4.5: Uniform Circular Motion
- Solve for the centripetal acceleration of an object moving on a circular path.
- Use the equations of circular motion to find the position, velocity, and acceleration of a particle executing circular motion.
- Explain the differences between centripetal acceleration and tangential acceleration resulting from nonuniform circular motion.
- Evaluate centripetal and tangential acceleration in nonuniform circular motion, and find the total acceleration vector.
Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is executing uniform circular motion. Other examples are the second, minute, and hour hands of a watch. It is remarkable that points on these rotating objects are actually accelerating, although the rotation rate is a constant. To see this, we must analyze the motion in terms of vectors.
Centripetal Acceleration
In one-dimensional kinematics, objects with a constant speed have zero acceleration. However, in two- and three-dimensional kinematics, even if the speed is a constant, a particle can have acceleration if it moves along a curved trajectory such as a circle. In this case the velocity vector is changing, or \(\frac{d\vec{v}}{dt}\) ≠ 0. This is shown in Figure \(\PageIndex{1}\). As the particle moves counterclockwise in time \(\Delta\)t on the circular path, its position vector moves from \(\vec{r}(t)\) to \(\vec{r}(t + \Delta t)\). The velocity vector has constant magnitude and is tangent to the path as it changes from \(\vec{v}\)(t) to \(\vec{v}\left(t + \Delta t\right)\), changing its direction only. Since the velocity vector \(\vec{v}(t)\) is perpendicular to the position vector \(\vec{r}\)(t), the triangles formed by the position vectors and \(\Delta \vec{r}\), and the velocity vectors and \(\Delta \vec{v}\) are similar. Furthermore, since
\[|\vec{r}(t) | = | \vec{r} (t + \Delta t)| \nonumber\]
and
\[| \vec{v} (t)| = | \vec{v} (t + \Delta t)|, \nonumber \]
the two triangles are isosceles . From these facts we can make the assertion
\[\dfrac{\Delta v}{v} = \dfrac{\Delta r}{r}\]
or
\[\Delta v = \dfrac{v}{r} \Delta r.\]
We can find the magnitude of the acceleration from
\[a = \lim_{\Delta t \rightarrow 0} \left(\dfrac{\Delta v}{\Delta t}\right) = \frac{v}{r} \left(\lim_{\Delta t \rightarrow 0} \dfrac{\Delta r}{\Delta t}\right) = \frac{v^{2}}{r} \ldotp\]
The direction of the acceleration can also be found by noting that as \(\Delta\)t and therefore \(\Delta \theta\) approach zero, the vector \(\Delta \vec{v}\) approaches a direction perpendicular to \(\vec{v}\). In the limit \(\Delta t → 0,\) \(\Delta \vec{v}\) is perpendicular to \(\vec{v}\). Since \(\vec{v}\) is tangent to the circle, the acceleration \(\frac{d \vec{v}}{dt}\) points toward the center of the circle. Summarizing, a particle moving in a circle at a constant speed has an acceleration with magnitude
\[a_{c} = \frac{v^{2}}{r} \ldotp \label{4.27}\]
The direction of the acceleration vector is toward the center of the circle (Figure \(\PageIndex{2}\)). This is a radial acceleration and is called the centripetal acceleration , which is why we give it the subscript \(c\). The word centripetal comes from the Latin words centrum (meaning “center”) and petere (meaning to seek”), and thus takes the meaning “center seeking.”
Let’s investigate some examples that illustrate the relative magnitudes of the velocity, radius, and centripetal acceleration.
A jet is flying at 134.1 m/s along a straight line and makes a turn along a circular path level with the ground. What does the radius of the circle have to be to produce a centripetal acceleration of 1 g on the pilot and jet toward the center of the circular trajectory?
Strategy
Given the speed of the jet, we can solve for the radius of the circle in the expression for the centripetal acceleration.
Solution
Set the centripetal acceleration equal to the acceleration of gravity: 9.8 m/s 2 = \(\frac{v^{2}}{r}\).
Solving for the radius, we find
\[r = \frac{(134.1\; m/s)^{2}}{9.8\; m/s^{2}} = 1835\; m = 1.835\; km \ldotp\]
Significance
To create a greater acceleration than g on the pilot, the jet would either have to decrease the radius of its circular trajectory or increase its speed on its existing trajectory or both.
A flywheel has a radius of 20.0 cm. What is the speed of a point on the edge of the flywheel if it experiences a centripetal acceleration of 900.0 cm/s 2 ?
Centripetal acceleration can have a wide range of values, depending on the speed and radius of curvature of the circular path. Typical centripetal accelerations are given in Table \(\PageIndex{1}\).
| Object | Centripetal Acceleration (m/s 2 or factors of g) |
|---|---|
| Earth around the Sun | 5.93 x 10 -3 |
| Moon around the Earth | 2.73 x 10 -3 |
| Satellite in geosynchronous orbit | 0.233 |
| Outer edge of a CD when playing | 5.75 |
| Jet in a barrel roll | (2-3 g) |
| Roller coaster | (5 g) |
| Electron orbiting a proton in a simple Bohr model of the atom | 9.0 x 10 22 |
Equations of Motion for Uniform Circular Motion
A particle executing circular motion can be described by its position vector \(\vec{r}(t)\). Figure \(\PageIndex{3}\) shows a particle executing circular motion in a counterclockwise direction. As the particle moves on the circle, its position vector sweeps out the angle \(\theta\) with the x-axis. Vector \(\vec{r}(t)\) making an angle \(\theta\) with the x-axis is shown with its components along the x- and y-axes. The magnitude of the position vector is \(A = |\vec{r}(t)|\) and is also the radius of the circle, so that in terms of its components,
\[\vec{r} (t) = A \cos \omega \hat{i} + A \sin \omega t \hat{j} \ldotp \label{4.28}\]
Here, \(\omega\) is a constant called the angular frequency of the particle. The angular frequency has units of radians (rad) per second and is simply the number of radians of angular measure through which the particle passes per second. The angle \(θ\) that the position vector has at any particular time is \(\omega\)t.
If \(T\) is the period of motion, or the time to complete one revolution (\(2 \pi\, rad\)), then
Velocity and acceleration can be obtained from the position function by differentiation:
\[\vec{v} (t) = \frac{d \vec{r} (t)}{dt} = -A \omega \sin \omega t \hat{i} + A \omega \cos \omega t \hat{j} \ldotp \label{4.29}\]
It can be shown from Figure \(\PageIndex{3}\) that the velocity vector is tangential to the circle at the location of the particle, with magnitude A\(\omega\). Similarly, the acceleration vector is found by differentiating the velocity:
\[\vec{a} (t) = \frac{d \vec{v} (t)}{dt} = -A \omega^{2} \cos \omega t \hat{i} - A \omega^{2} \sin \omega t \hat{j} \ldotp \label{4.30}\]
From this equation we see that the acceleration vector has magnitude A\(\omega^{2}\) and is directed opposite the position vector, toward the origin, because \(\vec{a}\)(t) = −\(\omega^{2} \vec{r}\)(t).
A proton has speed 5 x 10 6 m/s and is moving in a circle in the xy plane of radius r = 0.175 m. What is its position in the xy plane at time t = 2.0 x 10 −7 s = 200 ns? At t = 0, the position of the proton is 0.175 m \(\hat{i}\) and it circles counterclockwise. Sketch the trajectory.
Solution
From the given data, the proton has period and angular frequency:
\[T = \frac{2 \pi r}{v} = \frac{2 \pi (0.175\; m)}{5.0 \times 10^{6}\; m/s} = 2.20 \times 10^{-7}\; s \nonumber \]
\[\omega = \frac{2 \pi}{T} = \frac{2 \pi}{2.20 \times 10^{-7}\; s} = 2.856 \times 10^{7}\; rad/s \ldotp \nonumber \]
The position of the particle at t = 2.0 x 10 −7 s with A = 0.175 m is
\[\begin{align*} \vec{r} (2.0 \times 10^{-7}\; s) & = A \cos \omega (2.0 \times 10^{-7}\; s) \hat{i} + A \sin \omega (2.0 \times 10^{-7}\; s) \hat{j}\; m \\[4pt] & = 0.175 \cos (2.856 \times 10^{7}\; rad/s) (2.0 \times 10^{-7}\; s) \hat{i} + 0.175 \sin (2.856 \times 10^{7}\; rad/s) (2.0 \times 10^{-7}\; s) \hat{j}\; m \\[4pt] & = 0.175 \cos (5.712\; rad) \hat{i} + 0.175 \sin (5.172\; rad) \hat{j}\; m \\ & = 0.147 \hat{i} - 0.095 \hat{j}\; m \ldotp \end{align*}\]
From this result we see that the proton is located slightly below the x-axis. This is shown in Figure \(\PageIndex{4}\).
Significance
We picked the initial position of the particle to be on the x-axis. This was completely arbitrary. If a different starting position were given, we would have a different final position at t = 200 ns.
Nonuniform Circular Motion
Circular motion does not have to be at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of the motion.
In uniform circular motion, the particle executing circular motion has a constant speed and the circle is at a fixed radius. If the speed of the particle is changing as well, then we introduce an additional acceleration in the direction tangential to the circle. Such accelerations occur at a point on a top that is changing its spin rate, or any accelerating rotor. In Displacement and Velocity Vectors we showed that centripetal acceleration is the time rate of change of the direction of the velocity vector. If the speed of the particle is changing, then it has a tangential acceleration that is the time rate of change of the magnitude of the velocity:
\[a_{T} = \frac{d |\vec{v}|}{dt} \ldotp \label{4.31}\]
The direction of tangential acceleration is tangent to the circle whereas the direction of centripetal acceleration is radially inward toward the center of the circle. Thus, a particle in circular motion with a tangential acceleration has a total acceleration that is the vector sum of the centripetal and tangential accelerations:
\[\vec{a} = \vec{a}_{c} + \vec{a}_{T} \ldotp \label{4.32}\]
The acceleration vectors are shown in Figure \(\PageIndex{5}\). Note that the two acceleration vectors \(\vec{a}_{c}\) and \(\vec{a}_{T}\) are perpendicular to each other, with \(\vec{a}_{c}\) in the radial direction and \(\vec{a}_{T}\) in the tangential direction. The total acceleration \(\vec{a}\) points at an angle between \(\vec{a}_{c}\) and \(\vec{a}_{T}\).
A particle moves in a circle of radius r = 2.0 m. During the time interval from t = 1.5 s to t = 4.0 s its speed varies with time according to
\[v(t) = c_{1} - \frac{c_{2}}{t^{2}}, c_{1} = 4.0\; m/s, c_{2} = 6.0\; m \cdotp s \ldotp\]
What is the total acceleration of the particle at t = 2.0 s?
Strategy
We are given the speed of the particle and the radius of the circle, so we can calculate centripetal acceleration easily. The direction of the centripetal acceleration is toward the center of the circle. We find the magnitude of the tangential acceleration by taking the derivative with respect to time of |v(t)| using Equation \ref{4.31} and evaluating it at t = 2.0 s. We use this and the magnitude of the centripetal acceleration to find the total acceleration.
Solution
Centripetal acceleration is
\[v(2.0\; s) = \left(4.0 - \dfrac{6.0}{(2.0)^{2}}\right) m/s = 2.5\; m/s \nonumber \]
\[a_{c} = \frac{v^{2}}{r} = \frac{(2.5\; m/s)^{2}}{2.0\; m} = 3.1\; m/s^{2} \nonumber \]
directed toward the center of the circle. Tangential acceleration is
\[a_{T} = \Big| \frac{d \vec{v}}{dt} \Big| = \frac{2 c_{2}}{t^{3}} = \frac{12.0}{(2.0)^{3}} m/s^{2} = 1.5\; m/s^{2} \ldotp \nonumber \]
Total acceleration is
\[|\vec{a}| = \sqrt{3.1^{2} + 1.5^{2}} m/s^{2} = 3.44\; m/s^{2}\]
and \(\theta\) = tan −1 \(\left(\dfrac{3.1}{1.5}\right)\) = 64° from the tangent to the circle. See Figure \(\PageIndex{6}\).
Significance
The directions of centripetal and tangential accelerations can be described more conveniently in terms of a polar coordinate system, with unit vectors in the radial and tangential directions. This coordinate system, which is used for motion along curved paths, is discussed in detail later in the book.


1.7: Sexuality
Introduction
Individuals with intellectual disabilities experience difficulty in interpreting behavioural cues within their social environments. This may in turn create negative outcomes for their expression of sexuality (Meany-Tavaras & Gavidia-Payne, 2012). People with intellectual disabilities are overrepresented as both victims and perpetrators of sexual offences (Hogg et al., 2001; Lambrick & Glaser, 2004). According to Szollos and McCabe (1995), 50% of females with intellectual disabilities will be sexually assaulted in their lifetime, and males with intellectual disability are more likely to be sexually abused than other males.
  They can find it difficult to assert their own opinions and they may give in to the suggestions or directions given by others, particularly when expressing their sexuality (Hayashi, Arakida & Ohashi, 2011).
People with intellectual disabilities depend on family members and service providers to teach them how to appropriately express their sexuality, which is a critical aspect of social competence. Many individuals with intellectual disability need ongoing education about sexuality, particularly self-protective strategies, so that others will not take advantage of them.
However, depending on past life experiences, the kind of education needed varies from one person to another. Individuals with a mild to moderate disability who live with their own or a foster family may have attended sexual health classes as part of the social skills training provided in schools, vocational programs, and sheltered workshops. Those with a severe or profound disability who live in group homes or institutions surrounded by professional caregivers and others like themselves will have had fewer educational opportunities.
Those with more social skills training, more exposure to different life experiences, and more opportunities to function socially can be expected to demonstrate more social competencies (Abbott & McConkey, 2006; Simpson, 2010). Despite the diverse educational needs of individuals with intellectual disabilities, supporting them to show healthy expressions of their sexuality is important. In this chapter we discuss three critical areas that should be considered when providing sexual education support: discussion topics, understanding boundaries, and differentiating between challenging behaviours and sex offending behaviours.
Discussion Topics for Sexual Education Support
Although major gains have been made in the last two decades in normalizing, including, and integrating people with intellectual disability into community settings, their sexual health continues to be an overlooked area (Scotti et al., 1996; Thompson et al., 2014). Historically, in many countries intellectual disability or “feeble-mindedness” was considered hereditary, and individuals identified as mentally defective were sterilized without their knowledge to prevent procreation (Grekul, Krahn, & Odynak, 2004). Today, sexual education programs for people with intellectual disabilities are becoming more commonplace and researchers are beginning to understand the kinds of discussion topics that are most valuable.
Critical discussion topics that can help individuals begin to understand their own personal sexuality are puberty, menstruation, menopause, masturbation, relationships, protective behaviours, sexuality, safer sex practices, contraception, pregnancy and birth, sexual health screening tests, sexually transmitted infections, and legal issues regarding sexuality (Butler, Leighton, & Galea, 2003). Other topics are body grooming and cleanliness, first impressions in speaking to your partner, communication training, self-assertiveness training, a sense of space between participant and others, manners in public spaces, sexual harassment, stalker victimization, male–female relationships, and differences between male and female bodies (Hayashi, Arkida, & Ohashi, 2011). While support workers and family members themselves may not be the one delivering sexual education programs, it is helpful for all those involved to initiate discussions about these topic areas, invite further questions, and provide ongoing guidance.
 Both family members and caregivers have expressed concern about parenthood and marriage for adults with intellectual disabilities (Oliver et al., 2002). Parents with intellectual disabilities represent one of the most vulnerable parenting groups (Booth & Booth, 2005). Most concerns relate to neglect or emotional abuse, with 40% to 60% of parents with intellectual disabilities having their children removed by child protective agencies because they failed to meet the standard of good enough parenting (Cleaver & Nicholson, 2005). Researchers believe that these numbers could be lowered if parents with intellectual disabilities had adequate supports and education (Cleaver & Nicholson, 2005; Murphy & Feldman, 2002). Specific areas these parents need help with are generalizing information from one setting to another; knowledge about normal childhood development and the care needs of infants, children, and adolescents; and knowledge about how to play with and show appropriate affection to their children (Wilson et al., 2013).
According to the International Association for the Scientific Study of Intellectual Disabilities (2008), parents with intellectual disabilities need both parenting skill education and a strong social network. When parents, especially mothers, are surrounded by helpful family members, friends, and professionals, they develop an increased capacity to care for their children (Guinea, 2001; Koeske & Koeske, 1990; Wilson et al., 2013). Unfortunately, the reality is that these parents often find themselves with limited social and environmental support (Mayes, Llewellyn, & McConnell, 2006).
Discussion Topics for Sexual Education Support
Key Points for Caregivers
Sexual health is often overlooked in individuals with intellectual disabilities. They are very vulnerable to sexual abuse and may not understand what consenting to sexual activity means. They may not know how to express their sexuality.  These kinds of topics must also be part of the everyday conversations that take place between intellectually disabled individuals and the people in their lives. When individuals with intellectual disabilities are parents, they need a network of people around them and opportunities to learn about children’s development and showing appropriate affection to children.
Understanding Boundaries
Boundaries are the limits in relationships within which we feel psychologically safe (Kent, 2012). Individuals with intellectual disabilities may have difficulty understanding the boundaries that are expected in conventional social relationships. For example, they may interrupt, have difficulty taking turns or waiting for assistance, and steal other’s belongings. When interacting with caregivers, they may express sexual feelings through behaviours such as intruding into the caregiver’s personal space, requesting to be a boyfriend or girlfriend, and attempting to kiss or touch in a sexual manner. These behaviours leave caregivers feeling confused and uncomfortable. A fitting response is for staff groups to consistently and immediately provide straightforward feedback that these behaviours are not acceptable.
Similarly, individuals with intellectual disabilities may demonstrate inappropriate sexual behaviours in public.  They may walk into public areas naked, touch others, or allow themselves to be touched. They may grab others roughly to get attention or indicate a personal need. In individuals with dual diagnosis, these overt sexual demonstrations may indicate an escalating psychiatric disorder. Rather than simply viewing these behaviours as distasteful, it is vital for caregivers to document, report, and discuss them with other staff members and health professionals.
It is important to hold these individuals accountable for their behaviour. When behaviours seriously violate the boundaries and feelings of psychological safety for caregivers and others, it is important to ask what would happen to those who are not intellectually disabled if they engaged in these same behaviours. If the answer is that they would be charged with sexual or physical assault, then involving the police must be considered. Treating people with disabilities differently suggests that they are not responsible for their actions and thus not real members of society.
Caregivers model the process of setting boundaries through their own actions. They can use anatomical rather than slang or baby-talk words during discussions related to sexuality. They should avoid flirting, telling or listening to sexual jokes, and swearing or offensive language (Cooper, 2012). They can show respect for modesty by performing personal care in private rather than public spaces. Simple acts such as knocking before entering someone`s room and keeping doors open during private discussions communicate subtle cues about acceptable behaviour. Instead of allowing a non-verbal person to grab others in an aggressive way when he or she wants something, redirecting the action by demonstrating a more gentle way to reach out can be helpful. As previously mentioned and in accordance with any applicable agency policy, caregivers must confront and report inappropriate expression of sexual expression to their supervisors or even the police.
Providing Resources
For individuals with limited language or who use pictures as part of their communication strategies, signs and/or picture cards for yes , no , don’t touch , and stop are useful. As discussed in Chapter 5, prepared cards illustrating common needs and feelings are available at the Do2Learn (n.d.) website, http://www.do2learn.com .
Another useful resource to promote awareness about boundaries is the Circle of Relationships activity (Walker-Hirsch & Champagne, 1991). Here, different levels of intimacy and appropriate social behaviours are indicated by colour groups (see Table 7.1). A hand-out of Table 7.1 could be provided to participants, who can then be invited to link names of people they know to a colour group.
Table 7.1 Circle of Relationships activity
| Colour Code and Name | Description |
|
Purple Private Circle
|
You are important and you will decide who can touch you. No one should touch you unless you want to be touched. Sometimes people in your Blue, Green, Yellow, Orange, or Red Circles will try to get too close to you. You need to say STOP. No one touches you unless you want to be touched and you do not touch other people unless they want to be touched.
|
| Blue Hug Circle | It is a mutual decision to kiss and hug and be close. If you do not want to, you must say STOP. Sometimes you may not feel like being touched. This does not mean that you are no longer close with your partner, but only that you are not feeling loving at that moment. Your partner can say STOP to you too. |
| Green Faraway Circle | Sometimes a friend may want to be closer to you than you want. You just explain to your friend and say STOP.  You can say “You are not in my Blue Hug Circle.” |
| Yellow Handshake Circle | Sometimes someone whose name you know may ask for a Faraway Hug. You can say NO. No one can touch you unless you want to be touched. You can use a handshake to greet this person if it feels right for you. |
| Orange Wave Circle | Wave to an acquaintance who is too far away for a handshake. Sometimes children will want to hug and kiss you, but you can say NO. It is best to wave to children. Children do not know as much as you, so it is best to show them correct behaviour. |
| Red Stranger Circle | Some people stay strangers forever. You may talk about business to a stranger who is a community helper. Other strangers do not talk to you or touch you. If a stranger touches you after you have said STOP, go get help and tell someone. |
Understanding Boundaries and Providing Resources
Key Points for Caregivers
Establishing boundaries in relationships can create safe psychological spaces. When individuals with an intellectual disability express their sexuality in inappropriate ways, their behaviour needs to be addressed just as it would with non-disabled individuals. Open demonstrations of sexuality may be linked to mental illnesses and must be reported and discussed with other staff and health professionals. In some instances, the behaviour must be reported to police. Caregivers can model respectful behaviour that shows the difference between private and public actions. This is an important way for individuals with intellectual disability to learn about setting boundaries. Resources are available, such as picture cards and the Circle of Relationships activity.
 Staff from different professional groups may not agree on whether the behaviour should be viewed as challenging or sex offending , Problematic sexual behaviour can be aligned with clinical processes and viewed either way (Doyle, 2004). Although philosophies about challenging behaviour and sex offending behaviour have some characteristics in common, knowing that significant differences exist can be helpful in understanding how to provide consistent and informed support.
Challenging behaviours are viewed as violent and have been defined as “behaviour of such intensity, frequency or duration that the physical safety of the person or others is placed in serious jeopardy or behaviour which is likely to seriously limit or deny access to the use of ordinary community facilities” (Emerson, 1995, p. 4). Sexually violent behaviour includes actual, attempted, or threatened sexual contact with a person who is non-consenting or unable to give consent (Boer et al., 1997). This includes all sexual contact with children. The behaviour may interfere with the gaining of new skills and learning opportunities, so that the quality of life of others may be impacted as well as the quality of life of the individual with the challenging behaviour. Examples of challenging behaviours include self-injury, self-stimulation, physical and verbal aggression, sexually inappropriate behaviour, and property destruction (Doyle, 2004).
The term challenging behaviour has been used as an attempt to avoid further stigmatizing a population of individuals who are already marginalized. It is meant to demonstrate that the behaviour is an adaptive response to other factors or a means of communicating distress to others (as discussed in Chapter 6). Assessment is likely to incorporate indicators of psychiatric disorders. Interventions focus on exploring the environmental, biological, educational, and social factors responsible for the behaviour rather than placing the blame on the individual participating in the behaviour. It is within this way of thinking that clinicians are trying to come to terms with and develop interventions for sexually violent behaviour.
Understanding challenging behaviour requires believing that human behaviour occurs for some reason and within a certain context. Functional analysis is the way clinicians and workers in the intellectual disability field attempt to understand the meaning or communicative intent of the behaviour. The relationship between the behaviour, the preceding events, and the consequences of the behaviour are explored. Treatment processes then look at ways to alter preceding events or consequences in order to change the behaviour and to address the needs the individual is attempting to communicate.
Treatment approaches that view the behaviour as sexual offending regard the same actions as violent but emphasize protecting the community and preventing the behaviour from reoccurring. Rather than considering the meaning behind the behaviour, this view suggests that individuals must take responsibility for their behaviour and for the consequences of their actions. This way of thinking highlights that there is a risk for both the community and the offending individual if the seriousness of sex offending is underplayed. For example, we cannot hold children or vulnerable disabled adults responsible for triggering an offender`s behaviour, and we cannot just dismiss the damaging consequences of the sex offending behaviour.
There are two important arguments against viewing sex offending behaviour as being simply challenging. First, treatment framed from a sex offending view does not reflect the values inherent in the process of conducting a functional analysis. Second, there is a risk for both the community and the offending individual if the seriousness of sex offending is underplayed. Table 7.2 presents differences between behaviours that are challenging and those that are sex offending (Doyle, 2004).
Table 7.2 Values-based assumptions: Challenging behaviour versus sex offending behaviour
| Challenging Behaviour | Sex Offending Behaviour |
| The primary intention of a functional analysis approach to challenging behaviour is to identify the purpose, meaning, and communicative intent of a behaviour in order to provide behavioural support. | Evaluation of intent and motivation is key to understanding offending behaviour.  Sorting out the how and identifying the form the behaviour takes and the circumstances under which the behaviour occurs is paramount in order to develop relapse-prevention strategies. |
| Once the purpose of the individual’s behaviour has been determined, behavioural support is given with the primary aim to hold that individual’s dignity as a primary concern. | The risky nature of sexual offending behaviour means that the focus needs to be on the behaviour itself rather than the meaning behind the behaviour. The damage to vulnerable victims can have great impact on them for the rest of their lives. While the dignity of the offender is of concern, protecting the community and managing the risk of reoffending behaviour both compete for priority. |
| In functional analysis, the goal is to understand the purpose of the behaviour in order to teach and develop effective alternatives. The approach is educational and involves the systematic instruction of new adaptive skills. | Assessment of sexual offending behaviour is carried out to prevent and protect the public and not necessarily to understand the purpose of the behaviour for the offender. The educational focus is relapse prevention and addressing contributing factors such as problem solving and decision making, anger management, alcohol and drug abuse prevention, sexuality, and legal issues such as consent. The Association for the Treatment of Sexual Abusers website is a helpful resource ( http://www.atsa.com/index.html ). |
| Functional analysis is designed to determine the relationships between environmental conditions and the person’s behaviours. The environment has an ongoing reciprocal role in shaping the behaviour and is the focus of developing alternative strategies. Precipitating environmental factors and factors that reinforce or maintain the behaviour are adapted to facilitate the development of more adaptive behaviours. The individual is not blamed. | Removing personal responsibility for offending behaviour is potentially dangerous. In the case of the sexual offender, the environment may be seen as only eliciting the expression of an existing deviant sexual orientation and hence is not a true interaction. Children and vulnerable individuals cannot be held responsible for the offender’s behaviour.  It is important to emphasize that the behaviour is wrong, it hurts others, and it has legal and emotional consequences that may affect the quality of life of the offender as well as the victims. |
Differentiating between Challenging Behaviours and Sex Offending Behaviours
Key Points for Caregivers
Inappropriate expressions of sexuality are very serious. Whether they are open or violent, they can traumatize victims and leave offenders facing lifelong consequences. Different professional groups do not all agree on the best treatment approaches. Some view sexually violent behaviours that hurt others and interfere with quality of life for others as challenging. Others view these behaviours as sexual offending.
Treatment approaches that view the behaviour as challenging will try to find out why individuals act this way, what the behaviour means, and how it meets an otherwise unmet need. When caregivers are involved, they will admit that the behaviour is unacceptable and hurts others as well as themselves. They will also recognize that the behaviours are occurring for a reason and they will guide individuals toward meeting their needs with more acceptable behaviours.
Treatment approaches that view the behaviour as sexual offending will not focus on what the behaviour means. Here, when caregivers are involved, they will still admit that the behaviour is unacceptable and hurts others as well as themselves. However, they will pay more attention to strategies that prevent the behaviour from reoccurring and to protecting all the people in the community that the individual interacts with.
Although views about treatment approaches are different and each individual is unique, inappropriate expressions of sexuality must all be reported, discussed, and addressed as a team.
Conclusion
In this chapter we have discussed how caregivers can provide sexual education support to their clients through discussion topics, understanding boundaries, and differentiating between challenging behaviours and sex offending behaviours. Individuals with intellectual disabilities are very vulnerable to sexual abuse and victimization. They may not fully understand how to express their sexuality in socially acceptable ways and their consent for sexual activity may not be well informed. Those who are dually diagnosed with a psychiatric disorder are even more vulnerable. Their behaviour may be directly related to a psychiatric disorder and may indicate an escalating mental health crisis.
 Individuals with intellectual disabilities may be parents. For these parents to be supported toward retaining custody of their children and enjoying their family life, they need most to be surrounded by a network of caring, helpful people.
Understanding boundaries, or the limits we create within relationships to feel psychologically safe, is critically important.  When non-disabled individuals demonstrate this behaviour, it is viewed as inappropriate and often reported to police. Individuals with disabilities are just as accountable for their behaviour. Caregivers and others in their environment should not be made to feel uncomfortable or psychologically unsafe because of an individual’s behaviour. The behaviour should not be ignored. It should be discussed among agency staff, recorded, and reported according to agency policy. Caregivers can model how to set boundaries by requiring acceptable personal space during their interactions with clients.
Any inappropriate expression of sexuality must be taken seriously. People who witness, who are victimized, or who are assaulted as a consequence of these behaviours can be left devastated. Perpetrators are usually penalized. Although professionals do not always agree about whether the behaviour should be viewed as challenging or as sex offending, there is a clear consensus that the behaviour is hurtful, unacceptable, and must stop. Children and other adults must be protected and individuals must find strategies to prevent the behaviour from reoccurring.
Finally, adults with intellectual disabilities can embrace their sexuality every bit as fully as everyone else in society. Knowing this, seeking ways to ensure these adults have the knowledge they need can become a priority. Increasing clients’ expressions of their sexuality in healthy ways will allow others to see their capabilities and personalities as people we value and want to come to know.
Chapter Audio for Print
This chapter contains a number of short audio clips. If you are reading this in print, you can access the audio clips in this chapter by scanning this QR code with your mobile device. Alternatively, you can visit the book website at opentextbc.ca/caregivers and listen to all the audio clips.
References
Abbott, S. & McConkey, R. (2006), The barriers to social inclusion as perceived by people with intellectual disabilities. Journal of Intellectual Disabilities. 10, 275–287. DOI: 10.1177/1744629506067618.
Association for the Treatment of Sexual Abusers ATSA (n.d). Retrieved from http://www.atsa.com/
Bielecki, J., & Swender, S. L. (2004). The assessment of social functioning in individuals with mental retardation: A review. Behaviour Modification, 28(5), 694–708. doi:10.1177/0145445503259828.
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Circles Curriculum (n.d.). Retrieved from the James Stanfield Company websites at www.stanfield.com/products/family-life-relationships/social.
Cleaver, H. & Nicholson, D. (2005). Children living with learning disabled parents. London UK: London University.
Cooper, F. (2012). Professional boundaries in social work and social care: a practical guide to understanding, maintaining and managing your professional boundaries . London: Jessica Kingsley Publishers. Retreived from jpkc.fudan.edu.cn/picture/article/320/00/da/391bb47a43659403fac63ac3d1d7/749193e0-c1d5-4ced-a500-bfbde5f538b7.pdf
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Do2learn (n.d.). A resource for individuals with special needs. Retrieved from www.do2learn.com .
Doyle, D. M. (2004). The differences between sex offending and challenging behaviour in people with an intellectual disability. Journal of Intellectual & Developmental Disability, 29(2), 107–118.
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Galea, G., Butler, J., & Iacono, T. (2004). The assessment of sexual knowledge in people with intellectual disability. Journal of Intellectual & Developmental Disability, 29(4), 350–365.
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16.5: Applications of the Nernst Equation
Make sure you thoroughly understand the following essential ideas:
- Atmospheric oxygen is a strong oxidizing agent, but in the absence of a suitable catalyst this reaction is ordinarily too slow to be observable.
- The pE is a useful index of electron availability, especially in natural waters and biological systems in which multiple redox systems are usually present.
- Solubility products can often be measured by constructing a cell in which one of the electrodes involves the sparingly soluble salt, and the net cell equation corresponds to the solubility reaction.
- Potentiometric titrations are widely used to measure concentrations of species that are readily oxidized or reduced.
- Measurement of pH is accomplished with an electrode consisting of a thin membrane of glass in which Na + ions are exchanged with H + .
- Membrane (Donnan) potentials arise when passage of an ion across a semipermeable membrane is selectively facilitated or inhibited.
- Nerve conduction occurs not by a flow of charge through the nerve, but by a wave of depolarization resulting from the concerted action of active channels that govern the passage of ions (mainly K + and Na + ) across the membrane enclosing the nerve.
We ordinarily think of the oxidation potential being controlled by the concentrations of the oxidized and reduced forms of a redox couple, as given by the Nernst equation. Under certain circumstances it becomes more useful to think of E as an independent variable that can be used to control the value of Q in the Nernst equation. This usually occurs when two redox systems are present, one being much more concentrated or kinetically active than the other. By far the most important example of this is the way atmospheric oxygen governs the composition of the many redox systems connected with biological activity.
Oxygen and the Aquatic Environment
The presence of oxygen in the atmosphere has a profound effect on the redox properties of the aquatic environment— that is, on natural waters exposed directly or indirectly to the atmosphere, and by extension, on organisms that live in an aerobic environment.This is due, of course, to its being an exceptionally strong oxidizing agent and thus a low-lying sink for electrons from most of the elements and all organic compounds. Those parts of the environment that are protected from atmospheric oxygen are equally important because it is only here that electrons are sufficiently available to produce the "reducing" conditions that are essential for processes varying from photosynthesis to nitrogen fixation.
Estimate the redox potential of a natural water that is in equilibrium with the atmosphere at pH 7 and 298 K. What fraction of a dilute solution Fe 2 + will be in its oxidized form Fe 3 + in such a water?
Solution
The relevant E °s are
- 1.23 v for O 2 (g) + 4H + + 4 e – → 2H 2 O and
- 0.77 V for the Fe 3 + /Fe 2 + couple.
(a) The potential (with respect to the SHE, of course) is given by the Nernst equation
which works out to E = 0.82 volt. As the Le Chatelier principle predicts, the higher pH (lower [H + ] compared to that at the "standard" pH of zero) reduces the electron-accepting tendency of oxygen.
(b) The Nernst equation for the reduction of Fe 3 + is E = .77–.059 log Q, in which Q is the ratio [Fe 2 + ]/[Fe 3+ ]. With E set by the O 2 /H 2 O couple, this becomes
0.82 = 0.77 – 0.059 log Q
which gives Q = 10 –0.85 or [Fe 2 + ]/[Fe 3 + ] = 0.14/1, so the fraction of the iron in its oxidized form is 1/1.14 = 0.88.
If we can have pH, why not pE?
As you will recall from your study of acid-base chemistry, the pH of a solution (defined as –log {H + }) is a measure of availablity (technically, the activity ) of protons in the solution. As is explained in more detail here , protons tend to "fall" (in free energy) from filled donor levels (acids) to lower acceptor levels (bases.) Through the relation
\[[H^+] \approx K_a \dfrac{C_a}{C_b}\]
which can be rewritten as
\[\dfrac{C_a}{C_b} \approx \dfrac{[H^+]}{K_a}\]
in which the pH is treated as an independent variable that controls the ratio of the conjugate forms of any acid-base pairs in the solution:
\[\log \left(\dfrac{C_a}{C_b}\right) \approx pH – pK_a\]
In the same way, we can define the pE as the negative log of the electron activity in the solution:
\[pE = –\log{e^–}\]
of these particles (but not to their "concentrations") when we are considering their availability to donors and acceptors. We will not get into the details of how pE is actually calculated (it is of course related to the ordinary standard electrode potential). To get an idea of its significance, consider the following chart that shows the pE° values of some redox systems that are of immense importance in the aquatic environment.Environmentally-important redox systems
- These pE values refer to typical environmental conditions with pH=7 and oxygen partial pressure of 0.21 atm. The scale below shows the free energy of a mole of electrons relative to their level in H 2 O.
- The two conjugate forms of any redox pair are present in equal concentrations when the pE is at the level at which the pair is shown. At pE's above or below this level, the reduced or oxidized form will predominate.
- The sugar glucose , denoted by the general formula for carbohydrates {CH 2 O}, is the source of chemical energy for most organisms. Note that it is thermodynamically stable (and thus capable of being formed by photosynthesis) only under highly reducing conditions.
- Organisms derive their metabolic free energy when electrons fall from glucose to a lower-lying acceptor on the right.
- Delivery of electrons from glucose to O 2 ( 8 ) is the source of metabolic free energy for all aerobic organisms, yielding 125 kJ per mole of electrons transferred.
A few other points about this plot are worth noting:
- Anaerobic organisms must make do with electron-acceptors above oxygen. The poor bacteria that depend on reducing hydrogen ions ( 2 ) have it worst of all, gaining only a tiny amount of metabolic energy to produce a tiny puff of hydrogen gas.
- Reaction ( 3 ) is not much more efficient, but it is the vital first link in the process of natural nitrogen fixation that gets carried out in the protected electron-rich environment of the organisms that live in the root nodules of legumes.
- The consequences of ( 4 ) are readily apparent if you have ever noticed the rotten-egg odor of some poorly-aerated muddy soils.
- Reaction ( 6 ) is known as fermentation ; it takes place in the anarobic soils of marshes and bogs (hence the nickname "marsh gas" for methane) and in the insides of animals from termites to cows, and sometimes to our embarrassment, in ourselves. Notice that glucose plays the double role of electron donor and acceptor here; this is a disproportionation reaction.
- Finally, if you have ever had much to do with babys' diapers, you have likely noticed the smell of ammonia produced as the anaerobic bacteria from within deliver electrons to nitrate ions ( 7 ). It's important to bear in mind that the reactions discussed above are mediated by living organisms; without the necessary enzymes to catalyze them, their rates are essentially zero.
For a more detailed chart, see Falling through the respiratory chain .
Analytical chemistry applications
A very large part of Chemistry is concerned, either directly or indirectly, with determining the concentrations of ions in solution. Any method that can accomplish such measurements using relatively simple physical techniques is bound to be widely exploited. Cell potentials are fairly easy to measure, and although the Nernst equation relates them to ionic activities rather than to concentrations, the difference between them becomes negligible in solutions where the total ionic concentration is less than about 10 –3 M .
The concentrations of ions in equilibrium with a sparingly soluble salt are sufficiently low that their direct determination can be quite difficult. A far simpler and common procedure is to set up a cell in which one of the electrode reactions involves the insoluble salt, and whose net cell reaction corresponds to the dissolution of the salt. For example, to determine the K sp for silver chloride, we could use the cell
\[Ag_{(s)} | Ag^+(?\; M) || Ag^+,Cl^– | AgCl_{(s)} | Ag_{(s)}\]
whose net equation corresponds to the dissolution of silver chloride:
|
cathode:
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AgCl (s) + e – → Ag (s) + Cl – (aq) | E° = +0.222 v |
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anode:
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Ag (s) → Ag + (aq) + e – | E° = –(+0.799) v |
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net:
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AgCl (s) → Ag + + Cl – | E° = -0.577 v |
The standard potential for the net reaction refers to a hypothetical solution in which the activities of the two ions are unity. The cell potential we actually observe corresponds to E in the Nernst equation, which is then solved for Q which gives K sp directly.
Potentiometric titrations
In many situations, accurate determination of an ion concentration by direct measurement of a cell potential is impossible due to the presence of other ions and a lack of information about activity coefficients. In such cases it is often possible to determine the ion indirectly by titration with some other ion. For example, the initial concentration of an ion such as Fe 2 + can be found by titrating with a strong oxidizing agent such as Ce 4 + . The titration is carried out in one side of a cell whose other half is a reference electrode:
Pt (s) | Fe 2 + , Fe 3 + || reference electrode
Initially the left cell contains only Fe 2 + . As the titrant is added, the ferrous ion is oxidized to Fe 3 + in a reaction that is virtually complete:
\[Fe^{2+} + Ce^{4+} → Fe^{3+} + Ce^{3+}\]
The cell potential is followed as the Fe 2 + is added in small increments. Once the first drop of ceric ion titrant has been added, the potential of the left cell is controlled by the ratio of oxidized and reduced iron according to the Nernst equation
\[E = 0.68 - 0.059 \; \log \dfrac{]Fe^{3+}]}{[Fe^{2+}]}\]
which causes the potential to rise as more iron becomes oxidized.
When the equivalence point is reached, the Fe 2 + will have been totally consumed (the large equilibrium constant ensures that this will be so), and the potential will then be controlled by the concentration ratio of Ce 3 + /Ce 4 + . The idea is that both species of a redox couple must be present in reasonable concentrations poise an electrode (that is, to control its potential according to the Nernst equation.) If one works out the actual cell potentials for various concentrations of all these species, the resulting titration curve looks much like the familiar acid-base titration curve. The end point is found not by measuring a particular cell voltage, but by finding what volume of titrant gives the steepest part of the curve.
Measurement of pH
Since pH is actually defined in terms of hydrogen ion activity and not its concentration, a hydrogen electrode allows a direct measure of {H + } and thus of –log {H + }, which is the pH. All you need is to measure the voltage of a cell
H 2 (g, 1 atm) | Pt | H + (? M ) || reference electrode
In theory this is quite simple, but when it was first employed in the pre-electronics era, it required some rather formidable-looking apparatus (such as the L&N vibrating-reed electrometer setup from the 1920's shown here) and the use of explosive hydrogen gas. Although this arrangement (in which the reference electrode could be a standard hydrogen electrode) has been used for high-precision determinations since that time, it would be impractical for routine pH measurements of the kinds that are widely done, especially outside the research laboratory.
The glass electrode for pH measurements
In 1914 it was discovered that a thin glass membrane enclosing a solution of HCl can produce a potential that varies with the hydrogen ion activity {H + } in about the same way as that of the hydrogen electrode. Glass electrodes are manufactured in huge numbers for both laboratory and field measurements. They contain a built-in Ag-AgCl reference electrode in contact with the HCl solution enclosed by the membrane.
The potential of a glass electrode is given by a form of the Nernst equation very similar to that of an ordinary hydrogen electrode, but of course without the H 2 :
E membrane = A + (RT/F) ln ( {H + } + B )
in which A and B are constants that depend on the particular glass membrane.
The reason a glass membrane would behave in this way was not understood until around 1970. It now appears that hydrogen ions in the external solution diffuse through the glass and push out a corresponding number of the Na + ions which are normally present in most glasses. These sodium ions diffuse to whichever side of the membrane has the lower concentration, where they remain mostly confined to the surface of the glass, which has a porous, gelatinous nature. It is the excess charge produced by these positive ions that gives rise to the pH-dependent potential. The first commercial pH meter was developed by Arnold Beckman (1900-2004) while he was a Chemistry professor at CalTech. He was unable to interest any of the instrumentation companies in marketing it, so he founded his own company and eventually became a multi-millionaire philanthropist.
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Arnold Beckman
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An early Beckman pH meter
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A typical modern pH meter
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Ion-selective electrodes
The function of the membrane in the glass electrode is to allow hydrogen ions to pass through and thus change its potential, while preventing other cations from doing the same thing (this selectivity is never perfect; most glass electrodes will respond to moderate concentrations of sodium ions, and to high concentrations of some others.) A glass electrode is thus one form of ion-selective electrode. Since about 1970, various other membranes have been developed which show similar selectivities to certain other ions. These are widely used in industrial, biochemical, and environmental applications.
Membrane potentials and nerve conduction
You may recall the phenomena of osmosis and osmotic pressure that are observed when two solutions having different solute concentrations are separated by a thin film or membrane whose porosity allows small ions and molecules to diffuse through, but which holds back larger particles. If one solution contains a pair of oppositely-charged ionic species whose sizes are very different, the smaller ions may pass through the semipermeable membrane while the larger ones are retained. This will produce a charge imbalance between the two solutions, with the original solution having the charge sign of the larger ion. Eventually the electrical work required to bring about further separation of charges becomes too large to allow any further net diffusion to take place, and the system settles into an equilibrium state in which a constant potential difference (usually around a volt or less) is maintained. This potential difference is usually called a membrane potential or Donnan potential after the English chemist who first described this phenomenon around 1930.
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Origin of a membrane potential If the smaller ions are able to diffuse through the membrane but the larger ions cannot, a potential difference will develop between the two solutions. This membrane potential can be observed by introducing a pair of platinum electrodes. |
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The figure shows a simple system containing the potassium salt of a protein on one side of a membrane, and potassium chloride on the other. The proteinate anion, being too large to diffuse through the membrane, gives rise to the potential difference. The value of this potential difference can be expressed by a relation that is essentially the same as the Nernst equation, although its derivation is different. The membrane potential can be expressed in terms of the ratio of either the K + or Cl – ion activities:
The membrane surrounding most living cells contains sites or "channels" through which K + ions are selectively transported so that the concentration of K + inside the cell is 10-30 times that of the intracellular fluid. Taking the activity ratio as about 20, the above equation predicts that the potential difference θ inside - θ outside will be
which is consistent with observed values. Transport of an ion such as K + from a region of low concentration into the more concentrated intercellular fluid requires a source of free energy, which is supplied by ATP under enzymatic control. The metabolic processes governing this action are often referred to as "ion pumps".
Nerve conduction
Transmission of signals through the nervous system occurs not by the movement of a charge carrier through the nerve, but by waves of differential ion concentrations that travel along the length of the nerve. These concentration gradients are reduced by protein-based ion channels and ATP-activated (and energy-consuming) ion pumps specific to K + and Ca 2 + ions.
We sometimes think of our nerves as the body's wiring, but the "electricity" that they transmit is not a flow of electrons, but a rapidly-traveling wave of depolarization involving the transport of ions through the nerve membrane. The normal potential difference between the inner and outer parts of nerve cells is about –70 mv as estimated above. Transmissin of a nerve impulse is initiated by a reduction of this potential difference to about –20 mv. This has the effect of temporarily opening the Na + channel; the influx of these ions causes the membrane potential of the adjacent portion of the nerve to collapse, leading to an effect that is transmitted along the length of the nerve. As this pulse passes, K + and Na + pumps restore the nerve to its resting condition.
Summary
Make sure you thoroughly understand the following essential ideas which have been presented above. It is especially important that you know the precise meanings of all the highlighted terms in the context of this topic.
- Atmospheric oxygen is a strong oxidizing agent, but in the absence of a suitable catalyst this reaction is ordinarily too slow to be observable. In organisms that possess the appropriate enzymes, the reaction is sufficiently fast to control the availability of electrons to other redox systems.
- The pE is a useful index of electron availability, especially in natural waters and biological systems in which multiple redox systems are usually present. Although electrons tend to "fall" (in free energy) from sources to sinks, the outcome depends very strongly on the rates of the various reactions. This is quite different from proton-exchange (acid-base) reactions which are uniformly fast.
- Solubility products can often be measured by constructing a cell in which one of the electrodes involves the sparingly soluble salt, and the net cell equation corresponds to the solubility reaction.
- Potentiometric titrations are widely used to measure concentrations of species that are readily oxidized or reduced. The reaction must be fast and have a very large equilibrium constant. The equivalance point is detected by the rapid change in potential that occurs when control of the cell potential passes from the redox system of the analyte to that of the titrant.
- Measurement of pH is accomplished with an electrode consisting of a thin membrane of glass in which Na + ions are exchanged with H + .
- Membrane (Donnan) potentials arise when passage of an ion across a semipermeable membrane is selectively facilitated or inhibited. The classic example is a sodium proteinate solution in which the protein anion is too large to pass through the membrane. In organisms, ion-specific channels or "pumps" have a similar effect.
- Nerve conduction occurs not by a flow of charge through the nerve, but by a wave of depolarization resulting from the concerted action of active channels that govern the passage of ions (mainly K + and Na + ) across the membrane enclosing the nerve.


5.7: Grammar (2) Verbs Patterns
In this section, you will be able to:
- Identify the verb stem (root) and their patterns.
Verb Stems and Their Patterns
- In Arabic grammar, the verb stem, also known as the "root," is the basic form of a verb consisting of three consonants. These consonants convey the core meaning of the verb. Arabic verbs can be categorized into different forms or patterns based on the arrangement of vowels and additional consonants around the root.
- As a symbol to represent the three root letters of any word, Arabic grammar uses the roots of the prototypical verb فعل “to do.
- The verb stems are categorized into ten main forms, often referred to as "verb forms" or "patterns." Each form has a specific arrangement of vowels and affixes that are added to the root consonants. Here's a brief overview of the ten verb forms in Arabic.
Verbs Patterns in Present Tense
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Form I (ُيفعلُ):
- Basic three-consonant root.
- e.g., يكتبُ (kataba) - to write.
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Form II (يفعّلُ):
- Adds a shadda شدّة ( ّ ) between the second and third root consonants.
- e.g., يُدرَّسُ to teach.
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Form III (يفاعلُ):
- Adds an extra long vowel "ا" (alif mad) between the first and second root consonants.
- e.g., يمارس - to perform.
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Form IV (يُفْعَلُ):
- Adds extra consonant Alif with hamza "أ" to the first form. However, you do not see the Alif hamza (أ) in the present form, and you add الضمة to the Yaa of the prefix.
- e.g., يُخرجُ to evict.
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Form V (يتفعّلُ):
- Adds the prefix "ت" (taa) before the Form II pattern.
- e.g., يتذكَّرُ- to remember.
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Form VI (يتفاعلُ):
- Adds the prefix "ت" (taa) before the Form III pattern.
- e.g., تعامل (ta'amal) - to deal with each other.
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Form VII (ينفعلُ):
- Adds the prefix "انْـ (in) before the Form I pattern.
- e.g., ينكسرُ- to be broke.
- Form VIII (يفْتَعِلُ):
- Adds the prefix "ا" (ifta) to the Form I pattern and places sukun over the first radical. Then, add the letter تاء after the first radical.
- e.g., يستمعُ.
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Form IX (يفعَّلُ):
- Built on form 1 by placing a sukuun over its first radical, and adding a shadda to the last radical. Relates to colors
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Form X (يستفعلُ):
- Built on form 1 by adding the prefix سْتـ to the form 1 verb and inserting a ت between the first and second radicals; a sukuun must be placed over the first radical
Ending these verb forms is crucial for conjugating verbs in various tenses and moods in Arabic. Each form has its own set of rules for conjugation and usage.


3.3: A Look at Power
Consider the voting system \([10: 11, 3, 2]\). Notice that in this system, player 1 can reach quota without the support of any other player. When this happens, we say that player 1 is a dictator .
A player will be a dictator if their weight is equal to or greater than the quota. The dictator can also block any proposal from passing; the other players cannot reach quota without the dictator.
In the voting system \([8: 6, 3, 2]\), no player is a dictator. However, in this system, the quota can only be reached if player 1 is in support of the proposal; player 2 and 3 cannot reach quota without player 1’s support. In this case, player 1 is said to have veto power . Notice that player 1 is not a dictator, since player 1 would still need player 2 or 3’s support to reach quota.
A player has veto power if their support is necessary for the quota to be reached. It is possible for more than one player to have veto power, or for no player to have veto power.
With the system \([10: 7, 6, 2]\), player 3 is said to be a dummy , meaning they have no influence in the outcome. The only way the quota can be met is with the support of both players 1 and 2 (both of which would have veto power here); the vote of player 3 cannot affect the outcome.
A player is a dummy if their vote is never essential for a group to reach quota.
In the voting system \([16: 7, 6, 3, 3, 2]\), are any players dictators? Do any have veto power? Are any dummies?
Solution
No player can reach quota alone, so there are no dictators.
Without player 1, the rest of the players’ weights add to 14, which doesn’t reach quota, so player 1 has veto power. Likewise, without player 2, the rest of the players’ weights add to 15, which doesn’t reach quota, so player 2 also has veto power.
Since player 1 and 2 can reach quota with either player 3 or player 4’s support, neither player 3 or player 4 have veto power. However they cannot reach quota with player 5’s support alone, so player 5 has no influence on the outcome and is a dummy.
In the voting system \([q: 10, 5, 3]\), which players are dictators, have veto power, and are dummies if the quota is 10? 12? 16?
- Answer
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In the voting system \([q: 10, 5, 3]\), if the quota is 10, then player 1 is a dictator since they can reach quota without the support of the other players. This makes the other two players automatically dummies.
If the quota is 12, then player 1 is necessary to reach quota, so has veto power. Since at this point either player 2 or player 3 would allow player 1 to reach quota, neither player is a dummy, so they are regular players (not dictators, no veto power, and not a dummy).
If the quota is 16, then no two players alone can reach quota, so all three players have veto power.
To better define power, we need to introduce the idea of a coalition . A coalition is a group of players voting the same way. In the example above, \(\left\{P_{1}, P_{2}, P_{4}\right\}\) would represent the coalition of players 1, 2 and 4. This coalition has a combined weight of \(7+6+3 = 16\), which meets quota, so this would be a winning coalition.
A player is said to be critical in a coalition if them leaving the coalition would change it from a winning coalition to a losing coalition. In the coalition \(\left\{P_{1}, P_{2}, P_{4}\right\}\), every player is critical. In the coalition \(\left\{P_{3}, P_{4}, P_{5}\right\}\), no player is critical, since it wasn’t a winning coalition to begin with. In the coalition \(\left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right\}\), only players 1 and 2 are critical; any other player could leave the coalition and it would still meet quota.
A coalition is any group of players voting the same way.
A coalition is a winning coalition if the coalition has enough weight to meet quota.
A player is critical in a coalition if them leaving the coalition would change it from a winning coalition to a losing coalition.
In the Scottish Parliament in 2009 there were 5 political parties: 47 representatives for the Scottish National Party, 46 for the Labour Party, 17 for the Conservative Party, 16 for the Liberal Democrats, and 2 for the Scottish Green Party. Typically all representatives from a party vote as a block, so the parliament can be treated like the weighted voting system:
\([65: 47, 46, 17, 16, 2]\)
Solution
Consider the coalition \(\left\{P_{1}, P_{3}, P_{4}\right\}\). No two players alone could meet the quota, so all three players are critical in this coalition.
In the coalition \(\left\{P_{1}, P_{3}, P_{4}, P_{5}\right\}\), any player except \(P_1\) could leave the coalition and it would still meet quota, so only P 1 is critical in this coalition.
Notice that a player with veto power will be critical in every winning coalition, since removing their support would prevent a proposal from passing.
Likewise, a dummy will never be critical, since their support will never change a losing coalition to a winning one.
A player is a dictator if the single-player coalition containing them is a winning coalition.
A player has veto power if they are critical in every winning coalition.
A player is a dummy if they are not critical in any winning coalition.


25.4B: Chemical Buffer Systems
Chemical buffers, such as bicarbonate and ammonia, help keep the blood’s pH in the narrow range that is compatible with life.
- Distinguish between buffer solutions, ventilation, and renal function as buffer systems to control acid–base balance
Key Points
- The body’s acid– base balance is tightly regulated to keep the arterial blood pH between 7.38 and 7.42. Buffer solutions keep the pH constant in a wide variety of chemical actions.
- A buffer solution is a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid.
- The bicarbonate buffering system maintains optimal pH levels and regulates the carbon dioxide concentration that, in turn, shifts any acid–base imbalance.
- Renal physiology controls pH levels through several powerful mechanisms that excrete excess acid or base.
Key Terms
- bicarbonate : An alkaline, vital component of the pH buffering system of the human body that maintains acid–base homeostasis.
- buffer : A solution used to stabilize the pH (acidity) of a liquid.
- pH : In chemistry, a measure of the activity of the hydrogen ion concentration.
EXAMPLES
Anything that adversely affects an individual’s bloodstream will have a negative impact on that individual’s health since the blood acts as a chemical buffer solution to keep all the body’s cells and tissues properly balanced.
Acid–Base Homeostasis
Acid–base homeostasis concerns the proper balance between acids and bases; it is also called body pH. The body is very sensitive to its pH level, so strong mechanisms exist to maintain it. Outside an acceptable range of pH, proteins are denatured and digested, enzymes lose their ability to function, and death may occur.
Buffer Solution
A buffer solution is an aqueous solution of a weak acid and its conjugate base, or a weak base and its conjugate acid. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications.
Many life forms thrive only in a relatively small pH range, so they utilize a buffer solution to maintain a constant pH. One example of a buffer solution found in nature is blood. The body’s acid–base balance is normally tightly regulated, keeping the arterial blood pH between 7.38 and 7.42.
Several buffering agents that reversibly bind hydrogen ions and impede any change in pH exist. Extracellular buffers include bicarbonate and ammonia, whereas proteins and phosphates act as intracellular buffers.
The bicarbonate buffering system is especially key, as carbon dioxide (CO 2 ) can be shifted through carbonic acid (H 2 CO 3 ) to hydrogen ions and bicarbonate (HCO 3− ):
H2O+CO2⇋H2CO3⇋H++CO−3H2O+CO2⇋H2CO3⇋H++CO3−
Acid–base imbalances that overcome the buffer system can be compensated in the short term by changing the rate of ventilation. This alters the concentration of carbon dioxide in the blood and shifts the above reaction according to Le Chatelier’s principle, which in turn alters the pH.
Renal Physiology
The kidneys are slower to compensate, but renal physiology has several powerful mechanisms to control pH by the excretion of excess acid or base. In response to acidosis, the tubular cells reabsorb more bicarbonate from the tubular fluid, and the collecting duct cells secrete more hydrogen and generate more bicarbonate, and ammoniagenesis leads to an increase of the NH 3 buffer.
In its responses to alkalosis, the kidneys may excrete more bicarbonate by decreasing hydrogen ion secretion from the tubular epithelial cells, and lower the rates of glutamine metabolism and ammonium excretion.
pH range : Buffering agents keep blood pH between 7.38 and 7.42.


6.2: Module 23 Helix
Module 23 Helix
Learning Outcomes
When you have completed this module, you will be able to:
- Describe and apply the HELIX command to create solid models of springs, coils, and threads.
Helix
Coils, springs, and threads are constructed by drawing a profile and then using the SWEEP command, sweeping it along a path that is a helix drawn with the HELIX command. See Figure 23-1. The shape of the coil, spring or thread is controlled by the shape of the profile. See Figure 23-2, 23-3 and 23-4.
The HELIX command is used to construct a helix. A helix is constructed by specifying one or more setting that consist of the base radius, top radius, height, number of turns, turn height or twist direction.
If the same value for both the base radius and the top radius is specified, a cylindrical helix is created. If different values are specified for the top radius and the base radius, a conical helix is created. If a height value of zero is specified, a flat 2D spiral is created.
AutoCAD Command: HELIX
The HELIX command is used to create a helix.
Shortcut: none
Drafting Lesson: Springs and Threads
Study the Figure 23-5, shown below, to learn the terms used when drawing coil, springs and threads. Pitch is an important term that must be understood and is required when drawing a helix using the HELIX command. AutoCAD’s HELIX command uses the term turn height for the pitch.
Figure 23-6 shows four common thread types and their specifications.
WORK ALONG: Creating Coils
Step 1
Using the NEW command, start a new drawing using template: 3D Layout English .
Step 2
Save and name the drawing: AutoCAD 3D Workalong 23-1 . (Figure Step 2A and 2B)
Step 3
Set layer: Helix as the current layer, the current view to SE Isometric, the current UCS to Top, and the current visual style to 3D Wireframe.
Step 4
Enter the HELIX command, as shown below, to draw the coil shown in Figure Step 2A. (Figure Step 4)
Command: HELIX
Number of turns = 3.0000 Twist=CCW
Specify centre point of base: 0,0,0
Specify base radius or [Diameter] <0.5000>: @1,0,0
(I used coordinates to ensure that the helix start along the X axis.)
Specify top radius or [Diameter] <1.0000>: 1
(Diameter of the coil is 2 inches.)
Specify helix height or [Axis endpoint/Turns/turn Height/tWist] <4.0000>: H
Specify distance between turns <1.000>: 0.5
(The pitch is 0.5 inches.)
Specify helix height or [Axis endpoint/Turns/turn Height/tWist] <4.0000>: T
Enter number of turns <3.0000>: 8
(8 turns means that the coil is 4 inches long.)
Command:
Step 5
Change the current UCS to Front and set layer: Profile as the current layer. Draw a 0.25 diameter circle with its centre located at the end of the helix. (Figure Step 5)
Step 6
Set layer: Solid 8 as the current layer.
Step 7
Using what you learned in Module 22, create the coil by entering the SWEEP command. Select the circle as the profile and the helix as the path. (Figure Step 7)
Step 8
Turn layers: Helix and Profile off. Set the current visual style to Realistic. Your completed 3D solid coil should appear as shown in the figure. (Figure Step 8)
Step 9
Save and close the drawing.
WORK ALONG: Creating Square Threads
Step 1
Using the NEW command, start a new drawing using template: 3D Layout English .
Step 2
Save and name the drawing: AutoCAD 3D Workalong 23-2 . (Figure Step 2A and 2B)
Step 3
Set layer: Pline as the current layer, the current UCS to Right, the current view to SE Isometric, and the current visual style to 3D Wireframe.
Step 4
Draw a circle, with a diameter of 1 inch. Locate its centre at 0,0,0. (Figure Step 4)
Step 5
Set layer: Solid 8 as the current layer and extrude the circle 5 inches in the negative Z direction. (Figure Step 5)
Step 6
Change the layer of the solid, that you created in Step 5, to layer: Solid Off . Turn off layers: Solid off and Pline . Set layer: Helix as the current layer.
Step 7
Enter the HELIX command, as shown below, to draw a helix for the thread. (Figure Step 7)
Command: HELIX
Number of turns = 3.0000 Twist=CCW
Specify centre point of base: 0,0,0
Specify base radius or [Diameter] <1.0000>: @0,0.5,0
(This starts the helix at the top at the radius of 0.5 inches.)
Specify top radius or [Diameter] <0.5000>:
(Press Enter)
Specify helix height or [Axis endpoint/Turns/turn Height/tWist] <1.0000>: T
Enter number of turns <3.0000>: 20
(Since there are 4 turns per inch and the shaft is 5 inches long, there are 20 turns.)
Specify helix height or [Axis endpoint/Turns/turn Height/tWist] <1.0000>: A
Specify axis end point: @0,0,-5
(The end of the axis is 5 inches in the negative Z direction.)
Command:
Step 8
Set layer: Profile as the current layer and the current UCS to Front.
Step 9
Using the figures as a reference, draw a closed pline starting at the end of the helix. (Figure Step 9A, 9B, and 9C)
Step 10
Set layer: Solid 8 as the current layer. Using the SWEEP command, create the square thread by sweeping the profile along the helix. (Figure Step 10)
Step 11
Turn layers: Helix and Profile off. Change the solid on layer: Solid Off to layer: S olid 8 .
Step 12
Using the UNION command, union the two solids to form one solid model. (Figure Step 12)
Step 13
Turn layer: Pline on and set it as the current layer.
Step 14
Change the current UCS to Right. Draw a 2 Inch diameter circle with its centre located at 0,0,0. (Figure Step 14)
Step 15
Change the current view to Front . (Figure Step 15)
Step 16
Using the MOVE command, move the 2 inch diameter circle 0.125 inches in the negative Z direction. Using the SLICE command, as shown below, slice the solid model using the 2 inch diameter circle as the Object to create a plane at the slice location. (Figure Step 16)
Command: SLICE
Select objects to slice: 1 found
(Select the solid model.)
Select objects to slice:
(Press Enter.)
Specify start point of slicing plane or [planar Object/Surface/Zaxis/View/XY/YZ/ZX/3points]
<3points>: O
Select a circle, ellipse, arc, 2D-spline, 2D-polyline to define the slicing plane:
(Select the circle.)
Specify a point on desired side or [keep Both sides] <Both>:
(Press Enter.)
Command:
Step 17
Delete the end of the solid that you sliced off. (Figure Step 17)
Step 18
Move the circle 4 inches in the negative Z direction. Using what you learned in the last two steps, slice the solid and delete the portion you sliced off. Set the current view to SE Isometric. (Figure Step 18A, 18B, and 18C)
Step 19
Locate the UCS at the centre of the end of the solid thread. Draw a 0.75 inch diameter circle locating the centre at 0,0,0. On layer: Solid 8 , extrude the circle 0.5 inches in the positive Z direction. (Figure Step19)
Step 20
On layer: Pline , draw a 1.5 inch diameter circle locating its centre at the end of the extrusion that you created in Step 19. On layer: Solid 8 , extrude the circle 1 inch in the positive Z direction. (Figure Step 20A and 20B)
Step 21
Using what you just learned, orbit the model, relocate the UCS and extrude a 1 inch diameter circle 0.5 inches in the negative Z direction. (Figure Step 21A, 21B, and 21C)
Step 22
Chamfer the end of the shaft 0.125 inches at 45 degrees. (Figure Step 22)
Step 23
Fillet the two edges of the head of the bolt using the radius 0.0625.
Step 24
Change the current view to SE Isometric. Using the UNION command, union the four solids to create on solid model. Your completed model should appear as shown in the figure. (Figure Step 24)
Step 25
Save and close the drawing.
WORK ALONG: Using the HELIX Command – Part 3
Step 1
Using the NEW command, start a new drawing using template: 3D Layout English .
Step 2
Save and name the drawing: AutoCAD 3D Workalong 23-3 . (Figure Step 2A and 2B)
Step 3
Using what you learned in the last workalong and using Figure Step 2A as a reference, draw the solid model on layer: Solid 8 to match the figure. Ensure that you union the hexagon and cylinder to create one solid model. (Figure Step 3)
Step 4
Using what you learned in the last workalong, on layer: Helix , draw the helix using the figure as a reference. (Figure Step 4A and 4B)
Step 5
Change the layer of the solid that you drew in Step 3 to layer: Solid Off. Turn off layers: Solid off and Pline .
Step 6
Set layer: Construction as the current layer and the current UCS to Front. (Figure Step 6)
Step 7
On layer: Construction , draw the construction lines for the thread profile. (Figure Step 7A and 7B)
Step 8
On layer: Profile , snapping to the ends of the construction lines, draw the thread profile as a closed pline. (Figure Step 8)
Step 9
Turn layer: Construction off. (Figure Step 9A and 9B)
Step 10
Set layer: Solid 8 as the current layer and the current UCS to Top.
Step 11
Using the SWEEP command, sweep the profile using the helix as a path. (Figure Step 11)
Step 12
Turn layers: Helix and Profile off. Change the solid from layer: Solid Off to layer: Solid 8 .
Step 13
Using the SUBTRACT command, subtract the solid thread, that you created in the SWEEP command, from the solid model to create the bolt. (Figure Step 13)
Step 14
Using what you learned in the last workalong, on layer: Pline , draw 1.5 diameter circle locating its centre at the centre of the bottom of the bolt. (Figure Step 14)
Step 15
Set the current view to Front. Move the circle 0.0625 inches in the positive Z direction. (Figure Step 15)
Step 16
Slice the bolt and delete the end. (Figure Step 16)
Step 17
Draw a circle at the end of the threaded shaft and extrude it 0.0625 inches. (Figure Step 17)
Step 18
Union the two solids together and chamfer the end of the bolt using the dimensioned drawing as a reference. (Figure Step 18A and 18B)
Step 19
On layer: Solid 8 , anywhere in model space, draw the solid model of the nut to match the figure. Do not draw the hole in the centre. (Figure Step 19A and 19B)
Step 20
On layer: Center Line , draw a line on the centerline of the bolt and the nut. The length of the lines is not important. (Figure Step 20)
Step 21
Using the centerlines to snap to, copy the bolt exactly in the centre of the nut. The vertical location is not important as long as the nut is totally in the threaded area. (Figure Step 21)
Step 22
Using the SUBTRACT command, Subtract the bolt from the nut to leave the nut threaded. (Figure Step 22)
Step 23
Using the centerlines, copy the solid models to create an assembly solid model. After you assemble the two parts by snapping to the centerlines, with Ortho enabled, move the nut, by eye, to locate it vertically. Do not union the bolt and nut together. (Figure Step 23A and 23B)
Step 24
Save and close the drawing.
Key Principles
Key Principles in Module 23
- Coils, springs and threads are constructed by drawing a profile and then using the SWEEP command, sweeping it along a path that is a helix drawn with the HELIX command.
- A helix is constructed by specifying one or more setting that consist of the base radius, top radius, height, number of turns, turn height or twist direction.


9: Ocean Circulation
Learning Objectives
After reading this chapter you should:
- know the major ocean surface currents of the world (i.e. the gyres) and how they are created
- know the features of the Gulf Stream, including the formation of warm and cold core rings
- understand the causes and effects of the Ekman spiral
- understand geostrophic flow, and how it helps keep the gyres flowing even when wind dies down.
- understand why gyre currents are more intense on the western side of the oceans – i.e. western intensification
- know what causes upwelling and downwelling, and the impacts of these events on primary production
- know the locations of some of the major upwelling regions on Earth
- understand the causes and effects of ENSO events
- understand Langmuir cells
- understand the processes that drive thermohaline circulation
- understand how T-S diagrams work
- know the major global sites of deep water formation
- be familiar with the major global water masses
- understand how deep water circulates throughout the world ocean
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1.9: Precautions When Using Hazardous Materials
Although the corrosive action of chemicals can vary, the safety precautions required for each should be the same when they are handled. The following are some important points to consider when working with any cleaning products or chemicals in the workplace:
- Many substances are harmless enough by themselves, but when combined, they release toxic fumes. For example, two common household cleaning agents, ammonia and bleach, will produce toxic chlorine gas when mixed together.
- Do not mix any chemicals found on the job site unless you are absolutely certain that the combined mixture will not be harmful.
- Sometimes chemical changes are triggered by heat or radiation. For example, many oven cleaners produce fumes that are toxic when heated.
- All chemicals should be stored in their original containers and the containers should be labelled and sealed.
- If you do need to transfer a cleaning product into a smaller container for use, ensure it has the appropriate workplace label.
- Whenever there is the slightest risk of being splashed by these substances, wear safety glasses.
- Wear rubber gloves if your hands are likely to come in contact with a chemical.
- Rinse off and neutralize any spills on your personal clothing. If the spill is large, the clothing affected should be taken off to prevent any injury.
- Corrosive chemicals and flammable substances should be used only in well-ventilated areas. Avoid breathing the fumes.
- Many cleaners and some food products come in aerosol cans that use pressure to release their contents. These cans should not be kept near heat or exposed to flames, as the containers are explosive and the residual contents are often highly flammable. When the contents are finished, the empty cans must be recycled appropriately.


18.4: Entropy Changes Associated with State Changes
Phase Changes
When a system receives an amount of energy \(q\) at a constant temperature, \(T\), the entropy increase \(\Delta S\) is defined by the following equation. Hence, the magnitude of \(ΔS\) for a reversible process such as a phase change is calculated
\[ \Delta S = \dfrac{q_{rev}}{T}\]
with the temperature in Kelvin. Since entropy changes are much smaller than enthalpy changes, they are usually reported in J K
–1
mol
–1
.
Examples of reversible processes are
- Boiling: As temperature is constant, \[ΔS = \dfrac{ΔH_{vap}}{T} \label{boiling}\]
- Melting: As temperature is constant, \[ΔS = \dfrac{ΔH_{fus}}{T} \label{melting}\]
For many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings as a result of some process represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules undergoing reaction) to surroundings that are significantly more massive (the earth’s atmosphere). As a result, \(q_{surr}\) is a good approximation of \(q_{rev}\), and the second law may be stated as the following:
\[\begin{align} ΔS_\ce{univ}&=ΔS_\ce{sys}+ΔS_\ce{surr} \nonumber\\[4pt] &=ΔS_\ce{sys}+\dfrac{q_\ce{surr}}{T} \label{4} \end{align}\]
We may use this equation to predict the spontaneity of a process as illustrated in Example \(\PageIndex{1}\).
The entropy change for the process
\[\ce{H2O}(s)⟶\ce{H2O}(l) \nonumber\]
is 22.1 J/K and requires that the surroundings transfer 6.00 kJ of heat to the system. Is the process spontaneous at −10.00 °C? Is it spontaneous at +10.00 °C?
Solution
We can assess the spontaneity of the process by calculating the entropy change of the universe. If Δ S univ is positive, then the process is spontaneous. At both temperatures, \(ΔS_{sys} = 22.1\, J/K\) and \(q_{surr} = −6.00\, kJ\).
At −10.00 °C (263.15 K), the following is true:
\[\begin{align*} ΔS_\ce{univ} &=ΔS_\ce{sys}+ΔS_\ce{surr} \\[4pt] &=ΔS_\ce{sys}+\dfrac{q_\ce{surr}}{T} \\[4pt] &= 22.1\: J/K+\dfrac{−6.00×10^3\:J}{263.15\: K} \\[4pt] &=−0.7\: J/K \end{align*}\]
Since \(S_{univ} < 0\), melting is nonspontaneous ( not spontaneous) at −10.0 °C .
At 10.00 °C (283.15 K), the following is true:
\[\begin{align*} ΔS_\ce{univ} &=ΔS_\ce{sys}+\dfrac{q_\ce{surr}}{T} \\[4pt] &= 22.1\:J/K+\dfrac{−6.00×10^3\:J}{283.15\: K} \\[4pt] &=+0.9\: J/K \end{align*}\]
Since \(S_{univ} > 0\), melting of ice is spontaneous at 10.00 °C.
Using this information, determine if liquid water will spontaneously freeze at the same temperatures. What can you say about the values of S univ ?
Answer
Entropy is a state function, and freezing is the opposite of melting. At −10.00 °C spontaneous, +0.7 J/K; at +10.00 °C nonspontaneous, −0.9 J/K.
Ice Melting
Ice melting provides an example in which entropy increases in a small system, a thermodynamic system consisting of the surroundings (the warm room) and the entity of glass container, ice, water which has been allowed to reach thermodynamic equilibrium at the melting temperature of ice. In this system, some heat ( δQ ) from the warmer surroundings at 298 K (25 °C; 77 °F) transfers to the cooler system of ice and water at its constant temperature ( T ) of 273 K (0 °C; 32 °F), the melting temperature of ice. The entropy of the system, which is δQ/T , increases by δQ/273K . The heat δQ for this process is the energy required to change water from the solid state to the liquid state, and is called the enthalpy of fusion, i.e. ΔH for ice fusion.
It is important to realize that the entropy of the surrounding room decreases less than the entropy of the ice and water increases: the room temperature of 298 K is larger than 273 K and therefore the ratio, (entropy change), of δQ/298K for the surroundings is smaller than the ratio (entropy change), of δQ/273K for the ice and water system. This is always true in spontaneous events in a thermodynamic system and it shows the predictive importance of entropy: the final net entropy after such an event is always greater than was the initial entropy.
As the temperature of the cool water rises to that of the room and the room further cools imperceptibly, the sum of the δQ/T over the continuous range, “at many increments”, in the initially cool to finally warm water can be found by calculus. The entire miniature ‘universe’, i.e. this thermodynamic system, has increased in entropy. Energy has spontaneously become more dispersed and spread out in that ‘universe’ than when the glass of ice and water was introduced and became a 'system' within it.
Calculate entropy change when 36.0 g of ice melts at 273 K and 1 atm.
Solution
This is a directly application of Equation \ref{melting}, which requires the enthalpy of fusion for this reaction and the temperature is already given. If you look up the enthalpy of fusion for ice, you would get a molar enthalpy of 6.01 kJ/mol.
\[\Delta S = \left( \dfrac{6.01\, kJ\, mol^{-1}}{273\, K} \right) \nonumber\]
This is a molar value that needs to be scaled by the amount of the material (36 g). So a standard mass-to-moles conversion factor is needed (along with the molar mass of water - 18.01 g/mol).
\[\begin{align*} \Delta S &= \left( \dfrac{6.01\, kJ\, \bcancel{mol^{-1}}}{273\, K} \right) \left(\dfrac{36\, \cancel{g}}{18.01\, \cancel{g}\, \bcancel{mol^{-1}}}\right) \\[4pt] &= 0.044\, kJ / K \end{align*}\]


Learning Objectives
-
Analyze the reasons behind attending college and how personal motivations influence academic success.
-
Compare and contrast different student experiences in college based on cultural, socioeconomic, and personal backgrounds.
-
Evaluate the importance of college culture and expectations in shaping a successful college experience.
-
Identify and apply strategies for navigating social and academic challenges within a college environment.
-
Develop a personal definition of success in college by integrating self-awareness and goal-setting principles.
Figure 1.1
Student Survey
How do you feel about your ability to meet the expectations of college? These questions will help you determine how the chapter concepts relate to you right now. As we are introduced to new concepts and practices, it can be informative to reflect on how your understanding changes over time. We’ll revisit these questions at the end of the chapter to see whether your feelings have changed. Take this quick survey to figure it out, ranking questions on a scale of 1 – 4, 1 meaning “least like me” and 4 meaning “most like me.”
Don’t be concerned with the results. If your score is low, you will most likely gain even more from this book.
-
I am fully aware of the expectations of college and how to meet them.
-
I know why I am in college and have clear goals that I want to achieve.
-
Most of the time, I take responsibility for my learning new and challenging concepts.
-
I feel comfortable working with faculty, advisors, and classmates to accomplish my goals.
You can also take the
Chapter 1 survey(opens in new window)
anonymously online.
STUDENT PROFILE
“As students transitioning to college, responsibility is an inherent component of self-advocacy. As someone accepted on full funding to a 4-year university, but whose life’s circumstances disallowed attending college until years later, I used to dream of a stress-free college life. The reality is, college can be a meaningful place, but it can also be challenging and unpredictable. The key is to
be your own best advocate
, because no one else is obliged to advocate on your behalf.
“When I began my community college studies, I knew what I wanted to do. Cybersecurity was my passion, but I had no understanding of how credits transfer over to a 4-year university. This came to haunt me later, after I navigated the complex processes of transferring between two different colleges. Not everyone involved volunteers information. It is up to you, the student, to be the squeaky wheel so you can get the grease. Visit office hours, make appointments, and schedule meetings with stakeholders so that you are not just buried under the sheaf of papers on someone’s desk.”
—Mohammed Khalid
, University of Maryland
About this Chapter
In this chapter, you will learn about what you can do to get ready for college. By the time you complete this chapter, you should be able to do the following:
-
Recognize the purpose and value of college.
-
Describe the transitional experience of the first year of college.
-
Discuss how to handle college culture and expectations.
-
Identify resources in this text and on your campus for supporting your college success.
|
Reginald
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Madison
|
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Reginald has, after much thought and with a high level of family support, decided to enroll in college. It has been a dream in the making, as he was unable to attend immediately after high school graduation.  Because it has been almost a decade since he sat in a classroom, he is worried about how he will fit in as an adult learner returning to college. Will his classmates think he is too old? Will his professors think he is not ready for the challenges of college work? Will his family get tired of his long nights at the library and his new priorities? There is so much Reginald is unsure of, yet he knows it’s a step in the right direction.
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It has been only three months since Madison graduated from high school. She graduated in the top 10 percent of her class, and she earned college credit while in high school. She feels academically prepared, and she has a good sense of what degree she wants to earn. Since Madison was 5 years old, she’s wanted to be an engineer because she loved building things in the backyard with her father’s tools. He always encouraged her to follow her dreams, and her whole family has been supportive of her hobbies and interests. However, Madison is concerned that her choice of major will keep her from dance, creative writing, and other passions. Furthermore, Madison is heading to a distant college with no other people she knows. Will she be able to find new friends quickly? Will her engineering classes crush her or motivate her to complete college? Will she be able to explore other interests? Madison has a lot on her mind, but she aims to face these challenges head-on.
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While Reginald and Madison have had different experiences before and certainly have different motivations for enrolling in college, they have quite a bit in common. They are both committed to this new chapter in their lives, and they are both connected to their families in ways that can influence their commitment to this pursuit. What they don’t know just yet—because they haven’t started their classes—is that they will have even more in common as they move through each term, focus on a major, and plan for life after graduation. And they have a lot in common with you as well because you are in a similar position—starting the next chapter of the rest of your life.
In this chapter, you will first learn more about identifying the reason you are in college. This is an important first step because knowing your
why
will keep you motivated. Next, the chapter will cover the transitions that you may experience as a new college student. Then, the chapter will focus on how you can acclimate to the culture and meeting the expectations—all of which will make the transition to a full-fledged college student easier. Finally, the chapter will provide you with strategies for overcoming the challenges that you may face by providing information about how to find and access resources.