11.4: Atmospheric methane
Total global \(CH_4\) emissions are approximately 550 teragrams (Tg) of \(CH_4\) per year (1 Tg \(CH_4\) per year = 1012 grams of \(CH_4\) per year; Saunois et al., 2016). Of this, roughly 40% comes from natural sources. The largest (and most uncertain) natural emissions of \(CH_4\) are from wetlands, defined as regions that are permanently or seasonally waterlogged. Natural wetlands include high-latitude bogs and fens, tropical swamps, and temperate wetlands. Saturated soils in warm tropical environments tend to produce the most \(CH_4\). However, warming Arctic temperatures raise concerns of increasing emissions from high-latitude wetlands and future decomposition of carbon currently stored in frozen Arctic soils (e.g., Schaefer et al., 2011; Schuur et al., 2015). Figure \(\PageIndex{1}\), provides a pictorial representation of the main components of the global methane cycle.
Estimates of global \(CH_4\) emissions from wetlands range from 127 to 227 Tg \(CH_4\) per year (Saunois et al., 2016), with most probable values between 167 and 185 Tg \(CH_4\) per year. Most emissions occur in tropical regions (Matthews 1989; Melton et al., 2013; Saunois et al., 2016). Currently, only about 25 Tg \(CH_4\) per year (i.e., 4% of global emissions) are thought to be emitted from high northern latitudes (AMAP 2015; Saunois et al., 2016). Because emissions are sensitive to temperature and precipitation they exhibit significant seasonal cycles, especially at high latitudes, as well as interannual variability caused by moisture and temperature variability. Smaller amounts of CH4 are emitted from fires, the ocean, and enteric fermentation in termites and wild animals (20 Tg CH4 per year or less for each). In addition, up to 60 Tg CH4 per year may be emitted from geological sources, such as seeps, clathrates, mud volcanoes, and geothermal systems (Etiope et al., 2008; Schwietzke et al., 2016).
Table \(\PageIndex{1}\): Historic a and Decadal b Global Mean Emissions and Their Partitioning to the Carbon Reservoirs of Atmosphere, Ocean, and Land 1750–2011 Cumulative Pg Cc 1980–1989 Pg C per Year 1990–1999 Pg C per Year 2000–2009 Pg C per Year 2007–201
| 1750–2011 Cumulative Pg Cc | 1980–1989 Pg C per Year | 1990–1999 Pg C per Year | 2000–2009 Pg C per Year | 2007–2016 Pg C per Year | 2016 Pg C per Year | |
|---|---|---|---|---|---|---|
| Emissions | ||||||
| Fossil Fuels and Industry | 375 ± 30 | 5.5 ± 0.3 | 6.3 ± 0.3 | 7.8 ± 0.4 | 9.4 ± 0.5 | 9.9 ± 0.5 |
| Land-Use Change | 180 ± 80 | 1.2 ± 0.7 | 1.3 ± 0.7 | 1.2 ± 0.7 | 1.3 ± 0.7 | 1.3 ± 0.7 |
| Partitioning to Carbon Reservoir | ||||||
| Partitioning to Carbon Reservoir | 240 ± 10 | 3.4 ± 0.1 | 3.1 ± 0.1 4 | 4.0 ± 0.1 | 4.7 ± 0.1 | 6.0 ± 0.2 |
| Ocean Uptake | 160 ± 80 | 1.7 ± 0.5 | 1.9 ± 0.5 | 2.1 ± 0.5 2 | 2.4 ± 0.5 | 2.6 ± 0.5 |
| Land Uptake | 155 ± 30 | 2.0 ± 0.6 | 2.5 ± 0.5 | 2.9 ± 0.8 3.0 | 3.0 ± 0.8 | 2.7 ± 0.9 |
|
Unlike CO2, CH4 has an atmospheric chemical sink that nearly balances total global emissions. Removal of atmospheric CH4 by reaction with the hydroxyl radical (OH) results in a CH4 atmospheric lifetime of about 9 to 10 years. Observationally constrained estimates of CH4 lifetime suggest either small decreases of about 2% from 1980 to 2005 (Holmes et al., 2013) or stable CH4 lifetimes with the possibility of interannual variability of about 2% (Montzka et al., 2011). CH4 is a much more powerful greenhouse gas than CO2 (on a per mass basis and over 100 years, CH4 is about 25 times more effective at trapping heat than CO2).
As shown in Figure \(\PageIndex{2}\)b, this page, atmospheric CH4 increased rapidly during the 1980s and early 1990s before its growth leveled off between the mid-1990s and early 2000s. Methane has resumed its increase in the atmosphere since 2006, and observations show that this growth has even accelerated since 2014. The changing atmospheric CH4 growth rate has been the subject of much debate, questioning why growth rate slowed for a decade starting in the mid-1990s. Several studies suggested that this slower rate was due to decreases in fugitive emissions from fossil fuel production (Aydin et al., 2011; Simpson et al., 2012) or to decreased emissions from anthropogenic microbial sources, such as rice agriculture (Kai et al., 2011). On the other hand, Dlugokencky et al. (1998, 2003) proposed that the slowing of CH4 growth in the atmosphere was due to an approach to a quasi–steady state, reached when global sources and sinks are in balance. Consistent with this view, the study of Schwietzke et al. (2016) found that emissions from oil and gas production have remained stable over the past several decades, implying increasing efficiency in fossil fuel production industries while their production was increasing over time.
Dlugokencky et al. (2003) predicted that CH4 would approach a steady state in the atmosphere of about 1,780 ppb by the 2010s if there were no major changes in its budget. The methane budget did change, however, because the atmospheric growth of CH4 resumed its rise in 2006. The cause of the recent increase in CH4 growth also has been much debated. Based on global observations of the CH4 isotope, 13CH4, the global growth in CH4 appears likely to have been dominated by microbial sources in the tropics (wetlands or agriculture and waste), rather than fossil fuel production (Nisbet et al., 2016; Schaefer et al., 2016), as suggested by some studies (e.g., Rice et al., 2016). Other studies have argued that 13CH4 may not be a very strong constraint on the global methane budget and that changes in the atmospheric CH4 chemical sink are responsible for the global methane changes (Rigby et al., 2017; Turner et al., 2017). However, plausible chemical mechanisms that could explain the changes in the CH4 sink have not been identified. Using space-based retrievals of carbon monoxide, Worden et al. (2017) argued that the isotopic data record also can be consistent with increased fossil fuel emissions if global biomass-burning emissions have decreased twice as much as estimates based on space-based observations of burned areas. If the recent rise of global atmospheric CH4 is indeed due to increases in microbial emissions, then the question becomes whether anthropogenic or natural microbial sources are responsible. Some studies have suggested that anthropogenic microbial sources, such as livestock, are behind the increased atmospheric growth of CH4 (Schaefer et al., 2016; Saunois et al., 2016). If the increase is due to emissions from wetlands, especially in the tropics, then this raises the possibility that changing climate could be changing natural emissions.
Methane Perturbations in the Global Carbon Cycle
The carbon cycle undergoes perturbations caused by a variety of natural processes such as wildfires, droughts, insect infestations, and disease. These processes can themselves be affected by human activities, for example through GHG emissions that change climate, wildfire suppression, and land-use change. During longer periods, variations in the Earth’s orbit also drive significant perturbations to the global carbon cycle. Over the recent several centuries, human activity has resulted in perturbations to the carbon cycle that have no precedent in geological records. Anthropogenic emissions also can directly alter the chemistry of the atmosphere, possibly affecting its ability to remove pollutants.
Atmospheric CH4 also is influenced by diverse human activities, ranging from food production (e.g., ruminants and rice) to waste (e.g., sewage and landfills) to fossil fuel production (e.g., coal, oil, and gas). Future increases in population likely will increase CH4 emissions from agriculture and waste as demand rises for more food production. Furthermore, the current boom in shale oil and gas exploitation has focused attention on leakage from drilling, storage, and transport of fossil fuel (e.g., Peischl et al., 2015; Pétron et al., 2014). Chemical reaction with OH accounts for about 90% of the total CH4 sink (Ehhalt 1974). These OH radicals, produced through the photolysis of ozone (O3) in the presence of water vapor, are destroyed by reactions with CH4 and other compounds. Uncertainty in the sink due to chemical loss by OH is 10% to 20%, because the OH distribution remains uncertain at regional to global scales (Saunois et al., 2016).
Current estimates reported by Saunois et al. (2016) for anthropogenic emissions average 328 Tg CH4 per year (ranging from 259 to 370 Tg CH4 per year). Extraction and processing of fossil fuels account for 32% to 34% of all anthropogenic emissions. Livestock, agriculture, landfills, and sewage together account for another 55% to 57%, with the remainder due to biomass and biofuel burning. A recent study using observations of the isotopic composition of CH4 suggests that emissions from fossil fuel production and geological emissions may be 20% to 60% higher than previously thought. This increase would require a compensating reduction in microbial emissions from natural and anthropogenic sources (Schwietzke et al., 2016) for the atmosphere to be in balance with the observed global average CH4 abundance. Current CH4 levels are unprecedented in over at least 800,000 years (Loulergue et al., 2008). Recent National Oceanic and Atmospheric Administration atmospheric network observations have shown that global CH4 increased rapidly through the late 1990s, leveled off during the early 2000s, and began to increase again in 2007 (Dlugokencky et al., 2009; Rigby et al., 2008). These changes in global CH4 are not well understood and are under debate. Although Dlugokencky et al. (1998, 2003) suggested that the plateau in CH4 growth resulted from an approximate balance between global sources and sinks, some studies suggested that decreases in anthropogenic emissions (Aydin et al., 2011; Kai et al., 2011; Simpson et al., 2012) led to the period of slow CH4 growth. Isotopic evidence points toward increased emissions from microbial sources as an explanation for the recent rise in global CH4 (Nisbet et al., 2016; Schaefer et al., 2016; Schwietzke et al., 2016). However, increases in anthropogenic emissions also have been proposed (Rice et al., 2016), as well as decreases in the chemical loss (Rigby et al., 2017; Turner et al., 2017). Worden et al. (2017) have recently suggested a significant role for fossil fuel emissions in the recent growth of atmospheric CH4 based on decreases in biomass burning that could change the interpretation of methane isotope observations. This result is based on space-based observations of atmospheric CO, which itself may be responding to changes in other sources besides biomass burning. Figure 1.1, p. 45, shows that CH4 contributed just over 0.5 W/m2 in 2017 to global total anthropogenic radiative forcing, an amount which is about one-fourth of that from CO2. Although CH4 is much more effective at absorbing infrared radiation (Hofmann et al., 2006; Myhre et al., 2013),3 it is about a hundred times less abundant in the atmosphere than CO2.
Future Changes in Atmospheric Methane
Coupled carbon cycle–climate models forced with future “business as usual” emissions scenarios suggest that the changing carbon cycle will be a net positive feedback on climate, reinforcing warming, but the size of the projected feedback is highly uncertain (Friedlingstein et al., 2014). Besides the uncertain trajectories of human factors such as fossil fuel emissions, land use, or significant mitigation efforts, various natural processes can lead to the carbon cycle being a positive feedback. For example, a warming climate can lead to increased fires and droughts and less storage of carbon in the terrestrial biosphere. In particular, warming is expected to decrease carbon uptake in the tropics and midlatitudes. In the high latitudes, a warmer climate is expected to lead to a more productive biosphere and more uptake but also may result in increased respiration and release of stored CO2 and CH4 in soils and lakes. Negative feedbacks also are possible, such as increased atmospheric CO2, leading to increased carbon storage in the terrestrial biosphere (e.g., Schimel et al., 2015), although the relative roles of this effect relative to land-use change, nitrogen deposition, and temperature increases on the cumulative land carbon sink over the last century are not fully understood (Huntzinger et al., 2017). Human impacts on land use can directly impact climate. Deforestation and agriculture can affect carbon storage in soil and biomass. Fertilizer use also affects the global nitrogen budget and can increase carbon storage. Large-scale drainage of wetlands and conversion to agricultural land can reduce CH4 emissions from anaerobic respiration while potentially increasing faster soil carbon loss through aerobic respiration.
Frozen Arctic soils compose another potential carbon cycle–climate feedback (see Ch. 11: Arctic and Boreal Carbon, p. 428, and Ch. 19: Future of the North American Carbon Cycle, p. 760). An estimated 1,460 to 1,600 Pg C are frozen in Arctic soils, and warming has proceeded in the Arctic faster than in any other region. Current understanding suggests that approximately 146 to 160 Pg C, primarily as CO2, could be vulnerable to thaw and release to the atmosphere over the next century (Schuur et al., 2015; see Ch. 11: Arctic and Boreal Carbon). This release of carbon from permafrost is likely to be gradual and occur on century timescales (Schuur et al., 2015). If the amount of carbon estimated to enter the atmosphere by Schuur et al. (2015) were released annually at a constant rate, emissions would be far lower than annual fossil fuel emissions (about 9 Pg C per year) but comparable to land-use change (0.9 Pg C per year).
References
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Excerpted from
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15.21B: Poliomyelitis
- Describe poliomyelitis and its effect on motor neurons
OVERVIEW
Poliomyelitis, often called polio or infantile paralysis, is an acute, viral, infectious disease spread from person to person, primarily via the fecal-oral route.
Although approximately 90% of polio infections cause no symptoms at all, affected individuals can exhibit a range of symptoms if the virus enters the blood stream. In about 1% of cases, the virus enters the central nervous system, preferentially infecting and destroying motor neurons, leading to muscle weakness and acute flaccid paralysis.
Different types of paralysis may occur, depending on the nerves involved. Spinal polio is the most common form, characterized by asymmetric paralysis that most often involves the legs. Bulbar polio leads to weakness of muscles innervated by cranial nerves. Bulbospinal polio is a combination of bulbar and spinal paralysis.
BACKGROUND
Poliomyelitis was first recognized as a distinct condition by Jakob Heine in 1840. Its causative agent, poliovirus, was identified in 1908 by Karl Landsteiner. Although major polio epidemics were unknown before the late 19 th century, polio was one of the most dreaded childhood diseases of the 20 th century. Polio epidemics have crippled thousands of people, mostly young children; the disease has caused paralysis and death for much of human history.
Polio had existed for thousands of years quietly as an endemic pathogen until the 1880s, when major epidemics began to occur in Europe; soon after, widespread epidemics appeared in the United States. By 1910, much of the world experienced a dramatic increase in polio cases and epidemics became regular events, primarily in cities during the summer months. These epidemics—which left thousands of children and adults paralyzed—provided the impetus for a “Great Race” towards the development of a vaccine.
DEVELOPMENT OF A VACCINE
Developed in the 1950s, polio vaccines are credited with reducing the global number of polio cases per year from many hundreds of thousands to today under a thousand. Enhanced vaccination efforts led by the World Health Organization, UNICEF, and Rotary International could result in global eradication of the disease.
Key Points
- Spinal polio is the most common type of polio and results in asymmetric paralysis, usually involving the legs.
- Bulbar polio is infection of the cranial nerves and causes weakness and paralysis in muscles innervated by the cranial nerves, while bulbospinal polio occurs when both the cranial nerves and spinal nerves are affected.
- Although approximately 90% of polio infections cause no symptoms at all, affected individuals can exhibit a range of symptoms if the virus enters the blood stream.
Key Terms
- motor neuron : A neuron located in the central nervous system that projects its axon outside the CNS and directly or indirectly control muscles.
- spinal polio : Spinal polio is characterized by asymmetric paralysis that most often involves the legs.
- poliomyelitis : acute infection by the poliovirus, especially of the motor neurons in the spinal cord and brainstem, leading to muscle weakness, paralysis and sometimes deformity
- paralysis : The complete loss of voluntary control of part of person’s body, such as one or more limbs.


34.7: Practice Exercises
Serialism: Day One
1.
Given the prime form of the twelve-tone row in pitch integers, write the specified row forms in the staves below.
-
P1
-
R4
-
I8
-
RI10
Answer.
2.
Given the prime form of a twelve-tone row, label the row forms and transpositions of the permutations given on the staves below.
-
Row form:
-
Row form:
-
Row form:
Answer.
Serialism: Day Two
3.
Construct a 12 by 12 matrix for the prime form of the following twelve-tone row, given in pitch integers: 3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9. Include labels for all row forms including all transposition levels (P0, R3, I8, RI6, etc.). Use note names in the matrix , not integers.
| I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | I↓ | ||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| P→ | ←R | ||||||||||||
| ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI | ↑RI |
Answer.
4.
For the following excerpt, determine P5 and identify each row form and statement. This example contains overlap.
Answer.
5.
Referring to the twelve-tone row used to construct the matrix in the practice exercise above (3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9), find the normal form and prime form for each discrete three-note set from the row, and provide an interval vector for each.
- Set 1: 3, 7, 11. Normal form: Prime form: Interval vector:
- Set 2: 1, 5, 0. Normal form: Prime form: Interval vector:
- Set 3: 2, 10, 6. Normal form: Prime form: Interval vector:
- Set 4: 4, 8, 9. Normal form: Prime form: Interval vector:
Answer.
Click here to download the first homework assignment for this chapter. Click here to download the second homework assignment for this chapter.


3.3: Precious Materials, Spolia, and Borrowed Glory
Objects made for sacred or royal use were often wrought of such lavish and treasured components as vellum, silk, linen, wool, ivory, gold, silver, gems, and rare stones and minerals. Frequently crafted for further refinement, such works show their precious properties to advantage. In ancient Rome/Byzantium, there were quarries for porphyry, a rich purple marble stone (the basis for the association of the color purple with royalty). Because it was restricted to royal purposes, its very appearance carried connotations of the imperial significance of any work made from it. It was often used for columns and other architectural components that thereby accentuated important structures or parts of them. Once the imperially controlled mines were abandoned in the fifth century CE, new items could not be made of porphyry, so older monuments were sometimes pillaged and re-used, with the royal significance transferred to the plunderers, implying not only the replacement of the old order by the new, but also the superiority of the conquerors.
Porphyry burial containers were especially prized in antiquity and the Middle Ages. Constantina was the eldest daughter of Emperor Constantine the Great (r. 306-337 CE), the Roman ruler who in 313 CE decreed early Christians could practice their faith without persecution and confiscated land should be returned to the Church. Although Constantine considered himself a Christian, he did not abandon the Roman gods and religious rituals. For example, in 321 CE he stated that Christians and pagans alike should observe the day of the sun (later named Sunday); the cult of the sun god had been popularly observed in Roman culture for centuries, and associations of the sun as the source of light, warmth, and life had been adopted by those of the Christian faith. Constantine, according to legend, was baptized a Christian on his deathbed in 337 CE.
When his daughter Constantina died in 354 CE, she was entombed in a porphyry sarcophagus , or stone coffin, that was richly carved with motifs from both the pagan Roman and Christian faiths. (Figure 3.12) There are small, winged cupids gathering grapes among garlands of grape vines with peacocks and a ram below on the front and back of the coffin, and cupids treading on grapes on both ends. In Roman mythology, such scenes were associated with Bacchus (known to the Greeks as Dionysus), the god of the wine harvest and wine making who as a baby was reborn after having been slaughtered by the Titans. Interpreted as Christian motifs, the cupids, who became known as putti or small, winged angels, are seen as preparing the grapes for the Eucharist , the sacrament commemorating the Last Supper by consecration of the bread and wine as the Body and Blood of Jesus Christ. Such re-imaging and re-purposing of motifs and their meanings were frequently seen at this time of transition from paganism to Christianity; further, having been adopted by Constantine and his family, they were associated with imperial power and carried connotations of the Christian conquest of paganism.
Figure 3.12 | Sarcophagus of Constantina. Author: User “Jean-Pol GRANDMONT” Source: Wikimedia Commons License: CC BY-SA 3.0
Figure 3.13 | Aachen, Palace Chapel of Charlemagne. c. 800. Author: User “Velvet” Source: Wikimedia Commons License: CC BY-SA 3.0
Later, in the eighth and ninth centuries CE, Charlemagne (r. 768-814 CE) used pillaged porphyry columns inside arches on the upper level of his imperial chapel, a building intended for his own entombment. (Figure 3.13) The Palatine Chapel (c. 796-798 CE, consecrated 805 CE) was part of the palace complex Charlemagne had built at Aachen, in what is now Germany. The interior of the chapel is an octagon topped by a dome supported by heavy piers with arches on the second level, where the imperial throne is located, with a view to the high altar (the table or other surface where religious rituals are carried out) located across the church on the first floor below. (Figure 3.14) The design of the building is modeled on mausolea , or buildings containing tombs, and churches from the late Roman, early Christian, and early Byzantine periods (fourth-seventh centuries), such as San Vitale (526-647 CE) in Ravenna, Italy. (Figure 3.15) Charlemagne, who was not only King of the Franks and King of the Lombards but was also crowned as the first Holy Roman Emperor in 800 CE, used that design and the plundered columns to signify the revival and replacement of the old Roman Empire with his own reign as a Christian world ruler.
Figure 3.14 | Cross-sections of the Palace Chapel of Aachen. Author: User “Sir Gawain” Source: Wikimedia Commons License: Public Domain
Figure 3.15 | San Vitale, Ravenna. Author: User “Väsk” Source: Wikimedia Commons License: Public Domain
Among others, Holy Roman Emperor Henry (or Heinrich) II (r. 973-1024) similarly borrowed and supplanted Charlemagne’s glory by adopting his palace complex at Aachen and adding to its structure and furnishings with his own statements of imperial power. Henry II commissioned a lavish pulpit for the chapel that was completed in 1014. (Figure 3.16) The semi-circular pulpit has a smaller semi-circle to either side, a shape known as a trefoil . The center is made up of nine rectangular panels covered with chased gilt copper that has been formed by hammering into low relief images of the Four Evangelists. The panels are adorned with gemstones and embellished with enamel , powdered glass fused to the surface by heat, and filigree , beads or threads of gold or silver arranged in designs on a metal surface. The three ivory panels on each of the smaller semi-circles depict pagan mythological figures; the panels were made in Egypt in the sixth century CE. Re-used parts such as the porphyry columns, gemstones, and ivory panels are known as spolia , remnants that had been taken from older art and architecture and incorporated into new art objects and places with the implications of conquest, superiority, and heritage for the new patrons.
Figure 3.16 | Ambon (11thcentury) of Henry II, Holy Roman Emperor. Aachen Cathedral, Germany. Author: User “HOWI” Source: Wikimedia Commons License: CC BY-SA 3.0
Figure 3.17 | The Barbarossa chandelier. Author: User “Lokilech” Source: Wikimedia Commons License: CC BY-SA 3.0
Figure 3.18 | Shrine of Charlemagne, Interior of palatine chapel in Aachen Cathedral, Germany. Author: User “ACBahn” Source: Wikimedia Commons License: CC BY-SA 3.0
Figure 3.19 | Shrine of Charlemagne. Author: User “HOWI” Source: Wikimedia Commons License: CC BY-SA 3.0
Figure 3.20 | Cross of Lothair Author: CEphoto, Uwe Aranas Source: Wikimedia Commons License: CC BY-SA 3.0
Another, later Holy Roman Emperor, Frederick I (r. 11551190), and his wife, Beatrice, commissioned a chandelier to hang below the octagonal dome in the chapel. (Figure 3.17) This was called the Barbarossa chandelier, reflecting the emperor’s nickname after his red beard; it was installed between 1165 and 1170 in honor of the Virgin Mary and as a tribute to Charlemagne. The chandelier’s forty-eight candles cast a tremendous spread of light in an age when artificial illumination was costly, emphasizing its association with earthly wealth and heavenly light.
As a continuation of the work undertaken by his grandfather Frederick I, which also included exhuming Charlemagne’s bones, Frederick II (r. 1220-1250), following the plans Barbarossa had made, completed the creation of a lavish, new jeweled and gilded shrine for the remains of Charlemagne, seeking to elevate him to the rank of sainthood. These statements in rich material forms, imply the surpassing glory of their imperial predecessor, shared by those who followed in his lineage. Moreover, the associations of royalty and honor for earthly rulers was often intertwined in very pointed ways to artwork associated with the Christian God and saints. Notable in this regard
Figure 3.22 | Screen of Charlemagne. Artist: Piersac. Source: www.medart.pitt.edu License: Public Domain
Figure 3.21 | Augustus cameo. Author: User “Absalypson2” Source: Wikimedia Commons License: CC BY-SA 3.0
is the shrine for Charlemagne—clearly a statement of imperial power—made of rich materials that reflect popular Christian notions of the Heavenly Jerusalem, where these saintly rulers were thought to act as intercessors for the believer. (Figures 3.18 and 3.19) Often such imperial works actually featured objects or significant decorative details from imperial Roman works, such as the antique cameo of the Roman Emperor Augustus that was applied to the Cross of the Emperor Lothair II . (Figures 3.20 and 3.21) The gilded cross, dated to c. 1000, is covered with 102 gemstones and thirty-two pearls
and has a rock crystal seal near its base bearing a portrait of Lothair II (r. 835-869). Including the portraits of earlier emperors further emphasized the wealth
and power of the ruler who had it made, believed to be Otto III (r. 983-1002). In addition, gemstones on such devotional works were selected for their qualities associated with healing, good fortune, the ability to ward off evil, and their mystical translucence, that fostered spiritual illumination.


15.1: Why It Matters- Customer Service Strategies
Why learn about customer service strategies?
In this module you’ll learn why customer service strategies are an integral part of making all aspects of retail operations successful. In fact, customer service is arguably the most important aspect of retail.
Walmart founder Sam Walton himself once said, “There is only one boss. The customer. And he can fire everybody in the company from the chairman on down, simply by spending his money somewhere else.”
Walton’s understanding of the importance of developing long-term, mutually beneficial relationships with customers by using critical strategies like profiling customer characteristics and excelling at service was critical in amassing millions of loyal shoppers over the past four decades. (Source: Entrepreneur – Sam Walton: Bargain Basement Billionaire .)
Contributors and Attributions
- Why It Matters: Customer Service Strategies. Authored by : Wade Hyde. Provided by : Lumen Learning. License : CC BY: Attribution
- Diverse people with shopping bags. Authored by : rawpixel.com. Provided by : rawpixel.com. Located at : https://pxhere.com/en/photo/1448533 . License : CC0: No Rights Reserved


7: Work Motivation for Performance
Learning Outcomes
After reading this chapter, you should be able to answer these questions:
- Define motivation, and distinguish the direction and intensity of motivation.
- Describe a content theory of motivation, and compare and contrast the main content theories of motivation: manifest needs theory, learned needs theory, Maslow’s hierarchy of needs, Alderfer’s ERG theory, Herzberg’s motivator-hygiene theory, and self-determination theory.
- Describe the process theories of motivation, and compare and contrast the main process theories of motivation: operant conditioning theory, equity theory, goal theory, and expectancy theory.
- Describe the modern advancements in the study of human motivation.


9: Putting It All Together
Distillation Science (a blend of Chemistry and Chemical Engineering)
This is Part IX, Putting It All Together of a ten-part series of technical articles on Distillation Science, as is currently practiced on an industrial level. See also Part I, Overview for introductory comments, the scope of the article series, and nomenclature.
Part IX, Putting It All Together uses the information from Parts III through VII , showing how to combine them in a practical example for bulk separation; and how using the techniques detailed in previous articles give answers that differ from the ideals of basic Raoult/Dalton Law application.
See previous articles per the following detail:
- Part III for critical properties and acentric factor, especially Table 3-3
- Part IV for the recommended vapor pressure equation, especially Equation 4-3 and Table 4-1
- Part V for Equation of State, especially Equations 5-3 and 5-4
- Part VI, especially Equation 6-4 for partial pressure and Equations 6-7 and 6-8 for fugacity coefficients
- Part VII for Liquid Activity Coefficients, especially Equation 7-3
In this article a practical distillation example is developed, showing the Y/X relationship with temperature for the DCS-TCS binary system with pressure is held constant at 11.0 atmospheres, and showing the results as a T XY /P plot as well as in tabular form. From such data, a distillation column designer would consider the best arrangement for column feed, “tops” and “bottoms” recovery, tray count and external reflux ratio ( and from that, the energy required for the reboiler and condenser, as well as hydraulic loading per unit mass flow of feedstock). Two variations of this example are worked-up, showing the application of distillation science: one which only uses ideal Raoult/Dalton, and one that uses the full set of ideality departure coefficients. Table output and plots below are done using MS Excel. Then at the end of the article, the table results are graphically demonstrated using a McCabe-Theile plot to step off the trays for an appropriate reflux rate and show the best feed tray.
The table of Figure 9-1 is set up to cover the range of DCS liquid mole fraction from unity to zero, in increments of 0.05 mole fraction, with 0.01/0.99 mole fraction added to illustrate asymptotic effects. For each non-zero table row, a temperature is first assumed, and then the vapor mole fractions calculated per Raoult/Dalton, with p=11.0 atmospheres; then that row’s temperature is iteratively adjusted until the total pressure = 11.0 atmospheres.
In the plot of Figure 9-1 shows the calculation results in T XY /P form, with the value of X DCS =1.0 representing the tightest possible “tops” product at the distillation column condenser; and a value of X DCS =0.0 representing the tightest possible “bottoms” product at column reboiler, all at a total reflux condition. For a finite column, the mole fraction of the “tops” product would be a cropping of the upper X DCS values of the T XY /P curves; and the mole fraction of the “bottoms” product a would be a cropping of the lesser X DCS values of the T XY /P curves. In such instance, the column feed tray would be identified as that point in the column where the tray temperature is identical to the feed mixture’s boiling point. The accompanying plot of solution shows what the T XY /P curves would look like, for such a Raoult/Dalton solution to the DCS-TCS binary at 11.0 atmospheres.
\( Y_{1}=(X_{1} \times VP_{1})/(X_{1} \times VP_{1} + X_{2} \times VP_{2}) \nonumber\) \( Y_{2}=(X_{2} \times VP_{2})/(X_{1} \times VP_{1} + X_{2} \times VP_{2}) \nonumber\) repeat Equation 6-1
If the data plot of Figure 9-1 plot is carefully examined, one can see that the T- X and T- Y curves are exactly symmetrical when “folded” along a line running from abscissa/ordinate points of (0,124.76) to (1,92.40); or “folded” orthogonally to that same line. In other words, there are no departures from ideality in either vapor or liquid phase, either with DCS or TCS.
Now X and Y are re-calculated including the departures from ideality, both in fugacity (ø) as well as Liquid Activity Coefficients ( \(\gamma \nonumber\) ).
The table in above Figure 9-2 is likewise set up and calculations performed row-wise for each value of X DCS , but the liquid and vapor-phase fugacity coefficients (ø L and ø V ) and activity coefficients ( \(\gamma_{i} \nonumber\) ) are included in the calculation of vapor mole fractions (\(\gamma_{DCS} \nonumber\) ). For each row, the temperature is iterated until the sum of partial pressures = 11.0 atmospheres. Note that since the activity coefficients are mild functions of temperature, each row has its own Van Laar constants determined and the value of \(\gamma \nonumber\) calculated for that row’s liquid mole fraction. Thus all departure-from-ideality factors are included.
\[ Y_{i}= (\phi_{i}^L \times \gamma_{i} \times VP_{i} \times X_{i})/(\phi_{i}^V \times \pi) \label{9-1} \]
which is an algebraic re-arrangement of Equation 6-4 from previous Part VI .
To better show how the several ideality departure factors impact the T XY /P plot (as compared to Figure 9‑1 above), the table in Figure 9-2 is plotted. The symmetry of the Figure 9-1 Raoult/Dalton plot is no longer there, neither along the “fold” line running from abscissa/ordinate points of (0,124.76) to (1, 92.40); or “folded” orthogonally to that same line. Also note that the T- X and T- Y curves are closer together in Figure 9‑3, as opposed to Figure 9-1.
For a very simple approximation of tray count, for given distillation column “tops” product , “bottoms” product and feed mixture mole fractions, and for a given reflux rate, a McCabe-Thiele plot is constructed in Figure 9-4 to graphically step off the number of trays above and below the feed tray. For almost all industrial applications, this tray-by-tray analysis is done via computer modeling, such as ASPEN, VMG, HYSYS, ChemCad, etc. To apply the technique to a computer model, the user would specify the critical constants ( as per Part III ), the vapor pressure equation to be used (as per Part IV ), the EOS to be used to calculate fugacity coefficients (as per Part V ), and the Liquid Activity Coefficient model to be used (as per Part VI ).
To construct a McCabe-Thiele plot, the X - Y equilibrium (in red below) is plotted on a set of axes where X = liquid mole fraction of the most volatile component = X DCS ; and Y = vapor mole fraction of the most volatile component = Y DCS . The total reflux line (in black below) connects ( X , Y ) = (0,0) and (1,1); representing the maximum reflux possible. The lines are added (in dashed blue below) for the feed ( X F ), and distillate product ( X D ) and the bottoms product ( X B ), from the X -axis to the total reflux line. The feed line is extended toward the equilibrium curve, and from that intersection a line is drawn to the end of the distillate product line. The slope of that drawn line represents the minimum internal reflux needed to make the separation (i.e., with an infinite number of trays). The upper column operating line (in magenta below) is then drawn connecting the end of the distillate product line with the feed line, with a slope somewhat greater than the minimum reflux slope. In normal practice the upper column operating line slope is usually about 1.3 times the minimum slope, depending on the relative value of operating energy vs capital cost. Then the lower column operating line is drawn, intersecting the bottoms product line with the upper column operating line (and the feed line). The number of theoretical trays (aka stages) can then be stepped off ( in green below) from X D to X B , and best tray determined for the feed.
To illustrate an example of using a McCabe-Thiele plot, assume the mixture to be separated is a 35% DCS molar liquid, pre-heated to its boiling point of 108.61°C (as shown on the 35% of Figure 9-2). Further, assume that the column “tops” distillate product is to be 98% molar DCS and the column “bottoms” product is to be 98% molar TCS. Per the text above, the minimum reflux (i.e., the slope of the line between X D = X DCS of 0.98, X B = X DCS of 0.02) is determined to be 3.9:1, reflux-to-distillate. To allow a reasonable number of trays, a reflux rate of 5:1 is chosen (about 1.3 times the minimum), so the slope of the upper column operating line is R/(R+1) = 5/(5+1) =0.8333. Stepping off trays, it is determined that the total number of theoretical trays required is 34, with the feed tray at #22. Conventional tray counting starts at the column condenser = tray #1.
As can be seen by examining Figure 9-4, as the column’s reflux rate is increased, upper column ( magenta ) operating line’s slope increases, and the gap opens up between the ( red ) X-Y Equilibrium Line and the (black) Total Reflux Line. So increasing the reflux decreases the number trays required to make the specified separation.
In a normal industrial process application, all of the calculations are done via computer simulators, allowing for variations in operating line slope; feed quality condition (e.g., saturated vapor, saturated liquid, sub-cooled liquid, etc); changes in the internal liquid/vapor flow ratios due to physical properties; ambient heat effects; tray efficiencies, etc; as well as integrating the distillation column into the rest of the process design. So the McCabe-Thiele method is just used for graphical explanation.
However, the primary consideration of the distillation column design is the X-Y equilibrium relationship. If this is considerably in error – such as using only Raoult/Dalton – the column design will be a failure. Given the cost of industrial-scale distillation systems being in the millions of dollars (tens of $MM for larger ones), there is every reason to get the X-Y equilibrium relationship correct.
In the example of this article, the basic Raoult/Dalton model would result in the X-Y equilibrium relationship in the above example having more curvature (than shown in Figure 9-4) and therefore more open gap between the equilibrium curve and operating lines. The resulting reflux determined would be about 2/3 of required, and number of trays required would also be about 2/3 of needs - so a major error in design. Given what is at stake financially, there is no question that the use of proper distillation science is well worth it, even if the concepts are complex and the calculations are tedious.


19.5: The H-R and Cosmic Distances
By the end of this section, you will be able to:
- Understand how spectral types are used to estimate stellar luminosities
- Examine how these techniques are used by astronomers today
Variable stars are not the only way that we can estimate the luminosity of stars. Another way involves the H–R diagram, which shows that the intrinsic brightness of a star can be estimated if we know its spectral type.
Distances from Spectral Types
As satisfying and productive as variable stars have been for distance measurement, these stars are rare and are not found near all the objects to which we wish to measure distances. Suppose, for example, we need the distance to a star that is not varying, or to a group of stars, none of which is a variable. In this case, it turns out the H–R diagram can come to our rescue.
If we can observe the spectrum of a star, we can estimate its distance from our understanding of the H–R diagram. As discussed in Analyzing Starlight, a detailed examination of a stellar spectrum allows astronomers to classify the star into one of the spectral types indicating surface temperature. (The types are O, B, A, F, G, K, M, L, T, and Y; each of these can be divided into numbered subgroups.) In general, however, the spectral type alone is not enough to allow us to estimate luminosity. Look again at Figure 18.15. A G2 star could be a main-sequence star with a luminosity of 1 L Sun , or it could be a giant with a luminosity of 100 L Sun , or even a supergiant with a still higher luminosity.
We can learn more from a star’s spectrum, however, than just its temperature. Remember, for example, that we can detect pressure differences in stars from the details of the spectrum. This knowledge is very useful because giant stars are larger (and have lower pressures) than main-sequence stars, and supergiants are still larger than giants. If we look in detail at the spectrum of a star, we can determine whether it is a main-sequence star, a giant, or a supergiant.
Suppose, to start with the simplest example, that the spectrum, color, and other properties of a distant G2 star match those of the Sun exactly. It is then reasonable to conclude that this distant star is likely to be a main-sequence star just like the Sun and to have the same luminosity as the Sun. But if there are subtle differences between the solar spectrum and the spectrum of the distant star, then the distant star may be a giant or even a supergiant.
The most widely used system of star classification divides stars of a given spectral class into six categories called luminosity classes . These luminosity classes are denoted by Roman numbers as follows:
- Ia: Brightest supergiants
- Ib: Less luminous supergiants
- II: Bright giants
- III: Giants
- IV: Subgiants (intermediate between giants and main-sequence stars)
- V: Main-sequence stars
The full spectral specification of a star includes its luminosity class. For example, a main-sequence star with spectral class F3 is written as F3 V. The specification for an M2 giant is M2 III. Figure 19.15 illustrates the approximate position of stars of various luminosity classes on the H–R diagram. The dashed portions of the lines represent regions with very few or no stars.
With both its spectral and luminosity classes known, a star’s position on the H–R diagram is uniquely determined. Since the diagram plots luminosity versus temperature, this means we can now read off the star’s luminosity (once its spectrum has helped us place it on the diagram). As before, if we know how luminous the star really is and see how dim it looks, the difference allows us to calculate its distance. (For historical reasons, astronomers sometimes call this method of distance determination spectroscopic parallax , even though the method has nothing to do with parallax.)
The H–R diagram method allows astronomers to estimate distances to nearby stars, as well as some of the most distant stars in our Galaxy, but it is anchored by measurements of parallax. The distances measured using parallax are the gold standard for distances: they rely on no assumptions, only geometry. Once astronomers take a spectrum of a nearby star for which we also know the parallax, we know the luminosity that corresponds to that spectral type. Nearby stars thus serve as benchmarks for more distant stars because we can assume that two stars with identical spectra have the same intrinsic luminosity.
A Few Words about the Real World
Introductory textbooks such as ours work hard to present the material in a straightforward and simplified way. In doing so, we sometimes do our students a disservice by making scientific techniques seem too clean and painless. In the real world, the techniques we have just described turn out to be messy and difficult, and often give astronomers headaches that last long into the day.
For example, the relationships we have described such as the period-luminosity relation for certain variable stars aren’t exactly straight lines on a graph. The points representing many stars scatter widely when plotted, and thus, the distances derived from them also have a certain built-in scatter or uncertainty.
The distances we measure with the methods we have discussed are therefore only accurate to within a certain percentage of error—sometimes 10%, sometimes 25%, sometimes as much as 50% or more. A 25% error for a star estimated to be 10,000 light-years away means it could be anywhere from 7500 to 12,500 light-years away. This would be an unacceptable uncertainty if you were loading fuel into a spaceship for a trip to the star, but it is not a bad first figure to work with if you are an astronomer stuck on planet Earth.
Nor is the construction of H–R diagrams as easy as you might think at first. To make a good diagram, one needs to measure the characteristics and distances of many stars, which can be a time-consuming task. Since our own solar neighborhood is already well mapped, the stars astronomers most want to study to advance our knowledge are likely to be far away and faint. It may take hours of observing to obtain a single spectrum. Observers may have to spend many nights at the telescope (and many days back home working with their data) before they get their distance measurement. Fortunately, this is changing because surveys like Gaia will study billions of stars, producing public datasets that all astronomers can use.
Despite these difficulties, the tools we have been discussing allow us to measure a remarkable range of distances—parallaxes for the nearest stars, RR Lyrae variable stars; the H–R diagram for clusters of stars in our own and nearby galaxies; and cepheids out to distances of 60 million light-years. Table 19.1 describes the distance limits and overlap of each method.
Each technique described in this chapter builds on at least one other method, forming what many call the cosmic distance ladder . Parallaxes are the foundation of all stellar distance estimates, spectroscopic methods use nearby stars to calibrate their H–R diagrams, and RR Lyrae and cepheid distance estimates are grounded in H–R diagram distance estimates (and even in a parallax measurement to a nearby cepheid, Delta Cephei ).
This chain of methods allows astronomers to push the limits when looking for even more distant stars. Recent work, for example, has used RR Lyrae stars to identify dim companion galaxies to our own Milky Way out at distances of 300,000 light-years. The H–R diagram method was recently used to identify the two most distant stars in the Galaxy: red giant stars way out in the halo of the Milky Way with distances of almost 1 million light-years.
We can combine the distances we find for stars with measurements of their composition, luminosity, and temperature—made with the techniques described in Analyzing Starlight and The Stars: A Celestial Census. Together, these make up the arsenal of information we need to trace the evolution of stars from birth to death, the subject to which we turn in the chapters that follow.
| Method | Distance Range |
|---|---|
| Trigonometric parallax | 4–30,000 light-years when the Gaia mission is complete |
| RR Lyrae stars | Out to 300,000 light-years |
| H–R diagram and spectroscopic distances | Out to 1,200,000 light-years |
| Cepheid stars | Out to 60,000,000 light-years |


3.5: Case Study - Ten Years Later
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Beth's first attempt at college was ten years ago. She took a couple of classes but found the material more challenging than she expected and dropped out before the end of the semester. Now, ten years later, she has decided to try again. At the beginning of the semester, Beth feels overwhelmed. She hasn't written a paper in years, and she doesn't have a lot of experience with computers. Beth is confused in class, but no one else seems to be asking questions so Beth doesn't either. She's not sure she understands the directions for her first paper, but she tries her best anyway. When the paper is returned with D, Beth is extremely frustrated and upset. She thinks "I just don't belong in college." Beth begins missing classes and is considering dropping out of college again.
Reflection Questions:


6.2: Lead-Sheet Symbols
Lead-sheet symbols (also known as “lead-sheet notation” and “lead-sheet chord symbols”) are often used as shorthand for chords in popular music and jazz. These symbols allow a guitarist or pianist to choose how to “voice” the chords, i.e., how they want to arrange the notes.
Lead-sheet symbols for triads communicate the root and quality of a chord.
| Lead-sheet Symbol | Chord Quality | Notes in the Chord |
|---|---|---|
| FF | major | FF–AA–CC |
| GmGm | minor | GG–BB♭–DD |
| DD∘ | diminished | DD–FF–AA♭ |
| CC+ | augmented | CC–EE–GG♯ |
Here is a musical example with lead-sheet symbols and guitar tablature.
As you can see in the example above, major triads are represented by an uppercase letter (AA, EE, and DD) while minor triads are represented with the root in uppercase followed by a lowercase “m” (e.g., FmF♯m). Diminished triads are represented by including the diminished symbol (∘) after the chord root (e.g., CC∘) while augmented triads are represented by including the augmented symbol after the root (CC+).


8: Linear Regression and Correlation
Regression analysis is a statistical process for estimating the relationships among variables and includes many techniques for modeling and analyzing several variables. When the focus is on the relationship between a dependent variable and one or more independent variables.
-
- 8.1: Prelude to Linear Regression and Correlation
- In this chapter, you will be studying the simplest form of regression, "linear regression" with one independent variable (x). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.
-
- 8.2: Linear Equations
- Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form: y=a+bx where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
-
- 8.3: Scatter Plots
- A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either: High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable. High values of one variable occurring with low values of the other variable.
-
- 8.4: The Regression Equation
- A regression line, or a line of best fit, can be drawn on a scatter plot and used to predict outcomes for the x and y variables in a given data set or sample data. There are several ways to find a regression line, but usually the least-squares regression line is used because it creates a uniform line. Residuals measure the distance from the actual value of y and the estimated value of y . The Sum of Squared Errors, when set to its minimum, calculates the points on the line of best fit.
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- 8.5: Testing the Significance of the Correlation Coefficient
- The correlation coefficient tells us about the strength and direction of the linear relationship between x and y. However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient r and the sample size n, and perform a hypothesis test of the "significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to use to linear model.
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- 8.6: Prediction
- After determining the presence of a strong correlation coefficient and calculating the line of best fit, you can use the least squares regression line to make predictions about your data. The process of predicting inside of the observed x values observed in the data is called interpolation. The process of predicting outside of the observed x-values observed in the data is called extrapolation.


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8: Linear Correlation and Regression
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8.1: Introduction to Bivariate Quantitative Data
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In this chapter we consider bivariate data, which for now consists of two quantitative variables for each individual. Our first interest is in summarizing such data in a way that is analogous to summarizing univariate (single variable) data.
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8.2: Linear Correlation
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In this section, we begin to assess the strength of a linear relationship through the use of scatter plots and Pearson's correlation coefficient.
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8.3: Introduction to Simple Linear Regression
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If there is a linear relationship, it seems appropriate to think that there is a linear function that models the relationship giving us deeper understanding of the relationship and allow us to extrapolate values that were not explicitly measured in our collection of the data. In essence, such a function would enable us to make predictions about cases that were not explicitly studied. This section develops the ideas of constructing a linear function that is the best fit for the data at hand.


3.3: Speed and acceleration
Problem 84 Jack and Jill went up the hill, and averaged 2 mph on the way up. They then turned round and went straight back down by the same route, this time averaging 4 mph. What was their average speed for the round trip (up and down)?
Problem 85
(a) (i) A cycling road race requires one to complete 3 laps of a long road circuit. On the first lap I average 40 km/h; on the second lap I average 30 km/h; and on the third lap I only average 20 km/h. What is my average speed for the whole race?
(ii) I cycle for 3 hours round the track of a velodrome, averaging 40 km/h for the first hour, 30 km/h for the second hour, and 20 km/h for the final hour. What is my average speed over the whole 3 hours?
(b) Two cyclists compete in an endurance event.
(i) The first cyclist pedals at 60 km/h for half the time and then at 40 km/h for the other half. The second cyclist pedals at 60 km/h for half of the total distance and then at 40 km/h for the remaining half. Who wins?
(ii) In a two hour event, the first cyclist pedals at u km/h for the first hour and then at v km/h for the second hour. The second cyclist pedals at u km/h for half of the total distance and then at v km/h for the remaining half. Who wins?
(c) (i)Apply your argument in (b)(ii) to prove an inequality between
* the arithmetic mean
of two positive quantities u , v , and
* the harmonic mean
(ii) Give a purely algebraic proof of your inequality in (i).
Problem 86 A train started from a station and, moving with a constant acceleration, covered a distance of 4 km, finally reaching a speed of 72 km/hour. Find the acceleration of the train, and the time taken for the 4 km.
Problem 87 ( Average speed of an accelerating car ) A typical car (and maybe also a typical train!) does not move with constant acceleration. Starting from a standstill, a car moves through the gears and “accelerates more quickly” in lower gears, when travelling at lower speeds, than it does in higher gears, when travelling at higher speeds. Use this empirical fact to prove that the average speed of a car accelerating from rest is more than half of its final measured speed after the acceleration.


7.5: Writing Paragraphs and Topic Sentences
A previous chapter ( chapter 5 ) briefly introduced you to the fundamentals of writing in terms of paragraph and sentence construction. Here, you will learn more about developing paragraphs and topic sentences to support your ideas. Paragraphs are a group of sentences that form the main structural component of your paper. Each paragraph focuses on a single idea that relates to your main idea or thesis.
A topic sentence helps you introduce a paragraph. The job of the topic sentence is to control the development and flow of the information contained in the paragraph. It shapes the specific topic of the paragraph and how you present it to readers.
Placement of topic sentences
The topic sentence is often, but not always, the paragraph’s first sentence. Placing a topic sentence at or near the beginning of the paragraph is a good strategy. If you announce a topic clearly and early on in a paragraph, your readers are likely to grasp your idea and to make the connections that you want them to make.
One way to think about a topic sentence is that it presents the broadest view of what you want your readers to understand. You’re announcing or bringing into focus the purpose or meaning of the paragraph. If you think of the topic sentence as presenting the broadest view, then you can think of how every supporting detail within the paragraph brings a narrower, more specific view of the same topic. See Figure 7.3 .
Figure 7.3 : Topic sentence as an umbrella
Characteristics of good topic sentences
If an instructor or other reader comments that your paragraph lacks unity, you probably need a better topic sentence (or maybe you don’t have one yet). See Table 7.1 for examples of good and not-so-good topic sentences. A good topic sentence should meet the following criteria:
- Signals the topic and more focused ideas within the paragraph.
- Presents an idea or ideas that are clear and easy to understand.
- Provides unity to the paragraph (clarifies how all supporting ideas relate).
- Links to the purpose or thesis of your paper.
- Omits supporting details.
- Engages the reader.
Table 7.1: Examples of good and not-so-good topic sentences
| Topic | Not-so-good topic sentence | Good topic sentence |
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Sugar leads to ill-health |
Sugar is often used as a substitute for fat in many foods. *In this case, the sentence isn’t great because while it may speak to the pervasiveness of sugar, it doesn’t link the information back to how it serves as an agent of ill-health. |
High levels of sugar alter blood viscosity, rendering it thicker, which can lead to hypertension. *In this case, the sentence supports the main topic of sugar leading to ill-health, and hones in on one particular reason why sugar is not good for health. |
The paragraph body: Supporting your ideas
Whether you draft a paragraph based on a main idea, or whether the idea surfaces in the revision process, once you have the main idea you need to ensure that you support it. The job of the paragraph body is to develop and support the topic . Here’s one way to think about it:
- Topic sentence: What is the main claim of your paragraph? What is the most important idea that you want your readers to take away from this paragraph?
- Support in the form of evidence: How can you prove that your claim or idea is true (or important, or noteworthy, or relevant)?
- Support in the form of analysis or evaluation: What discussion can you provide that helps your readers see the connection between the evidence and your claim?
- Transition: How can you help your readers move from the current idea to the next idea?
Now that you have a good idea what it means to develop support for the main ideas of your paragraphs, let’s explore how to make sure that those supporting details are solid and convincing. Types of support might include: reasons, facts, statistics, quotations, and examples.
Attribution statement
Content from this page was remixed with our own original content and adapted from:
The Word on College Reading and Writing by Carol Burnell, Jaime Wood, Monique Babin, Susan Pesznecker, and Nicole Rosevear, licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.Download for free at: https://openoregon.pressbooks.pub/wrd/


2: Conception, Heredity, and Prenatal Development
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Learning Objectives
After this chapter, you should be able to:
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Evaluate roles of nature and nurture in development.
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Define genes and chromosomes.
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Differentiate mitosis and meiosis.
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Explain dominant and recessive patterns on inheritance.
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List common genetic disorders and chromosomal abnormalities.
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Describe changes that occur within each of the three periods of prenatal development.
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Recognize the risks to prenatal development posed by exposure to teratogens.
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Evaluate different types of prenatal assessment.
In this chapter, we will begin by examining some of the ways in which heredity helps to shape the way we are. We will look at what happens genetically during conception, and describe some known genetic and chromosomal disorders. Next we will consider what happens during prenatal development, including the impact of teratogens. We will also discuss the impact that both the mother and father have on the developing fetus.
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2.1: Heredity
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Most scholars agree that there is a constant interplay between nature (heredity) and nurture (the environment). It is difficult to isolate the root of any single characteristic as a result solely of nature or nurture, and most scholars believe that even determining the extent to which nature or nurture impacts a human feature is difficult to answer. In fact, almost all human features are polygenic (result of many genes) and multifactorial (result of many factors, both genetic and environmental).
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2.2: Prenatal Development
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Now we turn our attention to prenatal development which is divided into three periods: The germinal period, the embryonic period, and the fetal period. The following is an overview of some of the changes that take place during each period.
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2.S: Summary
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8.7: How Libraries Organize Materials
Two Systems
There are two main systems that California community college libraries use to organize materials on the shelves: the Dewey Decimal Classification (DDC) and the Library of Congress Classification (LCC, sometimes also informally called LC or LOC). Both classification systems provide a systematic way for the libraries to keep their materials organized.
Which classification system a library uses depends on local preferences and practices, but in general: academic and research libraries typically use the Library of Congress Classification, while public libraries tend to use the Dewey Decimal Classification. While we will introduce you to both systems, please note that your community college library probably only uses one of these.


10.12: Staying Healthy
Pregnancy and childbirth place great demands on a woman's body, it is important to keep healthy. The more healthy and relaxed the mother is, the better it will be to cope with the demands of pregnancy. A healthy lifestyle combines many factors:
Balanced Diet
A poor diet can cause a low birth weight. Excessive weight gain during pregnancy can cause back problems, varicose veins, or indicate preeclampsia. Advice on diet often includes eating foods that are high in nutritional content. Sufficient protein, vitamins, carbohydrates, fats, and minerals, as well as fiber. Limit intake of saturated fats and sugar, and salt. Drink plenty of fluids.
Regular Exercise
Mild exercise, such as walking or swimming, is beneficial and will help cope with the workload of pregnancy and the demands of labor. Mother's should listen to her body and stop exercising when it tells her to. Exercise should never be painful.
Baby's Health
Consumption of alcohol and cigarettes while pregnant are dangerous for your baby. Smoking reduces the oxygen and nutrients passing via the placenta to the baby. Avoid alcohol to avoid serious birth defects.


11.6.2: Case Study- The Jackson Water Crisis
The residents of Jackson, Mississippi are no strangers to boil-water advisories. The city has dealt with infrastructure problems for years; massive leaks, E. coli and lead concerns, and a lack of funding and staffing to maintain its aging water and sanitation facilities (Pettus, 2022). A cold snap in 2021, and heavy winter storms in 2022 caused pipes to burst and shut off water supplies to thousands (Adams, 2023). When heavy rains caused the nearby river to overflow in the summer of 2022, one of the city’s two water treatment facilities was compromised (Breslow, 2022). Since low water pressure allows bacteria and other contaminants to seep in through cracks in the aging pipes, residents were under yet another boil-water advisory, and bottled water was distributed (Pettus, 2022).
Jackson’s chronic water crisis demonstrates the complex interplay of social determinants of health, environmental health, public health policies, and politics. To begin with, 80% of the 150,000 residents in Jackson, Mississippi are Black, and a quarter of them (25%) are at or below the poverty threshold (Pettus, 2022). Mississippi has a long history of racism and white supremacy, with Jackson at the center of the Freedom Riders protest, when civil rights activists were arrested for riding segregated public transportation from DC (Contributors to Wikimedia projects, 2024). Jim Crow laws, housing discrimination and underinvestment in communities of color have disproportionately exposed Black populations to environmental hazards (USGCRP, 2023c). After the integration of schools in the 1960s, white families moved out of Jackson en masse over the next several decades - so called “white flight” to the surrounding suburbs (Wiggins & Morrow, 2022). For these and other reasons, tax income to the city has declined, and Jackson has long had problems with finding money to fix its infrastructure (Pettus, 2022), some of which is over 100 years old (SPLC, 2023). Jackson’s history of discrimination and underinvestment are compounded by emerging environmental factors. Climate change is contributing to more rainfall and severe storms - including hurricanes and more severe flooding in the southeast U.S. region (USGCRP, 2023c). While an EPA investigation into the recent water crisis concluded that state agencies did not racially discriminate against Jackson’s residents in distributing federal funds for infrastructure updates (Muhammad & Judin, 2024), it is clear that a combination of systemic and historic racism, poverty, policies, and climate change are contributing to the struggles Jackson is facing in providing clean water to its residents.


14.2: Stability of Conjugated Dienes- Molecular Orbital Theory
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Objectives
After completing this section, you should be able to
- write a reaction sequence to show a convenient method for preparing a given conjugated diene from an alkene, allyl halide, alkyl dihalide or alcohol (diol).
- identify the reagents needed to prepare a given diene from one of the starting materials listed in Objective 1, above.
- compare the stabilities of conjugated and non-conjugated dienes, using evidence obtained from hydrogenation experiments.
- discuss the bonding in a conjugated diene, such as 1,3-butadiene, in terms of the hybridization of the carbon atoms involved.
- discuss the bonding in 1,3-butadiene in terms of the molecular orbital theory, and draw a molecular orbital for this and similar compounds.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- delocalized electrons
- node
Study Notes
The two most frequent ways to synthesize conjugated dienes are dehydration of alcohols and dehydrohalogenation of organohalides, which were introduced in the preparation of alkenes ( Section 8.1 ). The following scheme illustrates some of the routes to preparing a conjugated diene.
The formation of synthetic polymers from dienes such as 1,3-butadiene and isoprene is discussed in Section 14.6. Synthetic polymers are large molecules made up of smaller repeating units. You are probably somewhat familiar with a number of these polymers; for example, polyethylene, polypropylene, polystyrene and poly(vinyl chloride).
As the hydrogenation of 1,3-butadiene releases less than the predicted amount of energy, the energy content of 1,3-butadiene must be lower than we might have expected. In other words, 1,3-butadiene is more stable than its formula suggests.
Some university-level general chemistry courses do not introduce the subject of molecular orbitals. If you have taken such a course, or forgotten what is meant by the term “molecular orbital,” combine a review of Section 1.11 with your study of this section.
Conjugated vs. Non-conjugated Dienes
Dienes are compounds which contain two double bonds. These dienes can be non-conjugated (the two double bonds are separated by at least one sp 3 hybridized atom. Conjugated dienes have the two double bonds separated by a single bond. Conjugated dienes have properties and reactivity which are distinctly different than non-conjugated dienes. Determining if double bonds are conjugated represents an important skill in organic chemistry.
Synthesis of Dienes
Conjugated dienes can be prepared using many of the methods used for the preparation of alkenes previously discussed ( Sections 11-7 , 11-8 , 11-9 , and 11-10 ). A convenient method starts with the free radical halogenation of the allylic carbon of an alkene using NBS. The resulting halide can then be reacted with a strong base to result in E2 elimination and create a diene product. The compound, 1,3-butadiene, is the simplest conjugated diene and has an important use in the synthesis of polymers which will be discussed in Section 14.6 . Many simple dienes, such as 1,3-butadiene and isoprene, can be prepared industrially by the double dehydration of alcohols and the double dehydrohalogenation of organohalides.
Stability of Conjugated Dienes
Conjugated dienes are known to be more stable than non-conjugated dienes as shown by their experimentally determined heats of hydrogenation. In Section 7-6 , it was shown that as alkenes become more stable, they contain less energy, and therefore release less heat during hydrogenation. Experiments have shown that conjugated dienes have a lower heat of hydrogenation (-226 kJ/mol) than non-conjugated dienes (-251 kJ/mol). Using the differences in heats of hydrogenation the stabilization energy in conjugated dienes can be estimate to be roughly 25 kJ/mol.
Here is an energy diagram comparing different types of bonds with their heats of hydrogenation to show relative stability of each molecule:
The stabilization of dienes by conjugation is less dramatic than the aromatic stabilization of benzene. Nevertheless, similar resonance and molecular orbital descriptions of conjugation may be written.
Each alkene carbon in 1,3 dienes are sp 2 hybridized and therefore have one unhybridized p orbital. The four p orbitals in 1,3-butadiene overlap to form a conjugated system which can be represented by the resonance forms shown below. This delocalization of charges stabilizes conjugated diene making them more stable than non-conjugated dienes.
Evidence of conjugation in 1,3 dienes is seen in the single bond being stronger and shorter (147 pm) than an ordinary alkane C-C bond (154 pm). The resonance hybrid of a 1,3-butadiene shows this bond to contain significant double bond character with its bond length being roughly the average of a single and double bond.
The delocalized electron density of a 1,3 diene can be seen when viewing an electrostatic potential maps. In conjugated dienes, it is observed that the pi electron density overlap (shown in red) is closer together and delocalized in conjugated dienes, while in non-conjugated dienes the pi electron density is located completely on the double bonds.
Molecular Orbitals of 1,3 Dienes
According to MO theory discussed in section 1-11 , when a double bond is non-conjugated, the two atomic 2 p z orbitals combine to form two pi ( π ) molecular orbitals , one a low-energy π bonding orbital and one a high-energy π -star ( π *) anti-bonding molecular orbital . These are sometimes denoted, in MO diagrams like the one below, with the Greek letter psi ( Ψ ) instead of π . In the bonding Ψ 1 orbital, the two (+) lobes of the 2p z orbitals interact constructively with each other, as do the two (-) lobes. Therefore, there is increased electron density between the nuclei in the molecular orbital – this is why it is a bonding orbital. In the higher-energy anti-bonding Ψ 2 * orbital, the (+) lobes of one 2 p z orbital interacts destructively with the (-) lobe of the second 2 p z orbital, leading to a node between the two nuclei and overall repulsion. By the aufbau principle, the two electrons from the two atomic orbitals will be paired in the lower-energy Ψ 1 orbital when the molecule is in the ground state.
With a conjugated diene, such as 1,3-butadiene, the four 2p atomic orbitals combine to form four pi molecular orbitals of increasing energy. Two bonding pi orbitals and two anti-bonding pi* orbitals. The combination of four pi molecular orbitals allow for the formation of a bonding molecular orbital that is lower in energy than those created by an unconjugated alkene. The 4 pi electrons of 1,3-butadiene completely fill the bonding molecular orbitals giving is the additional stability associated with conjugated double bonds.


8.1: Nucleotides -the building blocks of nucleic acids
- Understand the function of nucleic acids.
- Learn the structures and names of nucleotides -the building blocks of nucleic acids, and their constituents, including ribose, deoxyribose, nitrogen bases, and phosphate groups.
Nucleic acids are biopolymers that carry the codes for synthesizing proteins and pass them on from generation to generation, i.e., they are genetic materials. In other words, nucleic acids are the instruction manual for biochemical reactions in living things.
Nucleotides are the building blocks, i.e., the repeat units or monomers of nucleic acids.
Nucleotides are composed of three sub-units:
- a 5-carbon carbohydrate,
- a base that is an aromatic compound containing nitrogen, and
- an anion of phosphoric acid, i.e., phosphate (\(\ce{PO4^{3-}}\)).
5-Carbon carbohydrate
Two 5-carbon carbohydrates, i.e., ribose and deoxyribose, are found in nucleic acids, as shown in the figure below. Both are D-sugars in five-membered cyclic form with hydroxyl (\(\ce{-OH}\)) group at anomeric (\(\ce{C}\)#1') pointing towards \(\ce{O}\) in the ring, i.e., in a \(\beta\) configuration. The number labels have prime symbols, i.e., 1', 2', 3', etc., to distinguish them from regular numbers 1, 2, 3, etc., used for the nitrogen bases of the nucleic acids. The only difference between ribose and deoxyribose is that hydroxyl (\(\ce{-OH}\)) group at \(\ce{C}\)#2' is missing in the latter, which gives the deoxy- prefix to its name.
There are two types of nucleic acids: ribose in its nucleotides, called ribonucleic acid ( RNA ), and deoxyribose in its nucleotides, called deoxyribonucleic acid ( DNA ).
Nitrogen bases
Nitrogen bases in nucleic acids are derivatives of two aromatic compounds, purine and pyrimidine, shown below.
Cyclic compounds that contain atoms other than \(\ce{C's}\) in the cycle are called heterocyclic compounds. Purine and pyrimidine are heterocyclic aromatic compounds because they contain \(\ce{N's}\) in the cycles. Purine is bicyclic, containing a six-membered ring with two \(\ce{N's}\) fused with a five-membered ring with two \(\ce{N's}\). Pyrimidine is a six-membered cycle with two \(\ce{N's}\). Both purine and pyrimidine are planer molecules like benzene.
There are five nitrogen bases found in nucleic acids: two are purines, i.e., adenine (A) and guanine (G), and three are pyrimidines, i.e., cytosine (C), thymine (T), and uracil (U), as shown below. To remember what are pyrimidines, remember "cut pyramid" where 'c' is cytosine, 'u' for uracil, 't' for thymine, and 'pyramid' for pyrimidines
| Purines | Pyrimidines | |||
|---|---|---|---|---|
DNA contains four nitrogen bases, i.e., adenine, guanine, cytosine, and thymine. RNA also has four nitrogen bases, i.e., adenine, guanine, cytosine, and uracil. Note that the first three, i.e., adenine, guanine, and cytosine, are common in DNA and RNA, but the fourth, i.e., ti.e.ine in DNA, is replaced with uracil in RNA.
Nucleosides
When a monomer sugar like ribose or deoxyribose reacts with an amine, the \(\ce{-OH}\) group at \(\ce{C}\)#1' is replaced with a \(\ce{N}\) of the amine. The product is called N-glycoside, and the \(\ce{C-N}\) bond in the N-glycoside is called an N-glycosidic bond, as shown in the following example.
Purines connect through \(\ce{N}\)#9 and pyrimidine through \(\ce{N}\)#1 with anomeric carbon (\(\ce{C}\)#1') of ribose or deoxyribose to form the N-glycoside.
The N-glycosides are named by using the name of purine but ending with -osine e.g., adenine becomes adenosine and guanine becomes gunosine, or by using the name of pyrimidine ending with -idine, e.g., cytosine becomes cytidine and uracil become uridine. One letter abbreviation of the nitrogen bases remains the same for the corresponding nucleoside, e.g., adenine (A) and adenosine (A). The four nucleosides found in RNA are shown below with their names and one-letter abbreviations.
In DNA there is deoxyribose in place of ribose. So the names of nucleosides found in DNA begin with the deoxy- prefix. The four nucleosides found in DNA are shown below with their names and one-letter abbreviations.
Phosphate
Phosphoric acid (\(\ce{H3PO4}\)) is an oxyacid with three acidic protons, i.e., it is triprotic acid. Just as two carboxylic acids condense with each other and form a carboxylic acid anhydride with the elimination of water molecule, two phosphoric acids condense and form diphosphoric acid, also called pyrophosphoric acid, with the elimination of water.
Similarly, three phosphoric acids can condense to form triphosphoric acid. Phosphoric acid, diphosphoric acid, and triphosphoric acid are shown below.
Under physiological conditions at pH ~7.4, the phosphoric acids lose proton and exist as phosphate anions, as shown below.
Phosphoric acids also condense with alcohols (\(\ce{R-OH}\)) and form mono-, di-, or triesters, as illustrated below.
Nucleotide
Phosphate esters of nucleosides are called nucleotides. The nucleotides found in nucleic acids are formed when \(\ce{-OH}\) group at \(\ce{C}\)#5' of ribose or deoxyribose makes ester with a monophosphate, diphosphate, or triphosphate, as shown below.
The names of the nucleotides are derived by using the name of the corresponding nucleoside with monophosphate, diphosphate, or triphosphate added at the end. Abbreviation of the nucleotide starts with the one-letter abbreviation of the nitrogen base followed by MP, DP, or TP depending on whether the phosphate group is monophosphate, diphosphate, or triphosphate, as shown in the example structures above.
The nucleotides like ADP and ATP are high-energy molecules used as energy currency in biochemical systems. For example, when ATP converts to ADP by releasing a phosphate, energy is released to do work or synthesize other compounds. Synthesis of nucleic acids begins with triphosphate esters that convert into monophosphate esters when incorporated in the nucleic acid polymer. The energy released in converting triphosphate to monophosphate drives the reaction forward.
The four nucleotides found in RNA are shown below with their names and abbreviations.
, , , and
The nucleotides found in DNA are named similarly to those of RNA: start with the name of the corresponding nucleoside and end with monophosphate, diphosphate, or triphosphate. Remember that the names of DNA nucleosides begin with deoxy. The abbreviations of the nucleotides found in DNA start with a small alphabet d representing the deoxy- prefix of the nucleotides. The four nucleotides found in DNA are shown below with their names and abbreviations.
, , ,


7: Microbial Metabolism
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- 7.1: Energy, Matter, and Enzymes
- Cellular processes such as the building or breaking down of complex molecules occur through series of stepwise, interconnected chemical reactions called metabolic pathways. The term anabolism refers to those endergonic metabolic pathways involved in biosynthesis, converting simple molecular building blocks into more complex molecules, and fueled by the use of cellular energy.
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- 7.2: Catabolism of Carbohydrates
- Glycolysis is the first step in the breakdown of glucose, resulting in the formation of ATP, which is produced by substrate-level phosphorylation; NADH; and two pyruvate molecules. Glycolysis does not use oxygen and is not oxygen dependent. After glycolysis, a three-carbon pyruvate is decarboxylated to form a two-carbon acetyl group, coupled with the formation of NADH. The acetyl group is attached to a large carrier compound called coenzyme A.
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- 7.3: Alternate Forms of Catabolism- Fermentation, Lipids and Proteins
- Collectively, microbes have the ability to degrade a wide variety of carbon sources besides carbohydrates, including lipids and proteins. The catabolic pathways for all of these molecules eventually connect into glycolysis and the Krebs cycle. Several types of lipids can be microbially degraded. Triglycerides are degraded by extracellular lipases, releasing fatty acids from the glycerol backbone. Phospholipids are degraded by phospholipases, releasing fatty acids and phosphorylated head groups.
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- 7.4: Photosynthesis and the Importance of Light
- Heterotrophic organisms ranging from E. coli to humans rely on the chemical energy found mainly in carbohydrate molecules. Many of these carbohydrates are produced by photosynthesis, the biochemical process by which phototrophic organisms convert solar energy (sunlight) into chemical energy. Although photosynthesis is most commonly associated with plants, microbial photosynthesis is also a significant supplier of chemical energy, fueling many diverse ecosystems.
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- 7.5: Biogeochemical Cycles
- Energy flows directionally through ecosystems, entering as sunlight for phototrophs or as inorganic molecules for chemoautotrophs. The six most common elements associated with organic molecules—carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur—take a variety of chemical forms and may exist for long periods in the atmosphere, on land, in water, or beneath earth’s surface
Thumbnail: The Krebs cycle, also known as the citric acid cycle, is summarized here. Note incoming two-carbon acetyl results in the main outputs per turn of two CO 2 , three NADH, one FADH 2 , and one ATP (or GTP) molecules made by substrate-level phosphorylation. Two turns of the Krebs cycle are required to process all of the carbon from one glucose molecule.