me about the crisis in North American plastics and paper recycling, which China’s trade policies has brought about, I’m tempted to respond, “what did you expect?” Recycling firms are tails wagged by massive dogs: neither evil, nor earth-saving, but actually a reflection of the organization of material exchange under the global market system, today.
In part, the potential for recycling to actually conserve and preserve is an empirical question, and the answers will vary from place to place and material to material. But it’s not just a matter of collecting data, or organizing the right technical systems. It also means recognizing that recycling as we know it may start with an ethical impulse, but materially translates into nothing more or less than a set of business practices. As with the 19th and early 20th scrap trades, recycling is part of smart industrial operations (nothing wrong with that). But let us dismantle the faith that recycling, as practiced currently, will save the earth if we do more of it. Affirming this ideal is a potent tool used by powerful networks of big producers, big extractors, and constellations of firms at the global level. Make no mistake, they are undertaking this strategy daily , with increasing sophistication. They understand the nuances of material sourcing, production volumes, input substitution, and property acquisition all too well. They rely on the fact that you don’t — and, in fact, can’t — because much of the data you would need for such an understanding is proprietary to them.
It is no easy feat to press producers to explain how recycling stands to scale back their operations, reduce their net output, or redress the ravages they have left behind. Such questions are typically outside the scope of a particular recycling project; easy to evade. As a group, these are smart folks. They know which NGOs to fund, which scholars to support, and where to make public appearances. They even understand the critiques that come out of discard studies, so they start to speak of “ plasticity ” instead of plastics; and they use the term “litter” to name the crisis of marine plastics.
But if you are in a position to do so, politely ask corporate spokespeople how the tonnage they take credit for recycling fed back into their operations last year, in a specific country, and how it in turn measurably reduced virgin extraction. Be specific. Ask them where and when it led to a reduced material throughput in their company or industry. Query them on the documented, not speculative, environmental protection afforded by, say, making cheap picture frames made out of spent polystyrene packaging. Reject the notion that cheap picture frames are a social good that would have needed to be manufactured with fracked natural gas, had polystyrene recycling not yielded up secondary inputs .
In the meantime, sit for a while to contemplate the fact that recycling, as it exists today, does not in fact save ecosystems in a way that matters on the whole ecologically or socially. How would recycling need to be practiced to achieve this desired end? In a different context of extraction, production, and growth – with different politics, knowledge structures, and ideologies. I realize this is an unsatisfying conclusion, but I believe in the importance of critique as a precondition to developing collaborative solutions. I have presented this information as part of a process of thinking through short-, medium- and long-term characteristics of this different context. This is an ongoing project to which I invite responses, as well as empirical contributions that would refine or refute what I have presented here.
Footnotes
- Hays, S. (1999). Conservation and the gospel of efficiency: The progressive conservation movement, 1890–1920. No. 40. University of Pittsburgh Press.
- See Guha,R. (YEAR). “Radical American environmentalism and wilderness preservation: a third world critique” Environmental Ethics 11, no. 1:71–83; Faber, D., and D. McCarthy. “Neo-liberalism, globalization and the struggle for ecological democracy: linking sustainability and environmental justice.” Just sustainabilities: Development in an unequal world (2003): 38-63.
- See Geyer, R. et. al. (2016) “Common Misconceptions about Recycling” Journal of Industrial Ecology 20, no. 5: 1010–17
- Jevons, W. S. (1866) The coal question: an inquiry concerning the progress of the nation, and the probable exhaustion of our coal-mines . London, UK: Macmillan and Company .
- See Alcott, B. (2005). “Jevons’ paradox” Ecological Economics 54, no. 1: 9–21.
- See Dimitropoulos, J. (2007). “Energy productivity improvements and the rebound effect: an overview of the state of knowledge.” Energy Policy 35, no. 12: 6354–63.
- I am grateful to Bruce Lankford for helping me clarify this. See Lankford, B. (2013) Resource efficiency complexity and the commons: the paracommons and paradoxes of natural resource losses, wastes and wastages . London: Routledge.
- See Modaresi, R. and D.B. Müller. (2012) “The role of automobiles for the future of aluminum recycling.” Environmental Science & Technology 46, no. 16: 8587–8594.
- OECD (2019), G lobal material resources outlook to 2060: economic drivers and environmental consequences . Paris: OECD Publishing
- The closest I have come to identifying such a body is the OECD, which has published interesting research on the this subject for a range of materials, but not plastics. OECD (2019), http://www.oecd.org/environment/global-material-resources-outlook-to-2060-9789264307452-en.htm
- The OECD writes that, “Recycling is projected to become more competitive compared to the extraction of primary materials,” but that, “The strong increase in demand for materials implies that both primary and secondary materials use increase at roughly the same speed.” OECD (2019), p. 3
- Most estimates cite to data from the British Petroleum Federation, http://www.bpf.co.uk/press/oil_consumption.aspx
- Energy Information Administration (EIA).2018. “How much oil is used to make plastic?” accessed 1/29/2019 at www.eia.gov/tools/faqs/faq.php?id=34&t=6.
- EIA 2018.
- The plastics industry is careful about how it phrases conservation claims in its public relations. It tends to talk about the importance of growing plastics recycling to jobs, litter cleanup, and generally as an end unto itself.
- Geyer, R. et. al. (2017) “Production, use, and fate of all plastics ever made.” Science Advances 3, no. 7
- The Plastics Division of the American Chemistry Council (2018). “Life Cycle Impacts of Plastic Packaging Compared To Substitutes in the United States and Canada” accessed 1/29/2019 at https://plastics.americanchemistry.com/Plastic-Packaging-Life-Cycle-Study/
- See Lifset, R.(1995). “Foreward”, in Ince, P. What won’t get harvested, where, and when: the effects of increased paper recycling on timber harvest, Yale University School of Forestry and Environment.
____________________
Samantha McBride is an Assistant Professor at the Baruch College School of Public Affairs and works full time as a professional in urban waste governance in New York City. Her essay was originally published in Discard Studies .
Does recycling actually conserve or preserve things? by
Samantha McBride
is licensed under a
Creative Commons Attribution-NoDerivatives 4.0 International License
.


3.6: Mechanical Advantage and Power
Reconciling Work with Mechanical Advantage
Back when we first talked about pulleys, we said that the block-and-tackle device was useful for lifting heavy objects. The figure below shows two blocks lifted the same distance by pulling on a rope in a pulley system. We know that it requires less force to lift the same mass for the case on the left than the case on the right, but now let's compare the amount of work done by the pull force in the two cases. In both cases, the block is raised the same distance, and in both cases it starts and ends at rest.
Figure 3.6.1 – Work Done with Pulley Systems
The pull force acts downward on the end off the rope, and the direction the end of the rope moves is downward, so there is positive work done in both cases. With identical blocks, the force required to be applied to the rope for the left case is half as great as the force required to lift the block in the right case. However, in order to lift the block the same distance from where it started, the rope must be pulled twice as far in the right case than in the left case, thanks to the pulley ratio constraint. With half the force acting over twice the distance, the amount of work done is the same. The multiplicative factor by which the force needed for the load exceeds the force exerted on the system is called mechanical advantage (MA) :
\[MA \equiv \dfrac{force~on~load}{force~applied}\]
What we have found is that since the work done on the load is the same as the work done from outside, the mechanical advantage can also be expressed in terms of the ratio of the displacement of the object on which the applied force acts (e.g. the end of the rope in a block-and-tackle), and the displacement of the load:
\[W_{in}=W_{out}~~~\Rightarrow~~~F_{applied}\Delta x_{applied}=F_{on~load}\Delta x_{load}~~~\Rightarrow~~~MA=\dfrac{\Delta x_{applied}}{\Delta x_{load}}\]
The mechanical advantage can of course be multiplied by including more pulleys (or mor loops around the same pulley) – the pulley constraint ratio discussed earlier is the same as the mechanical advantage in every case.
So it appears that the block & tackle (and simple machines more generally) trade effort (force) for displacement, such that the amount of work done remains the same. Let's see if we see a similar result for the case of the inclined plane.
Figure 3.6.2 – Work Done with an Inclined Plane
Let's assume that the inclined plane shown in the figure above is frictionless, that the force applied to the block is parallel to the plane, and that it is just enough so that the block moves at a constant speed up the plane. A FBD (without the irrelevant normal force which acts perpendicular to the motion) looks like:
Figure 3.6.3 – Partial FBD of Block on Plane
For the block to stay at a constant speed, the force up the plane must equal the force down the plane, which means:
\[ F = mg \sin \theta \]
So the force required is reduced by the factor \(\sin \theta \) compared to lifting the block straight up. But from trigonometry, the distance the block must be pushed is:
\[ d = \frac{\Delta y}{ \sin \theta } \]
When we multiply the force by the distance to get the work done, we get:
\[ W = Fd = \left( mg \sin \theta \right)\left( \frac{\Delta y}{ \sin \theta } \right) = mg \Delta y \]
This is the amount of work required to lift the block straight up at a constant speed, so once again the simple machine trades extra distance for less force to get the same work. This agrees with the result we have already obtained, using gravitational potential energy. [ Note: The change in gravitational potential energy equals the negative of the work done by the gravity force . In this case, we have computed the work done by us, and since the force we apply to do the work is in the opposite direction as the gravity component, we get a positive value. ]
Power
We take a moment now to introduce yet another physics word whose common usage in English is very different from its meaning in physics.
Definition: Power
Power is the rate at which work is performed.
Note that just like we can talk about the work done by an individual force or a collection of forces, we can also talk about the power "delivered" to a system by one or more forces. For example, if a car is moving at a constant speed on level ground, its kinetic energy is not changing over time, so no total work is being done on it. If no work is done on it over time, there is no net power being delivered to it. But clearly the engine of the car is doing something . So it is useful to break up the power delivered by separate sources if we want to isolate the rate at which the engine is doing work, without worrying about the rate at which air resistance and friction are are doing negative work on the car to bring the total to zero.
Mathematically, we therefore have for the power delivered by a given force is:
\[ P \equiv \dfrac{dW}{dt} \]
Since the units of work is Joules, the units of power is Joules per second, which we rename as: watts ( \(W\) ).
One nice shortcut for power involves the force doing the work and the velocity of the object on which the work is being performed:
\[ dW = \overrightarrow F \cdot \overrightarrow{dl} \;\;\; \Rightarrow \;\;\; P = \dfrac{dW}{dt} = \dfrac{\overrightarrow F \cdot \overrightarrow{dl}}{dt} = \overrightarrow F \cdot \dfrac{\overrightarrow {dl}}{dt} = \overrightarrow F \cdot \overrightarrow v \]
Note that this is the power delivered to the moving object (i.e. the rate at which energy is added to or taken away from the object) at the instant that the force and velocity are the vectors given above. If this is integrated from a starting time to a final time, the result is the total work done over that time span by the force.
Exercise
Two forces act on a moving object of mass \(1.50kg\), causing its velocity to change over time. One of the two forces is given below, as is the velocity as a function of time.
\[\vec F_1 = \left(3.00N\right)\;\hat i + \left(4.00N\right)\;\hat j\;\;\;\;\;\;\vec v\left(t\right)=\left(0.800\frac{m}{s^2}t-4.0\frac{m}{s}\right)\;\hat i+\left(1.8\frac{m}{s}\right)\;\hat j\nonumber\]
At one moment in time, only the force not given above is delivering power to the object. Find the amount of power delivered by this force at this moment in time.
- Solution
-
First we need to find the time at which this is occurring. We know that the force given above is not delivering any power at this moment, so its dot product with the velocity vector must vanish, giving:
\[0=\vec F\cdot\vec v = \left(3.00N\right)\left(0.800\frac{m}{s^2}t-4.0\frac{m}{s}\right)+\left(4.00N\right)\left(1.8\frac{m}{s}\right) \;\;\;\Rightarrow\;\;\; t=2.00s \nonumber\]
We can find the net force on the particle as a function of time by computing the acceleration from the velocity and using Newton's 2nd Law:
\[\vec F_{net}=m\frac{d\vec v}{dt}=\left(1.50kg\right)\left(0.800\frac{m}{s^2}\right)\hat i = \left(1.20N\right)\hat i\nonumber\]
This results in a total power delivered to the object as a function of time that is:
\[P_{tot}=\vec F_{net}\cdot\vec v=\left(1.20N\right)\left(0.800\frac{m}{s^2}t-4.0\frac{m}{s}\right)\nonumber\]
At the time computed above, the force \(\vec F_1\) is not delivering any power, so all of the total power must be coming from the second force. Thus:
\[\text{at }t=2.00s:\;\;\;\; P_2=P_{tot} = -2.88W\nonumber\]
A particle starts from rest and experiences a net force that has a constant magnitude. This force does change direction, however, such that the particle is made to move in a circular path.
- Analysis
-
To get the particle moving, the force must be tangential to the circle around which the particle will eventually be traveling. But as the particle speeds up, in order to continue its motion in a circle, the component of the net force toward the center of the circle grows, and since the magnitude of the force remains fixed, there is a decreasing amount of tangential component of the force that goes into speeding up the motion of the particle.
For a given mass of particle and radius of circle, there is a limited speed at which the particle can travel – the speed at which the entire force acts to maintain the centripetal acceleration:
\[F=m\frac{v_{max}^2}{R}\;\;\;\Rightarrow\;\;\;v_{max}=\sqrt{\frac{FR}{m}}\nonumber\]


10.2: Populations and Samples
Before we begin gathering and analyzing data we need to characterize the population we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college. Or it might be:
- All first-year community college students in the state of Washington.
- All first-year students at public colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the entire United States.
- And so on.
The population of a study is the group the collected data is intended to describe.
Sometimes the intended population is called the target population , since if we design our study badly, the collected data might not actually be representative of the intended population.
Why is it important to specify the population? We might get different answers to our question as we vary the population we are studying. First-year students at the University of Washington might take slightly more diverse courses than those at your college, and some of these courses may require less popular textbooks that cost more; or, on the other hand, the University Bookstore might have a larger pool of used textbooks, reducing the cost of these books to the students. Whichever the case (and it is likely that some combination of these and other factors are in play), the data we gather from your college will probably not be the same as that from the University of Washington. Particularly when conveying our results to others, we want to be clear about the population we are describing with our data.
A newspaper website contains a poll asking people their opinion on a recent news article. What is the population?
Solution
While the target (intended) population may have been all people, the real population of the survey is readers of the website.
If we were able to gather data on every member of our population, say the average (we will define "average" more carefully in a subsequent section) amount of money spent on textbooks by each first-year student at your college during the 2009-2010 academic year, the resulting number would be called a parameter .
A parameter is a value (average, percentage, etc.) calculated using all the data from a population
We seldom see parameters, however, since surveying an entire population is usually very time-consuming and expensive, unless the population is very small or we already have the data collected.
A survey of an entire population is called a census .
You are probably familiar with two common censuses: the official government Census that attempts to count the population of the U.S. every ten years, and voting, which asks the opinion of all eligible voters in a district. The first of these demonstrates one additional problem with a census: the difficulty in finding and getting participation from everyone in a large population, which can bias, or skew, the results.
There are occasionally times when a census is appropriate, usually when the population is fairly small. For example, if the manager of Starbucks wanted to know the average number of hours her employees worked last week, she should be able to pull up payroll records or ask each employee directly.
Since surveying an entire population is often impractical, we usually select a sample to study;
A sample is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.
We will discuss sampling methods in greater detail in a later section. For now, let us assume that samples are chosen in an appropriate manner. If we survey a sample, say 100 first-year students at your college, and find the average amount of money spent by these students on textbooks, the resulting number is called a statistic .
A statistic is a value (average, percentage, etc.) calculated using the data from a sample.
A researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?
Solution
The sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens.
The 60% value was based on the sample, so it is a statistic.
To determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?
- Answer
-
The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.
A college reports that the average age of their students is 28 years old. Is this a statistic or a parameter?
- Answer
-
This is a parameter, since the college would have access to data on all students (the population)


1.9: Sound
Types of Sound in Theatre
Sound is important part of any theatrical experience. It communicates with the audience, creates atmosphere, supports the script, and supports the performer.
Often the sound design is the first design element the audience will come in contact with. If there is to be preshow music or other sound playing as the audience enters, it is the responsibility of the sound designer to create and the sound technicians to play. Most live entertainment events begin with an admonishment to turn of cell phones and instructions on what to do in the case of an emergency. Generally, this is either a prerecorded announcement or performed live on an off-stage microphone. Even if the pre-show announcement is pre-recorded, most venues require that a live microphone be set up so that in the event of an emergency announcements can be made by trained personnel to the audience.
Once the show has begun, there are several tasks that must be accomplished by the sound design and the sound team. The first of these is helping create the mood or atmosphere for the show. Especially in shows that have several locations during the course of the play, the sound designer may create a soundscape to play behind a scene. For example, a scene in a desolate field may have the sounds of wind mixed with occasional sounds of wildlife. Another example would be a scene in a sports bar where crowd sounds, muted sports commentary, and clinking glasses may create the appropriate environmental sounds. In some plays, a complex mix of individual songs and other instrumental noises may create underscoring, similar to that of a movie.
Sometimes the script of play calls for specific sounds. These might be door bells, or gun shots. These are distinguished from environmental sounds, by the fact that they need to come at a specific moment in the script. Often times, sound designers will create a long loop of sound for an environmental sound. A loop simply means that when it gets to the end it will start over again. Loops are often designed to be seamless so that the audience won’t notice it is the same sounds again. This does not work as well for the specific sounds called for in the script. The designer and sound crew will need to ensure that these sounds happen at just the right moment through the cuing process (see chapter 12).
The last category of sound in theatre is that sound that aids the performer. Often this work goes unnoticed by the audience, but would be detrimental if not executed very well at each performance. Most performances in large theatres use microphones and other sound equipment to amplify the voice of the performers. Some of these microphones are placed around the stage and auditorium and amplify the overall sound coming from the stage. Sometimes microphones that are attached to a wireless transmitter are attached to the performer’s body. A wireless receiver, attached to the sound mixing console will allow the sound to be transmitted to the audience. In musicals, the musicians in the orchestra are also generally surrounded by microphones. The sound is often mixed with the performers before being fed to the speakers in the audience. Sometimes the sound from the orchestra is actually being fed to speakers on the stage so that the cast can hear the instrumentalists better. Some theatres also find it necessary to feed the sound of the vocalists on stage into small speakers in the orchestra pit so that the musicians can hear them better. Many theatres also use their sound system to send a feed of what is happening on stage to the dressing rooms so that actors changing costume know how soon they need to be on-stage. The theatre may also send the sound on stage (often called show program) to the lobby of the theatre. This allows house staff and late arriving patrons to hear what is going on.
Ways of Creating Sound
In the theatre today, most sound effects, whether an environmental sound, underscoring, or specific sound cue (such as a door slam) are pre-recorded. Sound effect companies sell all sorts of individual sound effects that can be purchased and modified to fit the needs of the show. Some sound designers go out into the world and record sounds using portable recording devices and then edit those sounds to suit the needs of the show. Regardless of how it is gathered, pre-recorded sounds are generally played back by a specialized computer running special software. The software allows the sound team to carefully program how loud a sound is, what speakers it is played through, etc. All of these commands are recorded as “cues.” At a specific point in the script, the stage manager will instruct the sound operator to execute the cue, and the sound will playback exactly the same as it has for every previous performance. Some smaller theatres may still use sound effects played back by CD. In those cases, the sound team must work together to take careful notes of how loud each sound should be, if it needs to fade at the beginning or at the end and what speakers it needs to play out of. All of that will need to be written into the sound cue sheet and set up individually for each cue.
Before computers and CDs, sound was created live in the theatre. Some productions will still use some of these techniques.
- Crash box: This is a wooden, metal or sometimes cardboard box filled with scrap metal, glass and other items. It is tipped over or dropped to create a crashing sound. An experienced crew member backstage can adjust the loudness or ferocity of the crash to match the onstage action.
- Cap guns/Blank guns: These are ways of having a gun prop on stage create the bang as the trigger is pulled.  All venues have special procedures for using on stage weapons, and the venue must be consulted before using these items.
- Door slams: These look like a miniature door from “Alice in Wonderland.” They often have a working door knob, and possibly a working lock all built into a small frame (about ¼ of the size of a real door). When opened or shut offstage it gives the impression of a door being opened or shut. Again, an experienced sound technician can provide more variation from effect to effect using a prop such as this compared to a pre-recording.
- Door bells: A real set of door bells can be purchased at a hardware store and placed on stage instead of a prerecorded effect.
- Phone Ringers: Devices are made that will mimic the signal sent by the phone company to ring a land-line phone. This allows the real phone on stage to ring. Careful testing must be performed in advance. Many of these devices will cause the phone to ring even if the hand set has been picked up. Practice between the operator and the actor is essential to make it look real.
It should also be noted that in the “old days,” it was not uncommon to have a musician or small ensemble of musicians to provide underscoring for a non-musical play. Today, that sound is almost always created via a prerecorded track played back for the audience.
Sound effects are typically cued by the stage manager via whatever cueing system is available in the theatre. In some cases, especially with crash boxes and door slams, the stage manager may call the standby, but the responsible crew member may be watching the action on stage to precisely time the effect with the actors. Some sound effects may be actually executed by the actors on stage. If the design team has created a prop gun that fires a blank or a cap, it may actually be fire when the actor pulls the trigger in the course of the stage action. In cases such as this, it is not uncommon for a backup sound effect to be ready to go in case something goes wrong on stage. This could include a back-up prop gun in the hands of a crew member in the wings that could be cued by the stage manager, or a prerecorded sound effect that could be played in the event of a problem.
Sound Breakdown
Much like the breakdowns that have already been done, these are organized by act, scene and page number. Additional information is needed about what the cue is, and how it is created (live sound, playback etc.). Atmospheric sounds and underscoring are often created to be longer than they need to be, with the intention that they will fade out at a specific moment in the scene. This fade out is itself a sound cue, since it will need to be called by the stage manager and rehearsed with the cast and crew.
Take a look at this sound breakdown for “Box and Cox”
|
Scene |
Page |
Sound |
|---|---|---|
|
i |
2 |
Preshow Music (Pre Record) |
|
i |
2 |
Preshow Music Fade/Pre Show Announcement (Pre Record) |
|
i |
2 |
Knock on Door (Possibly live) |
|
ii |
4 |
Off stage voices (Possibly live) |
|
ii |
6 |
Fire crackle (Pre Record) |
|
ii |
6 |
Sound of bacon frying (Pre Record) |
|
iii |
6 |
Fade bacon frying |
|
iii |
6 |
Sound of pork chop frying (Pre Record) |
|
iii |
6 |
Fade pork chop |
|
iii |
6 |
Sound of bacon frying (Pre Record) |
|
iii |
7 |
Fade bacon frying |
|
iv |
18 |
Knock on the street door (Pre Record) |
|
iv |
19 |
Clock strikes 10 as an Ominbus passes (Pre Record) |
|
iv |
20 |
Bow Music(Pre Record) |
|
iv |
20 |
Bow Music fades / Post Show music (Plays out) (Pre Record) |
Sound Cue Sheet
|
BOX AND COX |
|||
|
Cue |
Level |
Sound |
NOTE |
|
A |
Preshow Music |
||
|
B |
Preshow Music Fade/Pre Show Announcement |
||
|
C |
Knock on Door (Back up) |
Safety in case cast is late |
|
|
D |
Off stage voices (Back up) |
Safety in case cast is late |
|
|
E |
Fire crackle |
||
|
F |
Sound of bacon frying |
||
|
G |
Fade bacon frying |
||
|
H |
Sound of pork chop frying |
||
|
I |
Fade pork chop |
||
|
J |
Sound of bacon frying |
||
|
K |
Fade bacon frying |
||
|
L |
Knock on the street door |
||
|
M |
Clock strikes 10 as an Ominbus passes |
||
|
N |
Fade Fire/ Bow Music |
||
|
O |
Bow Music fades / Post Show music |
While lighting cues are typically executed by the board operator by just pressing the go button, many shows have sound cues that are more complicated. Sound is still often a mix of sources and playback methods which may require more than simply pressing a go button. When creating a sound cue sheet, it is important to remember that the operators are probably using the sheet in dim lighting during the stress of a show. Consider simplicity and clarity as the guiding principles. If the sound levels are not preprogrammed, a space will be needed for the operator to write the information down during technical rehearsals.
Note how the sound designer decided to build back up prerecorded sounds for the live sounds on stage. Also note how in the final cue sheet, the designer notes that the fire sounds need to fade out.
Additional Materials


27.6A: Fifth Through Eighth Weeks of Development
Weeks five to eight of gestation develops the major organs, including the circulatory, nervous, and gastrointestinal systems.
- Outline embryonic development between five and eight weeks
Key Points
- Being susceptible to the effects of teratogens is high during embryonic development.
- At week five, the brain, spinal cord, vertebrae, heart, vasculature, and gastrointestinal tract begin to develop.
- During weeks six to seven, the embryo grows from 4 mm in length to 9 mm and begins to curve into a C-shape. The fetal heart bulges, develops further, and begins to beat in a regular rhythm. Rudimentary blood begins to move through the blood vessels. The neural tube, which forms the brain, closes.
- During weeks six and seven, the limb buds form. The eyes, mouth, and ear structures begin to form. The initial differentiation of the tissues that will become the spleen, gallbladder, pancreas, liver, kidneys, stomach, and lungs occurs.
- By week eight of gestation, the lungs begin to form, as well as the lymphatic system. The main development of the external genitalia begins, and the brain continues to develop. The arms and legs have grown longer, and the foot and hand areas can be clearly distinguished.
Key Terms
- chorionic membrane : One of the membranes that exist during pregnancy between the developing fetus and mother. The chorionic villi emerge from the chorion, invade the endometrium, and allow transfer of nutrients from maternal blood to fetal blood.
- Gestational age : The time that has passed since the onset of the last menstruation.
- Embryonic age : Measures the actual age of the embryo or fetus from the time of fertilization.
- teratogens : An agent, such as a virus, a drug, or radiation, that causes a malformation of an embryo or fetus.
Weeks five through eight of gestation are characterized by the development of the major organ systems, including the circulatory, nervous, lymphatic, and gastrointestinal systems. During this time, the embryo is extremely susceptible to the effects of teratogens.
Gestational age is the time that has passed since the onset of the last menstruation, which occurs two weeks before the actual fertilization. Embryonic age measures the actual age of the embryo or fetus from the time of fertilization. Thus, the first week of embryonic age is already week three counting with gestational age. The number of the week (used here) is one more than the actual age of the embryo/fetus. For example, the embryo is 0 whole weeks old during the first week after fertilization.
Week 5
At week five, the brain, spinal cord, vertebrae, heart, vasculature, and gastrointestinal tract begin to develop.
Week 6–7
Human embryo at seven weeks : An embryo from an ectopic pregnancy, still in the oviduct. This embryo is about five weeks old (or from the seventh week of menstrual age). The heart is the dark spot at the center of the image, bulging out of the embryo.
During weeks six and seven, the embryo grows from four millimeters in length to nine millimeters and begins to curve into a C-shape. The fetal heart bulges, develops further, and begins to beat in a regular rhythm. Rudimentary blood begins to move through the main embryonic blood vessels, connecting to the yolk sac and the chorionic membrane of the placenta.
The arm and leg buds, which will grow into the full limbs over the rest of development, become visible. The neural tube, which forms the brain, closes. The brain then develops into five areas and some cranial nerves are visible.
The eyes, mouth, and ear structures begin to form. The initial differentiation of the tissues that will become the spleen, gallbladder, pancreas, liver, kidneys, stomach, and lungs occurs.
Week 8
By week eight of gestation, the embryo measures 13 millimeters in length. The lungs begin to form, as well as the lymphatic system. The main development of the external genitalia begins, and the brain continues to develop.
The arms and legs have grown longer, and the foot and hand areas can be clearly distinguished. The hands and feet have fingers and toes, but may still be webbed.
Human embryo from an ectopic pregnancy: An embryo from an ectopic pregnancy, located in the part of the uterus to which the fallopian tube is attached. The features are consistent with a developmental age of seven weeks (the ninth week of menstrual age).
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SHARED PREVIOUSLY
- Curation and Revision. Authored by : Boundless.com. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- Fetal development: MedlinePlus Medical Encyclopedia. Provided by : National Insitute of Health. Located at : http://www.nlm.nih.gov/medlineplus/e...cle/002398.htm . License : Public Domain: No Known Copyright
- teratogens. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/teratogens . License : CC BY-SA: Attribution-ShareAlike
- chorionic membrane. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/chorionic%20membrane . License : CC BY-SA: Attribution-ShareAlike
- Prenatal Development. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Prenatal_development . License : CC BY-SA: Attribution-ShareAlike
- Tubal Pregnancy with embryo. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Tu...ith_embryo.jpg . License : Public Domain: No Known Copyright
- Human_Embryo_from_Ectopic_Pregnancy.jpg. Provided by : Wikipedia Commons. Located at : commons.wikimedia.org/wiki/File:9-Week_Human_Embryo_from_Ectopic_Pregnancy.jpg . License : CC BY-SA: Attribution-ShareAlike


12.6: Rigor in Interpretive Research
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While positivist research employs a ‘reductionist’ approach by simplifying social reality into parsimonious theories and laws, interpretive research attempts to interpret social reality through the subjective viewpoints of the embedded participants within the context where the reality is situated.  However, because interpretive analysis is subjective and sensitive to the experiences and insight of the embedded researcher, it is often considered less rigorous by many positivist (functionalist) researchers. Because interpretive research is based on a different set of ontological and epistemological assumptions about social phenomena than positivist research, the positivist notions of rigor—such as reliability, internal validity, and generalisability—do not apply in a similar manner. However, Lincoln and Guba (1985) provide an alternative set of criteria that can be used to judge the rigor of interpretive research.
Dependability. Interpretive research can be viewed as dependable or authentic if two researchers assessing the same phenomenon, using the same set of evidence, independently arrive at the same conclusions, or the same researcher, observing the same or a similar phenomenon at different times arrives at similar conclusions. This concept is similar to that of reliability in positivist research, with agreement between two independent researchers being similar to the notion of inter-rater reliability, and agreement between two observations of the same phenomenon by the same researcher akin to test-retest reliability. To ensure dependability, interpretive researchers must provide adequate details about their phenomenon of interest and the social context in which it is embedded, so as to allow readers to independently authenticate their interpretive inferences.
Credibility. Interpretive research can be considered credible if readers find its inferences to be believable. This concept is akin to that of internal validity in functionalistic research. The credibility of interpretive research can be improved by providing evidence of the researcher’s extended engagement in the field, by demonstrating data triangulation across subjects or data collection techniques, and by maintaining meticulous data management and analytic procedures—such as verbatim transcription of interviews, accurate records of contacts and interviews—and clear notes on theoretical and methodological decisions, that can allow an independent audit of data collection and analysis if needed.
Confirmability. Confirmability refers to the extent to which the findings reported in interpretive research can be independently confirmed by others—typically, participants. This is similar to the notion of objectivity in functionalistic research. Since interpretive research rejects the notion of an objective reality, confirmability is demonstrated in terms of ‘intersubjectivity’—i.e., if the study’s participants agree with the inferences derived by the researcher. For instance, if a study’s participants generally agree with the inferences drawn by a researcher about a phenomenon of interest—based on a review of the research paper or report—then the findings can be viewed as confirmable.
Transferability. Transferability in interpretive research refers to the extent to which the findings can be generalised to other settings. This idea is similar to that of external validity in functionalistic research. The researcher must provide rich, detailed descriptions of the research context (‘thick description’) and thoroughly describe the structures, assumptions, and processes revealed from the data so that readers can independently assess whether and to what extent the reported findings are transferable to other settings.


8.2: Taste
Gustation (Taste)
Only a few recognized submodalities exist within the sense of taste, or gustation . Until recently, only four tastes were recognized: sweet, salty, sour, and bitter. Research at the turn of the 20th century led to recognition of the fifth taste, umami, during the mid-1980s. Umami is a Japanese word that means “delicious taste,” and is often translated to mean savory.
Very recent research has suggested that there may also be a sixth taste for fats, or lipids. Gustation is the special sense associated with the tongue. The surface of the tongue, along with the rest of the oral cavity, is lined by a stratified squamous epithelium. Raised bumps called papillae (singular = papilla) contain the structures for gustatory transduction. There are four types of papillae, based on their appearance (Figure 8.3): circumvallate, foliate, filiform, and fungiform. Within the structure of the papillae are taste buds that contain specialized gustatory receptor cells for the transduction of taste stimuli. These receptor cells are sensitive to the chemicals contained within foods that are ingested, and they release neurotransmitters based on the amount of the chemical in the food. Neurotransmitters from the gustatory cells can activate sensory neurons in the facial, glossopharyngeal, and vagus cranial nerves.
Salty taste is simply the perception of sodium ions (Na + ) in the saliva. When you eat something salty, the salt crystals dissociate into the component ions Na + and Cl – , which dissolve into the saliva in your mouth. The Na + concentration becomes high outside the gustatory cells, creating a strong concentration gradient that drives the diffusion of the ion into the cells. The entry of Na + into these cells results in the depolarization of the cell membrane and the generation of a receptor potential. Sour taste is the perception of H + concentration. Just as with sodium ions in salty flavors, these hydrogen ions enter the cell and trigger depolarization. Sour flavors are, essentially, the perception of acids in our food. Increasing hydrogen ion concentrations in the saliva (lowering saliva pH) triggers progressively stronger graded potentials in the gustatory cells. For example, orange juice—which contains citric acid—will taste sour because it has a pH value of approximately 3. Of course, it is often sweetened so that the sour taste is masked. The first two tastes (salty and sour) are triggered by the cations Na + and H + . The other tastes result from food molecules binding to a G protein–coupled receptor. A G protein signal transduction system ultimately leads to depolarization of the gustatory cell. The sweet taste is the sensitivity of gustatory cells to the presence of glucose dissolved in the saliva. Other monosaccharides such as fructose, or artificial sweeteners such as aspartame (NutraSweet™), saccharine, or sucralose (Splenda™) also activate the sweet receptors. The affinity for each of these molecules varies, and some will taste sweeter than glucose because they bind to the G protein–coupled receptor differently. Bitter taste is similar to sweet in that food molecules bind to G protein–coupled receptors. However, there are a number of different ways in which this can happen because there are a large diversity of bitter-tasting molecules. Some bitter molecules depolarize gustatory cells, whereas others hyperpolarize gustatory cells. Likewise, some bitter molecules increase G protein activation within the gustatory cells, whereas other bitter molecules decrease G protein activation. The specific response depends on which molecule is binding to the receptor. One major group of bitter-tasting molecules are alkaloids. Alkaloids are nitrogen-containing molecules that often have a basic pH. Alkaloids are commonly found in bitter-tasting plant products, such as coffee, hops (in beer), tannins (in wine), tea, and aspirin. By containing toxic alkaloids, the plant is less susceptible to microbe infection and less attractive to herbivores. Therefore, the function of bitter taste may primarily be related to stimulating the gag reflex to avoid ingesting poisons. Because of this, many bitter foods that are normally ingested are often combined with a sweet component to make them more palatable (cream and sugar in coffee, for example). The highest concentration of bitter receptors appear to be in the posterior tongue, where a gag reflex could still spit out poisonous food. The taste known as umami is often referred to as the savory taste. Like sweet and bitter, it is based on the activation of G protein–coupled receptors by a specific molecule. The molecule that activates this receptor is the amino acid L-glutamate. Therefore, the umami flavor is often perceived while eating protein-rich foods. Not surprisingly, dishes that contain meat are often described as savory. Once the gustatory cells are activated by the taste molecules, they release neurotransmitters onto the dendrites of sensory neurons. These neurons are part of the facial and glossopharyngeal cranial nerves, as well as a component within the vagus nerve dedicated to the gag reflex. The facial nerve connects to taste buds in the anterior third of the tongue. The glossopharyngeal nerve connects to taste buds in the posterior two thirds of the tongue. The vagus nerve connects to taste buds in the extreme posterior of the tongue, verging on the pharynx, which are more sensitive to noxious stimuli such as bitterness.
Age Related Changes to Taste
While the number of taste buds does not decline until after 75 years of age, there is a general decrease in taste perception as part of the aging process. Other factors that may contribute to the reduction in taste in older persons are a decrease in the volume of saliva secreted, an increases in the viscosity of saliva, and the formation of fissures and furrows on the tongue.
Contributors and Attributions
- Chapter 14. Authored by : OpenStax College. Provided by : Rice University. Located at : openstaxcollege.org/files/textbook_version/low_res_pdf/13/col11496-lr.pdf. Project : AtD Course. License : CC BY: Attribution


14.4: Writing Effective Cover Letters
- Identify characteristics of an effective cover letter
What Is a Cover Letter?
A cover letter is a letter of introduction, usually three to four paragraphs in length, that you attach to your résumé. It’s a way of introducing yourself to a potential employer and explaining why you are suited for a position. Employers may look for individualized and thoughtfully written cover letters as an initial method of screening out applicants who may lack necessary basic skills or who may not be sufficiently interested in the position.
Often an employer will request or require that a cover letter be included in the materials an applicant submits. There are also occasions when you might submit a cover letter uninvited: for example, if you are initiating an inquiry about possible work or asking someone to send you information or provide other assistance.
With each résumé you send out, always include a cover letter specifically addressing your purpose. This purpose is to let the receiver know how well you match their needs. It is a careful blend of the direct and persuasive letters you read about earlier in this book.
Characteristics of an Effective Cover Letter
Cover letters should accomplish the following:
- Get the attention of the prospective employer
- Set you apart from any possible competition
- Identify the position you are interested in
- Specify how you learned about the position or company
- Present highlights of your skills and accomplishments
- Reflect your genuine interest
- Please the eye and ear
The following video features Aimee Bateman, founder of Careercake.com, who explains how you can create an incredible cover letter. You can download a transcript of the video “5 Steps to an Incredible Cover Letter.”
Cover Letter Resources
| WEBSITE | DESCRIPTION | |
| 1 | Student Cover Letter Samples (from About Careers) | This site contains sample student/recent graduate cover letters (especially for high school students and college students and graduates seeking employment) as well as cover letter templates, writing tips, formats and templates, email cover letter examples, and examples by type of applicant |
| 2 | How to Write Cover Letters (from CollegeGrad) | This site contains resources about the reality of cover letters, using a cover letter, the worst use of the cover letter, the testimonial cover letter technique, and a cover letter checklist |
| 3 | Article on Cover Letters via LinkedIn | This article on cover letters posted on LinkedIn may lend some helpful professional insights on writing an engaging cover letter. |
| 4 | Cover Letters (from the Yale Office of Career Strategy) | This site includes specifications for the cover letter framework (introductory paragraph, middle paragraph, concluding paragraph), as well as format and style |
Contributors and Attributions
- Practice question. Authored by : Susan Kendall. Provided by : Lumen Learning. License : CC BY: Attribution
- College Success. Authored by : Linda Bruce. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/waymaker-collegesuccess/ . License : CC BY: Attribution
- 5 Steps to an Incredible Cover Letter. Authored by : Aimee Bateman. Located at : https://youtu.be/mxOli8laZos . License : All Rights Reserved . License Terms : Standard YouTube License


6.7: Personality Theory in Real Life
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Feminine Psychology, Zen Mindfulness, Psychoanalysis, and Everyday Relationships
The ancient practice of mindfulness, which is associated with Buddhism but also has roots in other spiritual practices and religions, has become an important and fairly common psychotherapeutic technique (see, e.g., Germer, Siegel, & Fulton, 2005; Richards & Bergin, 2000; Sperry & Shafranske, 2005). There are also some interesting connections between the practice of Buddhist mindfulness and those who established feminine psychology. At the end of her life, Karen Horney went to Japan to study Zen Buddhism with the renowned Buddhist scholar D. T. Suzuki, and Janet Surrey, one of the founding members of the Stone Center (which will be introduced in the next chapter), has been practicing mindfulness and working to synthesize Buddhist practices with relational-cultural approaches to psychology for over 20 years (Surrey, 2005). Surrey is also on the faculty of the Institute for Meditation and Psychotherapy, and teaches seminars on the use of mindfulness in conjunction with relational-cultural therapy (and I can personally attest to the wonderful job she does).
Since Horney became interested in Zen near the end of her life, she wrote very little about it. Indeed, most of what is recorded is in the book Final Lectures (Ingram, 1987), which was published by Douglas Ingram many years after Horney died. However, her close friend and colleague Erich Fromm also worked with Suzuki. Fromm mentions Yoga and Buddhism often in his books, and Suzuki and Fromm (along with another colleague) co-authored Zen Buddhism & Psychoanalysis in 1960.
Horney equated Zen mindfulness with living fully in each moment, with wholehearted concentration (Horney, 1945, 1950; Ingram, 1987). This general theme is expressed quite eloquently in one of Horney’s favorite books, Zen in the Art of Archery (Herrigel, 1953), as well as in Herrigel’s other book, The Method of Zen (Herrigel, 1960). In the latter book, Herrigel expresses the essence of Zen from his perspective, presenting a psychological view that fits well with the relational-cultural perspective we will examine in the next chapter:
…the Zen Buddhist is far from limiting his feelings of joy and compassion to human beings and to every aspect of human existence. He embraces in these feelings everything that lives and breathes…The Zen Buddhist is constantly confirmed in his experience that there is a fundamental communication which embraces all forms of existence…He does not pass by the joys and sufferings of others without taking them to himself and reinforcing them with his own feelings… (pp. 119-120; Herrigel, 1960)
Fromm knew Suzuki at the same time as Horney, but the two men really got to know each other when Suzuki spent a week in Mexico in 1956, and Fromm then visited Suzuki in New York. In 1964, Fromm wrote to Suzuki that every morning he read a passage on Zen or something by Meister Eckhart (a well-known Christian mystic). In addition, Fromm was interested in Kabbalah and Sufism, as well as other spiritual approaches to understanding people (Funk, 2000). Fromm examined many of these diverse perspective in books such as The Nature of Man (Fromm & Xirau, 1968) and Psychoanalysis and Religion (Fromm, 1950), and he drew interesting connections between the physical activities of Yoga and Wilhelm Reich’s somatic psychology (Fromm, 1992). He was by no means an unqualified supporter, however, suggesting that some self-proclaimed gurus can do more harm than good when seeking to serve their own selfish interests (usually in order to make money; Fromm, 1994).
In their work together, Suzuki provided a brief overview of the essentials of Zen practice, which focuses on living life:
Zen may occasionally appear too enigmatic, cryptic, and full of contradictions, but it is after all a simple discipline and teaching:
To do goods,
To avoid evils,
To purify one’s own heart:
This is the Buddha-Way.
Is this not applicable to all human situations, modern as well as ancient, Western as well as Eastern? (pg. 76; Suzuki, Fromm, & DeMartino, 1960)
Fromm, for his part, identified ways in which Zen principles appeared to be compatible with psychoanalysis. He considered psychoanalysis to be the Western parallel to Zen, since Zen arose from Indian rationality and abstraction mixed with Chinese concreteness and realism, whereas psychoanalysis arose from Western humanism and rationalism. Fromm described the Western world as suffering from a spiritual crisis, resulting from a change in the pursuit of the perfection of humanity to the pursuit of the perfection of things (e.g., technology). Since we have lost our connection to nature, and to ourselves and our communities, we have become anxious and depressed. Psychoanalysis was developed to help us deal with these anxieties, as an alternative to the flawed ways in which we had been dealing with them in the past: religion (according to Freud). As described very simply in the quote above, Zen Buddhism also seeks to resolve human anxiety, simply by doing good and avoiding evil. In Freudian terms, doing good results from knowing oneself, and one can only know oneself through the process of psychoanalysis. Then, a person can act in accordance with reality, rather than being influenced by unconscious, repressed, and dysfunctional psychological processes. Therefore, Fromm considered the essential nature of psychoanalysis to be compatible with Zen (Suzuki, Fromm, & DeMartino, 1960), a perspective supported more recently by Mark Epstein in his comparison of Buddhist meditation and psychoanalysis, Thoughts Without a Thinker (Epstein, 1995).
Fitting even more closely with Fromm’s perspective on human development and psychoanalysis, Zen art is intimately involved with nature, and with humanity’s relationship with nature (Herrigel, 1953, 1960; Suzuki, Fromm, & DeMartino, 1960). Fromm used Zen perspectives to reform his views on psychoanalysis and development. He considered the development of the individual to be a re-enactment of the development of the species (i.e., ontogeny recapitulates phylogeny). Prior to birth there is no anxiety, following birth we must deal with anxiety. We can try to deal with our anxieties by regressing to our earliest state, or we can attempt to complete the process of birth, which Fromm described as a lifelong process:
Birth is not one act; it is a process. The aim of life is to be fully born, though its tragedy is that most of us die before we are thus born. To live is to be born every minute. (pg. 88; Suzuki, Fromm, & DeMartino, 1960)
Fromm does not suggest that this is easy, but it is possible. However, which method is to be preferred: psychoanalysis or the practice of Zen Buddhism? That would appear to be a personal matter, since both psychoanalysis and Zen Buddhism aim toward the same goal:
This description of Zen’s aim could be applied without change as a description of what psychoanalysis aspires to achieve; insight into one’s own nature, the achievement of freedom, happiness and love, liberation of energy, salvation from being insane or crippled…The aim of Zen transcends the goal of ethical behavior, and so does psychoanalysis. It might be said that both systems assume that the achievement of their aim brings with it an ethical transformation, the overcoming of greed and the capacity for love and compassion. (pp. 122-123; Suzuki, Fromm, & DeMartino, 1960)
Just as love is considered an essential element of being Christian, compassion is essential to Buddhism. In The Art of Loving, Fromm (1956) noted that a person cannot love themselves if they do not love others. Thus, love and compassion are intertwined, one must love and care for all people, indeed for all things, to be fulfilled. Zen teaches this peace in many ways, even sword fighting and archery become art when performed by a Zen master.  Although a classic psychoanalyst might insist that the sword master is motivated by some unconscious hatred or anger, Fromm says that such a psychoanalyst simply does not grasp the spirit of Zen. Likewise, citing Herrigel’s Zen in the Art of Archery again, Fromm notes how archery has been transformed from a military skill into an exercise of spirituality, or in non-spiritual terms, a form of playful violence (as opposed to aggressive violence; Fromm, 1964, 1973).
Thus, the practice of mindfulness, the art of love, compassion, all play similar roles in helping people to be aware of who they are and of their relationships with others. In addition, they encourage and support a genuine desire to be connected to others, and to maintain healthy interpersonal connections, even in such diverse activities as eating breakfast, going to work, or practicing archery.


1.7: Suggested Readings
Bottrill, M.C., L.N. Joseph, J. Carwardine, et al. 2008. Is conservation triage just smart decision making? Trends in Ecology and Evolution 23: 649–54. https://doi.org/10.1016/j.tree.2008.07.007 Should we let some species go extinct?
Elosegi, A., M.O. Gessner, and R.G. Young. 2017. River doctors: Learning from medicine to improve ecosystem management. Science of the Total Environment 595: 294–302. https://doi.org/10.1016/j.scitotenv.2017.03.188 Comparing conservation to the health sciences
Illingworth, S. 2017. Delivering effective science communication: Advice from a professional science communicator. Seminars in Cell and Developmental Biology 70: 10–16. https://doi.org/10.1016/j.semcdb.2017.04.002 Tips to help you better communicate with public audiences.
Kareiva, P., and M. Marvier. 2012. What is conservation science? BioScience 62: 962–69. https://doi.org/10.1525/bio.2<IP_ADDRESS> A review of an article published in 1985, offering a revised set of core principles that should guide conservation biology today.
Meyer, J.L., P.C. Frumhoff, S.P. Hamburg, et al. 2010. Above the din but in the fray: environmental scientists as effective advocates. Frontiers in Ecology and the Environment 8: 299–305. https://doi.org/10.1890/090143 Scientists have a responsibility to be advocates as well as researchers.
Sutherland, W.J., A.S. Pullin, P.M. Dolman, et al. 2004. The need for evidence-based conservation. Trends in Ecology and Evolution 19: 305–08. https://doi.org/10.1016/j.tree.2004.03.018 How do conservationists make decisions?
Tallis, H., and J. Lubchenco. 2014. Working together: A call for inclusive conservation. Nature 515: 27–28. https://doi.org/10.1038/515027a There is a risk that conservation can be polarising. We should rather be working together.
Tear, T.H., P. Kareiva, P.L. Angermeier, et al. 2005. How much is enough? The recurrent problem of setting measurable objectives in conservation. BioScience 55: 835–49. https://doi.org/10.1641/0006-3568(2005)055 [0835:HMIETR]2.0.CO;2 Guidelines for setting goals in conservation.


Learning Objectives
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Define culture and identify its defining characteristics.
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Define enculturation and its relationship to culture.
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Define and identify examples of cultural relativism and ethnocentrism.
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Explain and identify examples of the mechanisms of cultural change.
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Explain how culture is an adaptive mechanism.
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4.1.1: What is Culture?
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Anthropologists have long debated an appropriate definition of culture. Even today some anthropologists criticize the culture concept as oversimplifying and stereotyping cultures. This section discusses the concept of culture and its defining characteristics.
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4.1.2: The Capacity for Culture
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One aspect of life that humans and animals have in common is that we live in organized groups, or a society. There is evidence that some non-human species do have a rudimentary culture, which is learned and shared between members of their group. However, no other species demonstrates the cultural virtuosity of human beings.
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4.1.3: Culture As An Adaptive Mechanism
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An adaptation is any alteration in the structure or functioning of an organism (or group of organisms) that improves its ability to survive and reproduce in its environment. All organisms, including humans, have the ability to adapt biologically. However, what makes humans unique is the extent to which we rely on culture to adapt to our environment.
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4.1.4: Ethnocentrism and Cultural Relativism
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For anthropologists in the field, cultural relativism is especially important. We must set aside our innate ethnocentrisms and let cultural relativism guide our inquiries and interactions with others so that our observations are not biased. However, anthropology is unique among academic disciplines because of the diversity of approaches used to conduct research and for the broad range of orientations that fall under its umbrella.
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4.1.5: Patterns of Culture
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Often, a comparison of one culture to another will reveal obvious differences, but all cultures also share common elements. Anthropologist George Murdock first recognized the existence of cultural universals while studying systems of kinship around the world.
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4.1.6: Levels of Culture
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Anthropologists recognize three levels of culture: international, national, and subculture. Keep in mind that while anthropologists have classified these three general patterns, it is acknowledged that there is variation within any given culture. Even at the individual level there may be differences from the dominant culture. While most people don’t think about their culture at the most general levels, these levels do impact us even if we’re not aware of it.
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4.1.7: Culture Change
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One of the characteristics of culture is that it is dynamic. It is always changing. We are living in a world where globalization has increased the speed that our cultures are changing. In addition to globalization, there are three main mechanisms of cultural change: diffusion, independent invention, and acculturation.
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4.1.8: End of Chapter Discussion
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Thumbnail: Maori warriors perform a Haka, meaning dance of welcome, for Secretary of Defense Leon E. Panetta during a Powhiri ceremony while visiting Auckland, New Zealand Sept. 21, 2012. The ceremony is an ancient Maori tradition used to determine if visitors came in peace or with hostile intent. (Publc Domain; Erin A. Kirk-Cuomo).


3.5: Content Speaks
Social media and content go hand-in-hand. The purpose of creating social media websites was to provide users a platform where they can interact with each other and share information.  Hence it goes without saying that you need a content marketing strategy for social platforms.
Many companies post content on social websites without a documented strategy to back their actions. A well-documented strategy and plan streamlines actions and guides you in the right direction. It helps you stay on track towards long-term and short-term goals and get heard.
To create an effective content strategy, ask yourself the following questions:
- What are my goals?
- Who should I post content for?
- Which platforms would work best?
- What type of content is preferred by my audience?
- How often should I post content?
- Which KPIs should I use for measuring performance?
Creating Your “Voice”
Brand voice is the distinct personality of your business that sets you apart from the competition. It creates an image or perception in customers’ minds. If you promote a positive message through a captivating brand voice, then it won’t be difficult for you to achieve social media marketing goals through your unique brand voice.
On social media, you can attract the audience through storytelling. Your stories should portray a consistent image to build credibility. For instance, if you are an optimistic person in real life, you notice the positive aspect of every event and don’t linger in the negativity. Similarly, if you intend to portray your brand as adventurous, energetic, inspiring, or trustworthy, you should choose a tone that portrays this image and be consistent.
Customers consider the brand image of a business before they interact with them or make buying decisions. If your brand voice is intimidating or you often post controversial content, then you may end up losing them to more stable and friendly competitors.
Where to Find the Right Content?
Creating fresh content takes time and effort. If you engage with your audience on multiple social websites, it won’t be easy to generate unique content for every platform especially when you need to post content on a regular basis. Amidst the coronavirus outbreak, getting new ideas and creating unique content has become even more difficult. This is when content repurposing comes into the picture.
It’s a good idea to look at content generated by other social media users. You can get to know about the latest trends and get ideas for your business. An example is that you can work on some DIY projects and record the procedure via a time-lapse video to engage the audience.
You may have created some evergreen content in the past. Go check your social profiles and locate posts that can be reused. For example, you may find images posted on Pinterest or Instagram from previous vacations. You can create blog posts about your experiences around those images and post them on your blog. However, when repurposing the content, make sure it goes well with your brand voice and the general language of the specific social website.
You should also consider creating content around the products your business offers. You can create whitepapers to share detailed information about the product or process. It’s also a good idea to complement it with a how-to article or video to educate customers.
Content repurposing works great when you understand your weaknesses and strengthens. If you aren’t good at talking in front of a camera, then creating videos for social media may not be your best bet. Stammering out of nervousness portrays a negative image. You should rather choose platforms that go well with your personality and can help you promote your entrepreneurial venture.
Now that the world is moving towards online business, e-conferencing has become a norm. You can conduct business meetings as well as events via Zoom or other digital platforms. You should consider recording such online events and posting them on social media.
How to Create the Right Content?
As a marketer, you can learn from social media trends popular among other business people. Event marketing has become quite popular these days where professionals meet and communicate with each other about topics of mutual interest. These events provide you an opportunity to create engaging content for your social media audience.
You should consider recording these events and posting them on social media for the followers. You can record videos via any device, but you may wonder whether it’s better to share live and unprocessed videos or should you process them first before posting on social media. I would say both tactics can work in your favor.
In the case of live events, social media users expect to enjoy live coverage of the event. If you don’t want them to miss those golden moments, you should live broadcast the event on your social media pages. Facebook Live feature comes in handy for this purpose.
Back in the day, it was believed that brands may suffer if they share unprocessed video content with the audience as they are less attractive to viewers. But this isn’t the case anymore. People don’t mind this approach because they are aware you may not always have professional equipment at hand when attending a business event. Moreover, people today are more interested in authentic brands. Overly processed content leads to question marks on authenticity, which is why live videos should be added to your social media content strategy.
It’s also important to remember that posting live videos doesn’t mean processed and professional quality videos aren’t important. You can share the event live and process captured images and videos for later use. With this professional content, you can promote the brand, product, or event on an on-going basis. So, we can say that a combination of raw/live videos and processed videos works best for many businesses.
What Tools Do You Need?
Social media content creation may seem a difficult task but it’s no rocket science. You don’t need to invest a huge sum in buying equipment and tools to create the right content.
Many marketers avoid generating video content for social media because they don’t own professional equipment. However, you don’t need highly professional cameras to record videos. It’s perfectly fine to use a smartphone camera, digital cam, or GoPro for capturing events. But it’s recommended to get a portable tripod to ensure captured videos are stable and clear.
In the indoor environment, you may need to arrange lighting equipment. However, outdoor events can save you from this trouble too. Also, don’t forget to get a microphone to record audio along with the video content.
If you intend to share it live, you need not process it to enhance quality, but it’s important to edit and process them for professionally posting them on LinkedIn and other platforms.
There are many video editing software available that you can learn to use. However, it is a complex process that is best left to professionals. To find qualified professionals, you should visit Freelancer.com and Upwork websites. These are popular freelancing platforms where you can hire professionals on a project basis or an on-going as per your needs.
The Caption Game?
Posting images and videos on Instagram and other websites isn’t enough; you should complement it with captivating captions to increase engagement. Its length can vary, but Insta supports captions of up to 2,200 words. The shorter the text, the more effective it will be.
For your persona profile, you may add a quote that comes to your mind. But business branding shouldn’t be done this way. You should write a concise caption that represents the brand personality and resonates with your followers.
Writing long-form captions can work for brands as long as they aren’t boring. If you want to adopt this method, always remember to mention important phrases or words at the beginning. This way, when the post is truncated, users will still be able to get the information at a glance.
Aside from the descriptive text, you should also add the most appropriate hashtags to increase visibility.
What’s the Hashtag?
A hashtag is a combination of letters or numbers that represent a specific topic. It’s helpful for users because it helps them organize content and view posts based on their interests or the latest trends. You can follow hashtags that attract you the most so as to easily access information about that topic.
These hashtags are widely used on TikTok, Instagram, Twitter, and many other popular websites. As a marketer, you should up your game and master the art of creating and using the right hashtags to better promote your brand and products online.
You can use an existing hashtag or create a new one around your business or business event. On TikTok, brands often create viral challenges and come up with suitable hashtags for these challenge videos. You can follow in their footsteps and create a challenge of your own to get customer attention.
You can brainstorm to come up with innovative hashtags for business marketing, but hashtag tools can simplify this task for you. It’s recommended to explore Hashtagify, RiteTag, Trendsmap, and AutoHash to master the art of hashtagging.
Ask Your 8-Year-Old
Social media strategy gives the desired results when it’s focused on the needs of target customers. So, brands that create content that attracts their followers tend to get more views and can maintain a good conversion rate.
The population on social media is constantly increasing and more and more youngsters are creating profiles on social media. Therefore, the best way to understand what kind of content these people need is to get the opinion of kids and teenagers.
These youngsters are well-equipped with modern technology and understand how to use almost any platform. They can guide you about the content that attracts this young generation and even give you unique ideas to make your content more engaging.
With the help of these insights, you can develop a plan to increase the engagement rate and convince the audience to take action.
Is that Wrong? The Ethical Question in Social Media
Remember when Adidas faced a backlash by tweeting the following message to participants who completed the Boston annual race in 2018, due to its reference to painful Boston bombings at the 2013 event?
“Congrats, you survived the Boston Marathon!”
Or when the skincare company, Nivea, posted a social media ad emphasizing that “White is Purity”?
Many businesses grab the headlines from time to time due to a simple mistake on social media or due to their inappropriate posts. It’s a growing concern among social media users and can bring negative publicity to businesses.
Before you post content on social media, make sure it’s free of profanities, culturally inappropriate language, racism, or other negative aspects that can cause controversy. You need to respect everyone regardless of their beliefs, ethnic background, financial status, or sexual orientation, and create content that doesn’t harm anyone’s feelings. With an ethical approach, you can effectively promote your brand and build a positive brand image.
Am I Famous Yet?
Social media marketing is a cost-efficient yet effective way to promote your products and reach out to the audience. A common mistake made by some marketers is that they post content and ads on social media for a few days and opt out of social marketing if the posts go unnoticed.
There is no doubt that social media websites have become the leading platforms for marketing purposes. However, it doesn’t mean that your brand will suddenly become popular in a few days.
Nowadays, a majority of businesses rely on social media marketing. Under such circumstances, you can’t expect to become the market leader within a week.
What you need to do is to be consistent with your effort. During the initial few weeks, your social marketing campaigns may not do that great. However, you should follow the marketing strategy without losing hope. Furthermore, monitoring the performance of the campaign is also essential. It can guide you about what you are doing right and which areas of your social marketing need to be changed.
With this approach, your social marketing efforts will bring results in time and can become the customer choice through constant efforts.


1.14.63: Solubilities of Solids in Liquids
This very large subject can be divided into two groups. The first group concerns the solubility of a given solid substance \(j\) in a given solvent, liquid \(\ell_{1}\). The second group involves comparison of the solubilities of a given solid in two liquids, \(\ell_{1}\) and \(\ell_{2}\).
A closed system (at defined \(\mathrm{T}\) and \(\mathrm{p}\), the latter being close to the standard pressure) contains solid substance \(j\) in equilibrium with an aqueous solution containing solute \(j\). The system is characterized by the (equilibrium) solubility, \(\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq})\). At equilibrium,
\[\mu_{\mathrm{j}}^{*}(\mathrm{~s})=\mu_{\mathrm{j}}^{0}(\mathrm{aq})+\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) \, \gamma_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) / \mathrm{m}^{0}\right] \nonumber \]
Then
\[\Delta \mu_{\mathrm{j}}^{0}=\mu_{\mathrm{j}}^{0}(\mathrm{aq})-\mu_{\mathrm{j}}^{*}(\mathrm{~s})=-\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) \, \gamma_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) / \mathrm{m}^{0}\right] \nonumber \]
If the aqueous solution is dilute and the solubility is low, it can often be assumed that the properties of the solution are ideal. Hence,
\[\Delta \mu_{\mathrm{j}}^{0}=\mu_{\mathrm{j}}^{0}(\mathrm{aq})-\mu_{\mathrm{j}}^{\mathrm{*}}(\mathrm{s})=-\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) / \mathrm{m}^{0}\right] \nonumber \]
It should be noted that the sign of \(\Delta \mu_{j}^{0}\) depends on whether or not \(m_{j}^{e q}(a q)\) is larger or less than unity.
We illustrate the second approach by considering a combination of the experiment described above and an experiment where the solvent is a binary aqueous mixture, mole fraction composition \(\mathrm{x}_{2}\). At equilibrium,
\[\mu_{j}^{*}(s)=\mu_{j}^{0}\left(s \ln ; x_{2}\right)+R \, T \, \ln \left[m_{j}^{\mathrm{eq}}\left(s \ln ; x_{2}\right) \, \gamma_{j}^{\mathrm{eq}}\left(s \ln ; x_{2}\right) / m^{0}\right] \nonumber \]
\[\begin{aligned}
\Delta\left(\mathrm{aq} \rightarrow \mathrm{x}_{2}\right) \mu_{\mathrm{j}}^{0}=\mu_{\mathrm{j}}^{0}\left(\mathrm{~s} \ln ; \mathrm{x}_{2}\right)-\mu_{\mathrm{j}}^{0}(\mathrm{aq}) \\
=-\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}\left(\mathrm{s} \ln ; \mathrm{x}_{2}\right) \, \gamma_{\mathrm{j}}^{\mathrm{eq}}\left(\mathrm{s} \ln ; \mathrm{x}_{2}\right) / \mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq}) \, \gamma_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq})\right]
\end{aligned} \nonumber \]
If both solutions are dilute in substance \(j\), the ratio, \(\gamma_{j}^{\mathrm{eq}}\left(\mathrm{s} \ln ; \mathrm{x}_{2}\right) / \gamma_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq})\) can be assumed to be close to unity. In fact this is a better approximation than assuming both activity coefficients are unity. Then
\[\Delta\left(\mathrm{aq} \rightarrow \mathrm{x}_{2}\right) \mu_{\mathrm{j}}^{0}=-\mathrm{R} \, \mathrm{T} \, \ln \left[\mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}\left(\mathrm{s} \ln ; \mathrm{x}_{2}\right) / \mathrm{m}_{\mathrm{j}}^{\mathrm{eq}}(\mathrm{aq})\right] \nonumber \]
In other words if the solubility of substance \(j\) increases on adding solvent component 2 then \(\Delta\left(\mathrm{aq} \rightarrow \mathrm{x}_{2}\right) \mu_{\mathrm{j}}^{\mathrm{c}}\) is negative. This stabilization is a consequence of a difference in solute-solvent interactions.


2.7: Educational Influences [2]
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The individuals mentioned in roadmap were noted philosophers and educators who sought to change the status quo. By advocating for the welfare and education of children they were instrumental in bringing an awareness that childhood is an important stage of life. It is critical to note that there were other influences from the field of psychology and medicine that also informed the field of early care and education.
The following interdisciplinary influences have contributed directly and indirectly to education, they run separate but parallel from the philosophers and educators on the roadmap, moving through time on their own track. As you consider these influences think about how their philosophies and theories intersected with education and child development.