18.7: Work and Kinetic Energy
Check Your Understanding
7.1. No, only its magnitude can be constant; its direction must change, to be always opposite the relative displacement along the surface.
7.2. No, it’s only approximately constant near Earth’s surface.
7.3. W = 35 J
7.4. a. The spring force is the opposite direction to a compression (as it is for an extension), so the work it does is negative. b. The work done depends on the square of the displacement, which is the same for x = ± 6 cm, so the magnitude is 0.54 J.
7.5. a. The car; b. the truck
7.6. Against
7.7. 3 m/s
7.8. 980 W
Conceptual Questions
1. When you push on the wall, this “feels” like work; however, there is no displacement so there is no physical work. Energy is consumed, but no energy is transferred.
3. If you continue to push on a wall without breaking through the wall, you continue to exert a force with no displacement, so no work is done.
5. The total displacement of the ball is zero, so no work is done.
7. Both require the same gravitational work, but the stairs allow Tarzan to take this work over a longer time interval and hence gradually exert his energy, rather than dramatically by climbing a vine.
9. The first particle has a kinetic energy of 4(\(\frac{1}{2}\)mv 2 ) whereas the second particle has a kinetic energy of 2(\(\frac{1}{2}\)mv 2 ), so the first particle has twice the kinetic energy of the second particle.
11. The mower would gain energy if −90° < \(\theta\) < 90°. It would lose energy if 90° < \(\theta\) < 270°. The mower may also lose energy due to friction with the grass while pushing; however, we are not concerned with that energy loss for this problem.
13. The second marble has twice the kinetic energy of the first because kinetic energy is directly proportional to mass, like the work done by gravity.
15. Unless the environment is nearly frictionless, you are doing some positive work on the environment to cancel out the frictional work against you, resulting in zero total work producing a constant velocity.
17. Appliances are rated in terms of the energy consumed in a relatively small time interval. It does not matter how long the appliance is on, only the rate of change of energy per unit time.
19. The spark occurs over a relatively short time span, thereby delivering a very low amount of energy to your body.
21. If the force is antiparallel or points in an opposite direction to the velocity, the power expended can be negative.
Problems
23. 3.00 J
25. a. 593 kJ
b. –589 kJ
c. 0 J
27. 3.14 kJ
29. a. –700 J
b. 0 J; c. 700 J
d. 38.6 N
e. 0 J
31. 100 J
33. a. 2.45 J
b. – 2.45 J
c. 0 J
35. a. 2.22 kJ
b. −2.22 kJ
c. 0 J
37. 18.6 kJ
39. a. 2.32 kN
b. 22.0 kJ
41. 835 N
43. 257 J
45. a. 1.47 m/s
b. Answers may vary
47. a. 772 kJ
b. 4.0 kJ
c. 1.8 x 10 −16 J
49. a. 2.6 kJ
b. 640 J
51. 2.72 kN
53. 102 N
55. 2.8 m/s
57. W(bullet) = 20 x W(crate)
59. 12.8 kN
61. 0.25
63. a. 24 m/s, −4.8 m/s 2
b. 29.4 m
65. 310 m/s
67. a. 40
b. 8 million
69. $149
71. a. 208 W
b. 141 s
73. a. 3.20 s
b. 4.04 s
75. a. 224 s
b. 24.8 MW
c. 49.7 kN
77. a. 1.57 kW
b. 6.28 kW
79. 6.83 \(\mu\)W
81. a. 8.51 J
b. 8.51 W
83. 1.7 kW
Additional Problems
85. 15 N • m
87. 39 N • m
89. a. 208 N • m
b. 240 N • m
91. a. −0.9 N • m
b. −0.83 N • m
93. a. 10. J
b. 10. J
c. 380 N/m
95. 160 J/s
97. a. 10 N
b. 20 W
Challenge Problems
99. If crate goes up: a. 3.46 kJ
b. −1.89 kJ
c. −1.57 kJ
d. 0
100. I f crate goes down: a. −0.39 kJ
b. −1.18 kJ
c. 1.57 kJ
d. 0
101. 8.0 J
103. 35.7 J
105. 24.3 J
107. a. 40 hp
b. 39.8 MJ, independent of speed
c. 80 hp, 79.6 MJ at 30 m/s
d. If air resistance is proportional to speed, the car gets about 22 mpg at 34 mph and half that at twice the speed, closer to actual driving experience.


8.4: Cytogenetics –Introduction
The genetic material of humans is contained on 23 pairs of chromosomes in the nucleus of each somatic cell. 22 pairs are autosomes and 1 pair is the sex chromosomes.
Cytogeneticists examine chromosome structure, seek out causes of chromosomal abnormalities, and study how chromosome structure relates to an individual's phenotype (appearance and biochemical traits). Abnormalities in chromosomes can result in early embryonic death, congenital defects, development of cancer, and infertility or sterility.
Studies of chromosomes begin with the extraction of chromosomes from cells. Chromosomes are then placed on a glass slide, stained with dye, and examined under a microscope. Each chromosome pair is assigned a number (from 1 to 22, then X and Y) that is based on staining pattern and length. A karyotype is a representation of a person's chromosomes. The chromosomes are shown in pairs and arranged in order of decreasing size. Individual genes cannot be seen on karyotypes.
What to look for in a human karyotype
- Are there 46 chromosomes?
- Is there one pair of each autosome and 1 pair of sex chromosomes?
- Are there any deletions, rearrangements, or other abnormalities in the chromosomes?
Chromosomal notation : Karyotypes are presented in a standard form. First, the total number of chromosomes is given, followed by a comma, and the sex chromosome constitution.
Normal human female is designated as 46, XX
Human male with an extra chromosome 15 is designated as 47, XY, 15+
Human female with an extra X chromosome is designated as 47, XXX
There are many disorders that can be diagnosed by examining chromosomes. In Down syndrome , an extra chromosome 21 is present. In Turner syndrome , a sex chromosome is missing so that the individual has 45 total chromosomes. Fragile X syndrome , the most common inherited cause of mental retardation, takes its name from the appearance of the X chromosome.


10.4: Rubber and Other Elastomers
- Know the properties of rubber.
- Describe the process of vulcanization.
Natural rubber , also called India rubber or caoutchouc , as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds, plus water. Thailand and Indonesia are two of the leading rubber producers. Forms of polyisoprene that are used as natural rubbers are classified as elastomers.
Isoprene Polyisoprene (rubber)
Currently, rubber is harvested mainly in the form of the latex from the rubber tree or others. The latex is a sticky, milky colloid drawn off by making incisions in the bark and collecting the fluid in vessels in a process called "tapping". The latex then is refined into rubber ready for commercial processing. In major areas, latex is allowed to coagulate in the collection cup. The coagulated lumps are collected and processed into dry forms for marketing.
Natural rubber is used extensively in many applications and products, either alone or in combination with other materials. In most of its useful forms, it has a large stretch ratio and high resilience, and is extremely waterproof.
Vulcanization
In 1832–1834 Nathaniel Hayward and Friedrich Ludersdorf discovered that rubber treated with sulfur lost its stickiness. It is likely Hayward shared his discovery with Charles Goodyear, possibly inspiring him to make the discovery of vulcanization. Thomas Hancock (1786–1865), a scientist and engineer, was the first to patent vulcanization of rubber. He was awarded a British patent on May 21, 1845. Three weeks later, on June 15, 1845, Charles Goodyear was awarded a patent in the United States. It was Hancock's friend William Brockedon who coined term 'vulcanization'. Goodyear claimed that he had discovered vulcanization earlier, in 1839.
Sulfur vulcanization is a chemical process for converting natural rubber or related polymers into more durable materials by heating them with sulfur or other equivalent curatives or accelerators. Sulfur forms cross-links (bridges) between sections of polymer chain which results in increased rigidity and durability, as well as other changes in the mechanical and electronic properties of the material. A vast array of products are made with vulcanized rubber, including tires, shoe soles, hoses, and conveyor belts. The term vulcanization is derived from Vulcan, the Roman god of fire.
Synthetic Rubber
The expanded use of bicycles, and particularly their pneumatic tires, starting in the 1880s, created increased demand for rubber. In 1909 a team headed by Fritz Hofmann, working at the Bayer laboratory in Germany, succeeded in polymerizing isoprene, the first synthetic rubber. A synthetic rubber is any artifiical elastomer. These are mainly polymers synthesized from petroleum by products.
Polybutadiene rubber is a polymer formed from the polymerization of the monomer 1,3-butadiene. Polybutadiene has a high resistance to wear and is used especially in the manufacture of tires, which consumes about 70% of the production. Another 25% is used as an additive to improve the toughness (impact resistance) of plastics such as polystyrene and acrylonitrile butadiene styrene (ABS). Polybutadiene rubber accounted for about a quarter of total global consumption of synthetic rubbers in 2012. It is also used to manufacture golf balls, various elastic objects and to coat or encapsulate electronic assemblies, offering high electrical resistivity.
Neoprene (also polychloroprene or pc-rubber ) is a family of synthetic rubbers that are produced by polymerization of chloroprene. Neoprene exhibits good chemical stability and maintains flexibility over a wide temperature range. Neoprene is sold either as solid rubber or in latex form and is used in a wide variety of applications, such as laptop sleeves, orthopaedic braces (wrist, knee, etc.), electrical insulation, liquid and sheet applied elastomeric membranes or flashings, and automotive fan belts.Neoprene is produced by free-radical polymerization of chloroprene. In commercial production, this polymer is prepared by free radical emulsion polymerization. Polymerization is initiated using potassium persulfate. Bifunctional nucleophiles, metal oxides (e.g. zinc oxide), and thioureas are used to crosslink individual polymer strands.
Styrene-butadiene or styrene-butadiene rubber ( SBR ) describe families of synthetic rubbers derived from styrene and butadiene (the version developed by Goodyear is called Neolite ). These materials have good abrasion resistance and good aging stability when protected by additives. In 2012, more than 5.4 million tonnes of SBR were processed worldwide. About 50% of car tires are made from various types of SBR.
It is a commodity material which competes with natural rubber. The elastomer is used widely in pneumatic tires. Other uses include shoe heels and soles, gaskets, and even chewing gum.
Polymers in Paints
Polymers are one of the key components of modern paints that function as binders. The binder is the film-forming component of paint. It is the only component that is always present among all the various types of formulations. The binder imparts properties such as gloss, durability, flexibility, and toughness. Binders include synthetic or natural resins such as alkyds, acrylics, vinyl-acrylics, vinyl acetate/ethylene (VAE), polyurethanes, polyesters, melamine resins, epoxy, or siloxanes or oils.
Summary
The many uses of natural rubber has led to development and manufacture of synthetic rubber.
Sulfur vulcanization is a chemical process for converting natural rubber or related polymers into more durable materials by heating them with sulfur or other equivalent curatives or accelerators.
Three examples of synthetic rubber used in various applications are polybutadiene, polychloroprene (Neoprene), and styrene-butadiene rubber (SBR)


8.4: Treatments and Nutrition
By the end of this section, you should be able to:
- 8.3.1 Identify drug–food interactions for their impact on treatments used for endocrine disorders.
- 8.3.2 Identify treatments and medications that can cause nutritional deficiencies in clients with endocrine disorders.
Health Assessment Considerations
Not all foods are able to provide necessary nutrients, especially for individuals with endocrine disorders. Nutrition education plays a direct role in optimal health and wellness as well as in the management of disease processes because foods can either enhance or inhibit wellness in the endocrine system. Diet instruction requires careful explanation of scientific concepts in the context of the client’s specific situation. These concepts can seem overwhelming to the client who must balance evidence-based recommendations with real-world conditions. Clients’ food choices are not just by their knowledge of nutrition, but their ability to obtain and prepare nutritious foods that align with their culture and lifestyle.
Drug–Food Interactions Associated with Treatments for Endocrine Disorders
Endocrine-related medical interventions and medications are used to manage various endocrine disorders and conditions (Campbell & Jialal, 2022). These treatment options often involve the use of medications that interact with nutrition. Certain medications used in endocrine care affect nutrient absorption, metabolism, and utilization. These medications may also have specific recommendations regarding time frames with the food interaction. Nurses must understand these interactions to educate clients to avoid complications, promote optimal treatment outcomes, and ensure overall well-being.
Diabetes
Diabetes is an endocrine disorder that involves the amount of insulin the body creates, secretes, and utilizes (Sapra & Bhandari, 2023). The medications used to manage diabetes, such as insulin and oral antidiabetic medications, require careful observation, monitoring, and coordination with meals and carbohydrate intake to ensure proper blood sugar levels (Chen et al., 2020; Gray & Threlkeld, 2019; Pancheva et al., 2021; Rasmussen et al., 2020). When individuals take insulin incorrectly such that the dosage is not appropriate for the given amount of carbohydrates consumed, the individual can enter a state of either hypoglycemia (low serum blood glucose level) or hyperglycemia (high serum blood glucose level; Sapra & Bhandari, 2023). Health care providers may prescribe antidiabetic medications such as metformin to manage type 2 diabetes (Sapra & Bhandari, 2023). These medications need to be taken with meals to limit gastrointestinal adverse effects. Studies indicate that people who take metformin are at risk for vitamin B 12 deficiency (American Diabetes Association [ADA], n.d.). These individuals therefore need regular laboratory testing for B 12 deficiency.
Clients with diabetes need to understand how alcohol consumption affects their blood glucose levels. If an individual with diabetes drinks alcohol on an empty stomach or in excess, the liver cannot release stored glucose, resulting in hypoglycemia. Alcohol also impairs the body’s capability to indicate low blood glucose levels; for example, the individual may not experience the usual signs and symptoms of low blood glucose, such as shakiness or sweating. Alternatively, alcoholic drinks that contain sugary mixes potentially increase blood glucose levels. If clients with diabetes choose to drink alcohol, strict glucose monitoring and moderate consumption are recommended because excessive alcohol use is associated with increased liver, nerve, and heart damage. Some antidiabetic medications, such as sulfonylureas or insulin, interact with alcohol and increase the blood glucose–lowering effects of the medication, leading to hypoglycemia.
Some supplements, including chromium and niacin , may interact with diabetes medications and lead to hyperglycemia or hypoglycemia (ADA, n.d.). Chromium deficiency can increase blood glucose levels. In a client with kidney disease, chromium supplementation may further damage the kidneys (ADA, n.d.). Some individuals may take niacin to increase their “good” cholesterol levels; nurses should be aware that niacin can raise fasting glucose levels (ADA, n.d.). Individuals with diabetes should consult their health care provider before adding supplements to their daily dietary intake.
Thyroid Disorders
Thyroid conditions require individuals to take thyroid medications . Some medications for treating thyroid conditions are associated with potential nutritional interactions (Wiesner et al., 2021). Levothyroxine should be taken at a consistent time in the morning on an empty stomach 1 hour before a meal. Foods that interfere with absorption include soy, calcium supplements, and some fruit juices, including grapefruit, orange, and apple juice (Wiesner et al., 2021). Some clients who are prescribed levothyroxine concurrently take calcium to avoid osteoporosis, so the nurse should advise these clients to avoid taking calcium, as well as iron, supplements within 4 hours of taking levothyroxine because these supplements also reduce absorption of the medication (DailyMed, 2023).
Parathyroid Disorder
Calcium and loop diuretics balance sodium levels (Ellison, 2019). Loop diuretics inhibit the sodium–potassium–chloride transporter and increase calcium excretion. Furosemide increases calcium excretion and plasma parathyroid hormone (PTH) . This hormone is created in the four small parathyroid glands located near the thyroid. It regulates the homeostasis of calcium, vitamin D, and phosphate in the bloodstream, maintaining bone stability (Khan et al., 2022). PTH responds to low calcium levels detected in the blood and stimulates the production of vitamin D and calcitriol . The increase in calcium excretion from loop diuretics leads to the parathyroid gland decreasing the production of PTH. PTH, as the negative-feedback loop, signals the parathyroid glands to stop releasing PTH. A correlation has been noted between furosemide users and increased risk for hip fractures in the older adult female population (Mohn et al., 2018). Older adults absorb less calcium and are at an increased risk for fractures.
Thiazide diuretics affect the distal tubules, leading to increased calcium reabsorption (Mohn et al., 2018). A correlation study showed that individuals who took hydrochlorothiazide also had a decrease in urinary calcium in hyperparathyroidism, with no change in PTH observed (Mohn et al., 2018). However, more research is recommended in the field of thiazide diuretics and risk factors for fractures in the older population.


1.7: Mesoamerica – Aztecs, Mixtec, Maya (1400-1521 CE)
Introduction
When Europeans arrived in Mesoamerica, the Aztecs were one of the most powerful Empires of the Americas, ruling an extensive area in central and southern Mexico and south into Guatemala. They were known as the Mexica, a nomadic people from Aztlan who spoke the Indigenous language, Nahuatl. We know them by the name Aztecs today due to a nineteenth-century German explorer named Alexander van Humboldt. In 1325, the Aztecs settled and built the magnificent city of Tenochtitlan on a swampy island on Lake Texcoco. The founding legend of Tenochtitlan was based on a prophecy of Huitzilopochtli, a chief god among their pantheon of gods. He directed the Aztecs to settle and build their city, where they saw an eagle on a prickly pear cactus emerging out of a rock. The name Tenochtitlan comes from the Nahuatl words tetl, meaning rock, and nochtli, which means prickly pear, a symbol used regularly.
The Aztecs drained parts of the swampy lands, built islands, and created acres of agricultural land. They also became the dominant force in the region in the 1400s, conquering other territories and building robust trading routes and partners. The civilization was based on a caste system; rulers, nobles, priests, merchants, farmers, servants, and the lowest group – the slaves. The Aztecs formed alliances with some groups and subjugated other groups by requiring tax, tribute, and sacrificial victims. They were feared throughout Mesoamerica. Historians believe the overall territory Aztecs controlled included almost twelve million people. Often, they started wars, known as the flowery wars, to obtain sacrificial victims. Religion and religious rites, including human sacrifices, were an essential part of life and society. They constructed temples, statues, buildings, or homes, all dedicated to specific gods or goddesses who controlled all aspects of Aztec life.
Codices
Much of the Aztec empire is lost to scholars today; they generally believe only about 5% of the Aztec world remains, the loss from the conquest of the Aztecs by Hérnan Cortés, one of many Spanish conquistadors. Today, we rely on primary documents sent from the Spanish conquistador and his men back to Spain; most of the known information about the Aztecs comes from Spanish chronicles and records. The authentic facts, values, and beliefs of the Aztecs were interpreted and rewritten by the Spanish. Pre-conquest or Indigenous codices, hand-written and adorned books, document the shared cultural features of the Aztecs along with other civilizations and allies of the Aztecs. It's crucial to comprehend the values and beliefs of the Aztecs to understand the consequence of Spain's arrival on art and architecture.
In Mesoamerica, the Indigenous cultures of the Maya, Mixtec, and Aztec painted pictorial manuscripts known as codices to record and preserve calendrical, genealogical, historical, ritual, geographical, and divinatory knowledge. [1]
These manuscripts also include references to the basic Mesoamerican belief system – the people needed to balance opposing forces, such as life and death. The ritualistic sacrifices helped keep the forces of their pagan gods in balance and would ensure that life would continue due to the favors that the gods would grant to the people in response to the sacrifices offered.
Scholars believe twelve to fifteen codices survived--the codices had various cultural influences in common, including glyphs used in writing, abstract artistic styles, and subjects. Though some of the techniques varied slightly, they did have different writing systems. Generally, artists who created pre-Hispanic codices, or manuscripts, focused on concept and convention over illusionism. The codices were typically made from deer hide, paper made from the Agave plant, or bark paper. The two-dimensional, conceptual manuscripts were created in the Americas while European artists created some of the tremendous illusionistic masterpieces of the European Renaissance related to the Christian religion.
The Borgia Codex (1.7.1), which includes a page depicting the pagan deities Miclantecuhtli and Quetzalcoatl, is an example of pre-Columbian era codices. It is unclear which specific group created this codex, but there are shared stylistic features with the manuscripts produced by the Mixtec. On the page illustrated here, we see two primary deities of the Indigenous cultures – the god of life, Quetzalcoatl, is a black-masked human, who sits with its back Mictlantecuhtli, the god of death, who is shown as a white figure, like a skeleton. A depiction of the underworld, known as Mictlan, is below them (appearing like teeth or mouth of a great earth monster). Both of the gods, Miclantecuhtli and Quetzalcoatl, are vividly gesticulating. Overall, with the god of life back-to-back with the god of death, we are introduced to one of the main themes of the Indigenous cultures of Latin America – the inevitable relationship between life and death. The religious rituals and beliefs of balance between life and death are symbolized here. The symbols of the thirteen, 20-day divisions of the 260-day Mesoamerican ritual calendar are in the margins. Although most coded information is still poorly understood, historians recognize the connection between life and death and the mathematical advancements seen with dots and lines.
Once one of the greatest civilizations of the Americas, the Maya civilization was based in Yucatan at the time of Spain's arrival (Post-Classic period). The prosperity and influence of the Maya's high point date from 150 CE but declined when the Europeans arrived. Although the cause of the decline is unknown, it was probably around 900 CE when wars broke up centralized power centers into a village-based agricultural system before the Spanish arrived. It took the Spanish 170 years to establish control over the Yucatan because no single political center existed like other major Indigenous groups in the Americas.
The Maya were a complex civilization and made significant achievements in astronomy and math, as demonstrated by the manuscripts, achievements closely related to their pagan religious beliefs. Maya codices include their history but also astronomical tables, religious rituals, and calendrical calculations. The Maya thought of time as cyclical, and their very complex solar and sacred calendars revolved in a cyclical format. It is believed that only three or four original Maya codices exist. Today the manuscripts are viewed from an art-historical perspective. Still, they probably functioned as utilitarian or religious at the time of their creation, especially when considering the more sacred manuscripts. These manuscripts were read by priests conducting religious ceremonies.
In the Dresden Codex (1.7.2), standard glyphs are found in the writings. Glyphs were characters in Maya writing and complex to "read." Depending on the context of the text, one glyph character can refer to several different words. Glyphs were used in connection with lines (representing the count of 5) and dots (representing the count of 1) to calculate dates and movements of celestial bodies –all tied to religious beliefs. The Dresden Codex depicts pagan gods and rituals associated with astronomical calculations to assist daily life and agriculture. When the Spanish arrived, there were 40 million people who spoke more than 1000 languages throughout the Americas. Glyphic writing may have been a valuable communication tool between the cultures in Mesoamerica that spoke several languages. The Dresden Codex also demonstrates the achievement of using zero and place notation in mathematics – familiar to the Maya. Many of these pages are highly coded, symbolic, and misunderstood today. The Dresden Codex is believed to be a copy of an original text from around 700-900 CE.
The Mixtec culture, located in southern Mexico in the current states of Oaxaca, Puebla, and Guerrero, included multiple territories with different ruling families in each region. There is evidence of a friendly relationship between the Mixtec and Aztec. Surviving manuscripts from these cultures demonstrate similarities and connections, making it difficult to ascertain precisely who the manuscript was for, Aztecs or Mixtec. Examination of the art styles reveals the manuscripts were created before the arrival of the Spanish and lacked any European influence, such as shading.
In the Codex Vindobonensis (1.7.3), the abstract style of the Indigenous cultures is present. The figures have a bold outline, are flatly painted, and are not proportionate. Images are painted on both sides of the prepared deerskin. This manuscript documents the Mixtec ruling families and the early history of the Mixtec culture; red lines help to guide the "reading" of these images from right to left. Throughout the manuscript, the dots and glyphs represent important dates of ruling figures.
The Codex Borbonicus is one of the most famous Aztec ancient manuscripts, and historians believe the codex was written before or during the Spanish invasion. The imagery was painted on bark paper and arranged accordion-style with folded pages. Today, it is 14.2 meters long. Initially, the codex contained forty pages; however, the first and last two pages are missing over time. The actual use of the codex is unknown; however, researchers suggest the book was used for astrological information and the celebrations for different periods. The Aztecs shared many of the religious beliefs of other Mesoamerican cultures, including a similar 260-day Sacred Year and a 365-day Solar Year, seen in the Codex Borbonicus . The sacred year is "a 260-day sacred almanac…in which 20 named days were paired with 13 numerals, each advancing one count per day. Within this cycle, the sequence of numerals would repeat 20 times, each of these 13-day periods constituting a trecena…" [2] (Trecena was a word used by the Spanish conquerors to define the periods in the codex.) The Solar calendar was made up of 20 named days, of 18 numerals – with five days considered bad days, added to the end to create a 365-day year.
Page 12 (1.7.4) illustrates the different days representing the trecena along the bottom and right side, each one associated with some sort of god or bird. A dot defined the number of the days, and the image portrayed the name of the day. The first-day sign is one dot and the symbol for earthquake, the second with two dots and a knife, and the third have three dots and the character for rain. The large square was illustrated with images of the deity that sponsored the trecena; on the left side is the goddess Tlazolteotl who is giving birth.
Page 13 (1.7.5) is similar; in the first box is the head of a dog and one dot, the next box has two dots and the image of a monkey. The large square illustrates the deity who sponsors this trecena, Xipe Totec, and Quetzalcoatl. Priests are believed to use the twenty-six symbols to predict the future and produce horoscopes.
The next section of the codex defined the order for the fifty-two-year solar year cycle, documenting the first day of each year. Today, the system is known as the calendar round. It comprises three interlocking cycles, a 365-day solar year, a cycle of 20 names, and thirteen numbers. Days are named by the way they line up. The Aztec and other groups believed nine gods controlled every ninth night, defined as the Lords of the Night. The lords determined a good or bad fortune for the night they ruled, the days in the fifty-two-year cycle based on these Lords of the Night. The final section of the codex was based on ceremonial rituals needed by the end of each cycle. This section is believed to be incomplete.
The Codex Borbonicus was made of amatl paper from the fig tree bark and used throughout Mesoamerica to create thousands of books. How the paper was made is unknown; however, historians believe they soaked the fibers before pounding them into flat sheets.
The pigments of color were made from natural materials; "wild holly root (mustard color), red juniper root and Hematite (red), yellow sweet clover (yellow), prickly pear cactus fruit (tan), and red onion skin (green) are bright and vivid, with red, green, tan, and gray predominating." [3]
After the Spanish invasion, this type of paper was forbidden; only the European-approved material was allowed. The amatl paper was an essential part of Aztec writing.
Thousands of cultural documents were destroyed by the invaders, leaving few surviving works. When the European missionaries came to Latin America, the codices were filled with information viewed paganism and devil worship. The documents were a hindrance to the conversion efforts of the Spaniards, who conducted mass manuscript burnings throughout Mesoamerica. This loss of a great deal of information is a true tragedy and part of the destruction by the Spanish conquest of Latin America. The manuscript painting did not end with the book-burning; however, the Spanish Colonial era changed subject and style significantly. After the conquest, new books were created with European influences.
Aztec Empire
Hernán Cortés arrived in the Americas in 1519, following the footsteps of many explorers before him. He landed on the eastern coast of Mexico, where he was first met by the Tabascans, a local coastal tribe. The Tabascans provided Hernán Cortés and his men with supplies, slaves, and women hoping the intrigue and wealth of the Aztecs would be more appealing to the Spanish than their territory. One of the women given to Cortés was named Malinali, later known by her Spanish name, Doña Marina. Today she is referenced as La Malinche and historically seen as a traitor – a complicated figure in history. She is notable because she understood her position, had a facility with language, and became Cortés' main translator. Surviving works of art depict her as an important figure of the conquest.
When Cortés and his men first laid eyes on the Aztec city of Tenochtitlan in November of 1519, they were amazed. The city's population was over two hundred thousand people or more- one of the largest in the world at the time! Known in English as "the Letters of Cortés," he wrote a letter to the king of Spain and said, "The city is as big as Seville or Cordoba. The main streets are extensive and very straight; some of these are on the land, but the rest and all the smaller ones are half on land, half canals where they paddle their canoes." [4] He continued to write about the riches in the city and the extensive marketplace where thousands of people came daily, selling and buying jewelry and ornaments of all kinds made from colorful feathers, shiny gold, and silver, bones, or stone. Cortés had entered Tenochtitlán, the massive Aztec city constructed by the lake. (1.7.6).
The impression the Aztec capital made on the Spaniards is further evidenced by chronicler Bernal Diaz de Castillo, who wrote, "When we saw so many cities and villages built in the water and other great towns on dry land we were amazed and said it was like the enchantments . . . on account of the great towers and cues and buildings rising from the water, and all built of masonry. And some of our soldiers even asked whether the things that we saw were not a dream? . . . I do not know how to describe it, seeing things as we did that had never been heard of or seen before, not even dreamed about." [5]
Aztec art was based on the multiple artistic civilizations that preceded them, including making incredible stone sculptures, monumental architecture, and art related to the people, environment, and deities, frequently fashioned into abstract images. The Aztecs were masters of gold objects with few artifacts surviving the Spanish invasion. In an infamous quote by Cortés, he boasted that his men "suffer a disease of the heart that can only be cured with gold." Most of the small gold and silver metal works sculptures were melted down to fund the Spanish for various Christian conquests. Artifacts of stone sculpture and architecture were found documenting the Aztec beliefs and a wide variety of deities. Art was used reinforcing status, power, and religious beliefs, conveying the stories of the culture. Notably, many of the works of art reflect the values and beliefs of the Aztecs, especially the need for sacrifice.
Aztec Architecture
The Templo Mayor (1.7.7) was the heart of the capital city of Tenochtitlán. The Templo Mayor consisted of two temples on top of a pyramidal base (the pyramid base does not come to a point). One temple was dedicated to the God Tlaloc, associated with rain, and God Huitzilopochtli, the god of war and the sun. During the rainy season, the sun rose behind Tlaloc's temple, and during the dry season, the sun rose behind the temple of Huitzilopochtli. The most important rituals took place in Templo Mayor, including naming their leaders and religious ceremonies. A total of seven building phases were discovered incorporating temples built over previous temples, or an expanded façade, eventually ending with the most prominent, seventh temple. As the Aztec Empire increased, so did the expansion of the Templo Mayor. In each addition, captives from subjugated tribes could be sacrificed. The version seen by the Spaniards rose 39.6 meters in height, and the higher a person or a sacrificial victim climbed to the top of the pyramidal structure, the steeper the slope became. This change in slope partly enhanced the sense of awe people had when they reached the top and made sacrificial victims dizzy as they were brought to be sacrificed. The victims were also starved and drugged to subdue them in their final hours.
Because of the connection with religious rituals and sacrifice, and in his quest to Christianize the Aztecs, Hernán Cortés destroyed the Aztec city. They built what is now Mexico City – literally on top of the old Aztec capital. In the 1970s, authorities were repaving streets in Mexico City and discovered the Templo Mayor's ruins (1.7.8). Today, the top of the pyramidal base is visible, with temples of Tlaloc and Huitzilopochtli (covered by the green roof in the background).
The Templo Mayor was only one of many structures that made up the spiritual center of the city. Other vital buildings included temples to other deities, like Quetzalcoatl, and a ball court. The ball courts held a unique ball game played by indigenous cultures of Mesoamerica, each with a different format and rules. Sometimes those who won the ballgame were sacrificed and viewed as an honor, or those who lost were sacrificed. Which group was officially sacrificed is unclear because several diverse civilizations played different forms of the game. Although the ball court no longer survives in the Aztec capital, they are found in other Mesoamerican areas not as dominated by the Spaniards, for example, in the Mayan city of Chichen Itza (1.7.9). Skull racks often were placed near ball courts. Known as tzompantli , they displayed the skulls of sacrificial victims. Although it is an uncomfortable truth, the remains of sacrificial offerings are well documented in the second largest temple of the Aztec capital region, Tlateloco, and in the National Museum of Anthropology, Mexico City.
The excavated House of the Eagles also has evidence of sacrifice, not only in blood found in the temple but also in the artwork portraying Eagle warriors' self-sacrifice. Merging sculpture and architecture, the carved bas-relief banquets (1.7.10) depict armed warriors on either side of what represents a ball of dried moss or grass to hold the bloody spikes used in self-sacrifice.
Aztec Sculpture
Making stone sculptures was a tradition in Mesoamerican cultures, carving multiple materials found in local areas. The Aztecs continued with the stone sculptures making thousands of different statues, small personal items, or monumental temple works. Although the Spanish tried to demolish most of the sculptures when they invaded, many still survived. Images and sculptures of religious deities, made for personal use or religious ceremonies, formed the most significant number. The sculptors had to follow specific standards for the deities, which were very symmetrical in a frontal position. "Females are frequently kneeling, their hands resting on their knees, while male figures are often sitting with their knees drawn up and their arms crossed upon them. Ageless faces – inlaid eyes and half-open mouths lend them a lifelike look…" [6] On the primary image, sculptors added features from animals, ornaments, headdresses, or other decorations. The artists only had stone and wooden tools for carving with sand and water to help smooth the stone.
When different areas were excavated, they found beautiful works of art between buildings, some probably never seen by Hernán Cortés or his men. For example, in stage three, eight sculptures were found in a row (1.7.11), leaning against a staircase (three reproductions are shown in the image). Historians believe the sculptures represent the stars, siblings of Huitzilopochtli and Coyolxauhqui, and sons of Coatlicue.
The sculpture of Coatlicue (1.7.12), a Nauhatl word meaning "She of the Serpent Skirt," is one of the more famous surviving works, standing at an imposing almost three meters tall. The statue leans forward with her arms pulled in. Snakes from her skirt, belt, and head and seem to slither across the figure. She is wearing a huge necklace depicting a skull, hands, and hearts. Beneath her necklace is two flaccid breasts, a symbol of motherhood. Two enormous snakes curl upwards from her severed head to face one another. Their bifurcated, or split, tongues curl downwards; the resulting effect of the snakeheads and tongues appear to be a single, forward-facing serpent face. As we see here, snakes coming out of body parts was an Aztec convention for squirting blood. Coatlicue was decapitated, and her snaky head represents the blood squirting from her severed neck.  Her arms are also formed of snakeheads, suggesting she was dismembered there as well. [7]
Coatlicue is a potent visual expression of the Aztec beliefs; legends say she was a guardian princess of a shrine. While cleaning the shrine, Coatlicue miraculously became pregnant with Huitzilopochtli. To restore the honor of the family, her 400 sons and one daughter (Coyolxauqui) banded together to kill her.  He threw her head to the sky so his mother could remember her daughter – now known as the moon goddess--and threw the rest of her body down the temple stairs. Originally painted and sculpted on all sides, this image would have captivated those who worshiped the statue. Drawings completed in the early nineteenth century show a figure carved in low relief at the sculpture's base (1.7.13), seen in the reproduction. Historians believe the crouching figure carved on the bottom is an image of the earth deity and perhaps is a portal to the underworld.
A large stone disc, found between building stages of the Templo Mayor, represents Coyolxauhqui (1.7.14), an Aztec Nahuatl word for "She of the Golden Bells." Based on the specific ritual, historians believe sacrificial victims' bodies were thrown down the temple's steps and would land on this gruesome disc of the dismembered Aztec goddess. The Coyolxauqui stone is one of the few original large-scale Aztec sculptures perfectly capturing the Aztec view of their deities, a dismembered body, and representations of skulls. Coyolxauqui's depiction, along with Coatlicue, demonstrates the awesomeness and fear Aztecs felt toward their deities. Although these works of art are sculptures, they are in bi-level relief, enhancing the two-dimensional effect viewed in indigenous manuscripts. Although Hernán Cortés probably never laid eyes on the sculpture of Coyolxauhqui, he did bury Coatlicue after the statue's discovery. The large sculpture of Coatlicue has been subsequently buried, unburied, and reburied several times. Today, both works of art are displayed in Mexico City.
One of the most well-known Aztec sculptures is the Sun Stone (1.7.15) and was initially discovered near the Templo Mayor in 1790. The Sun Stone is a stone carved into a solar disk to represent the myth of five suns – four suns of the universe imperfectly made seen in the squares around the central circle, and the fifth sun, seen in the center disc, in which the Aztecs existed. The center face is shaped like an obsidian blade as a tongue – a reference to the need for human sacrifice for the sun to rise. The claws on either side of the face do not belong to the sun and represent the hearts offered to the sun; framing the face is the symbol of Ollin (movement). The boxes correspond to previous suns: 4-tiger, 4-wind, 4-rain, and 4-water; the previous worlds were destroyed based on these symbols (wind, rain, etc.). According to legend, earthquakes (movement) will destroy the world of the fifth sun. Some historians are not sure which world is in the center and might be either the day sun, the night sun, or the earth monster. Two jaguar heads and two serpents' heads move outward, while the next band around the center represents the 20 names for the days surrounded by fire serpents. The glyph at the very top represents the date 13-Reed (1427), the date of the fifth sun. It is unknown whether the stone was a tribute to a god or perhaps a sacrificial altar.
Small Carved Aztec Statues:
Maize and chocolate were two of the important plants used by the Aztecs, most notably in religious rituals and frequently reflected in their sculptures, along with other food items. The man (1.7.16) holding the oversized cacao pod is a stone sculpture representing one of the merchants transporting the cacao from the lowlands to the valley. Merchants were frequently part of a higher status and demonstrated economic power. Drinking chocolate made from cacao was a privilege enjoyed by the elites, warriors, merchants, priests, and nobles. It was noted, "The common folk, the needy did not drink it." [8] The statue was made from a volcanic stone with some red and white pigment remains, indicating the sculpture was painted.
Dogs were significant to Mesoamericans and were companions to humans as well as a source of protein. Xolotl (1.7.17) was the god who was associated with lightning and death. He was frequently depicted with a dog's head, the canine brother of Quetzalcoatl, and protector of the sun from the underworld. Dog sculptures were often found in burials to help their owners cross the river of the underworld.  His ears are generally ragged, and his teeth symbolize fangs.
Xiuhcoatl (1.7.18) was the mythological serpent, a fire deity, and a common representation in Aztec art. The serpent is shown with a curved snout, short legs with claws. The segmented body has a tail shaped into a triangle representing the solar rays and two trapezes the symbol for a year. The sculpture was probably part of a temple façade.
The Chacmool (1.7.19) is a sculptural form always made in the same position; the form is reclining, the head turned towards the front, elbows supporting the figure, and a bowl sitting on the chest. This Chacmool was found in the Great Temple, associated with the rain god. The bowl was used to place sacrificial items from feathers to food to human hearts. Carved from stone, some of the original paint remains on the figure. He is staring straight ahead, mouth open to expose his teeth, anticipating the sacrifice. Shared cultural features exist among various groups of Mesoamerica, and Chacmool sculptures were also found in Maya territories.
This female sculpture appears seated and wearing a simple skirt and belt. The detailed face with its huge eyes, exposed teeth, disheveled hair, and clawed hands demonstrate the potential fierceness of the demon. The Cihuateteo (1.7.20) came to earth on five specific days, haunting places associated with evil and escorting the sun each day as it traveled through the underworld before dawn. If a woman died in childbirth, her soul became one of these demons. This type of figure was found throughout Mesoamerica.
Chicomecoat (1.7.21) was a goddess responsible for the viability of corn and other edible crops. Wearing a long skirt, she holds ears of maize in one hand, with a large headdress. The headdress has a quadrangular shape and was called the amacalli or paper house. This type of adornment was common for a corn goddess, and during celebrations, representations of the headdress were made from bark and worn by celebrants. The statue was made from a flat stone slab, retaining the angular shape except for the rounded face peering out of the middle.
Aztec Featherwork
Featherwork was one of the most prestigious art forms. The amantecas (feather artists) were the most respected, well-paid artists and considered upper class. The amantecas formed into guilds and worked for the rulers, priests, and elites of the empire. The workers used multiple methods to work with the feathers and attach them, including sewing, wrapping with agave cord, and a form of glue or crimping. The mosaic technique was used for shields, clothing, or flat surfaces using fragments of feathers, the lesser quality of feather on the first layer, and the prized feathers for the top.
Birds were raised in aviaries, or the feathers had to be imported. Colorful birds lived naturally in the area, and the brighter the feather, the more value it carried. Macaw feathers were highly desired with bright red, blue, yellow, or green colors, but the Quetzal was the most treasured, producing vibrant green or blue colored feathers. Some documentation told stories of Moctezuma II carried by servants on a litter decorated with brilliant quetzal feathers and string of gold tassels to meet Cortés. In the Letters of Cortés, he writes to the king of Spain about the magnificent aviary of Moctezuma II and the spectacular featherworks.
The shield (1.7.22) with the pattern of meander and sun was a common theme. The design was a 'step fret' and resembles the Greek key design. Although historians do not know the actual meaning of the image, Aztecs used the method on everything; shields, clothing, sculptures, murals, and ceramics. The design was usually replicated several times; however, there is only one iteration on the shield. The shield was covered in feathers from less colorful birds, probably made for a lower-level warrior.
The most well-known surviving artifact is the Moctezuma headdress (1.7.23), although historians are not sure he or a surviving example wore it. The headdress had over 400 tail feathers from the Quetzal and other feathers from the Cotinga, Spoonbill, and Cuckoo, all attached to a net of fibers. The front was adorned with gold, including a bird's beak made of gold; unfortunately, it was lost.
A post-conquest page from the Codex Mendoza (1.7.24) illustrates feathers in the ornamentation of warriors' gear. Elaborate shields, headdresses, and banners were decorated with feathers as the warriors' scout a town in preparation for an attack. The high-ranking commanders on the bottom wear the most elaborate featherwork.
Gold
Gold was a significant metal for the Aztecs, who made thousands of pieces out of gold; unfortunately, gold was also one of the reasons for the invasion of the Europeans into Mesoamerica. The invaders took almost all of the Aztec gold art, melted it into ingots for easy transportation, and shipped them back to Europe. "Gold, in Aztec belief, was teocuitlatl, a godly excrement, closely associated with the sun's power, and ornaments made of it were worn by Aztec rulers and nobles." [9] The labret (1.7.25) was a plug made to be inserted into a hole pierced in the lower lip. The serpent has serrated teeth and fangs and a prominent nose. The oversized tongue was made to move back and forth as the person moved, adding to the snake's power. On the back of the plug is a flange that held the plug in the person's mouth. The labret was worn by an important noble or warrior, illustrating the importance of the person. Using a lost-wax method, the labret was made with melted metal in a mold and the finished gold highly polished.
The gold necklace (1.7.26) has thirty-four beads formed like the molars of a jaguar and thirty-four small bells. The beads were made with the lost-wax method, the bells attached with a filigree. The necklace was found in a tomb along with actual jaguar teeth, demonstrating the respect the Aztecs had for this animal with its powerful jaws, able to pierce through the skull of its prey with one bite. The jaguar warriors were the elite, wearing pelts and headgear resembling the jaguar. Someone of high status and importance wore this necklace.
Multiple animals were used as inspirations for necklaces, including the frogs, who were associated with fertility, water, and rain. Using the lost-wax method, each small frog (1.7.27) was made in a clay mold with slight differences in each figure. When the Spanish came to Mesoamerica, they were offered many of the exquisite ornaments of gold; however, the Spanish were only interested in melting the gold into ingots. Most of the surviving gold works were found in hidden places or undiscovered tombs.
Black-on-orange Pottery
The skill and methods to make pottery was passed through the potters, defining the clay recipes, how vessels were fired, or the shape of a bowl or pot. Different types of clay were plentiful in the lakes, and the recipe for pottery usually mixed one kind of clay with a sandier form to aid in its stability. They did not use a potter's wheel and formed clay by hand or in molds. Most of the vessels were made for cooking or eating, the earlier forms rounded as in the distinctive ollas used over fires to cook beans or maize. Generally, not covered with slip, the pottery was fired in updraft kilns or open-pit kilns, both using low temperatures.
The Aztec made decorative pottery; some covered with a simple red slip to polychrome ware covered with a white or orange-colored slip and painted with black, brown, red, or orange designs. The most well-known was the 'black on orange,' which had an orange slip and then painted with decorations in black. The simple bowl (1.7.28) was probably made for everyday use and painted with a scroll design on the sides.
The plate (1.7.29) was covered in orange slip and then painted with a black and white design of the nagual – the human who can transform into an animal form, and on this plate, it takes the form of a coyote. Decorated ceramics were used in Aztec culture as serving dishes at festivals and ordinary meals. The presence of Black-on-orange ceramics at Late Aztec sites ranging from the smallest communities to Tenochtitlan indicates that Black-on-orange pottery was not exclusively for high-status households but rather was available to commoners as well as to cities. [10]
Large numbers of animal-shaped vessels were found throughout the area, usually used for ceremonial purposes. The animals represented some part of the cultural beliefs and were associated with cosmic definitions. Birds represented the celestial realm, messengers between those on earth, and astrological events. The bird on the tripod vessel (1.7.30) is covered with shiny red, black, and matte feet. Supporting legs and tail represented the king vulture.
Although king vultures feed primarily on carrion, they will occasionally kill for food; they are therefore connected with human sacrifice in ancient Mexican thought. The rendering of the bird includes three significant human aspects: from its projecting "ear" flanges hang pendant ornaments; its talons are shown as hands with prominent thumbs; and its head is adorned with a pleated paper fan often seen on headdresses of Aztec deity figures. The contours of the vessel are well-balanced—the lines of the sloping wings echoing the angles of the legs—and the bulging chest of the bird is perfectly centered between its strong legs. [11]
Much Aztec art was lost, destroyed, or buried; fortunately, the artifacts buried in tombs or under buildings are the survivors of the period. Much of Mexico City covers the great Templo Mayor, a major part of the city of Tenochtitlan. Today, the area around the Templo Mayor and many other areas in Mesoamerica are under excavation, and further study by archaeologist may lead us to have an even greater understanding of the magnificent cultures of the beautiful cultures Mesoamerica.
[1] Retrieved from https://www.lib.uci.edu/sites/all/ex...so/sacred.html "Realms of the Sacred in Daily Life: Early Written Records of Mesoamerica." Realms of the Sacred in Daily Life: Early Written Records of Mesoamerica . The Regents of the University of California, 2009. Web. 1
[2] Pool, C., Kidder, B., UKnowledge, A Glimpse into Ancient Mexico: Writings of the Aztecs, Mixtec and Maya. Retrieved from https://uknowledge.uky.edu/world_mexico_codices/9/ .
[3] Retrieved from http://mati.eas.asu.edu/chicanarte/html_pages/CodexIssOutl.html .
[4] Retrieved from https://www.livescience.com/34660-tenochtitlan.html
(From “An Age of Voyages: 1350-1699,” by Mary Wiesner-Hanks, Oxford University Press, 2005).
[5] Retrieved from: https://www.oercommons.org/coursewar...tudent/?task=4
[6] King, Heidi. “Aztec Stone Sculpture.” In Heilbrunn Timeline of Art History . New York: The Metropolitan Museum of Art, 2000–. http://www.metmuseum.org/toah/hd/azss/hd_azss.htm (October 2003)
[7] Retrieved from https://www.khanacademy.org/humanities/art-americas/early-cultures/aztec-mexica/a/coatlicue .
[8] Moran, E., (2016). Sacred Consumption: Food and Ritual in Aztec Art and Culture, University of Texas Press, p. 45.
[9] Retrieved from https://www.metmuseum.org/art/collection/search/321343?searchField=All&sortBy=relevance&ft=aztec+gold&offset=0&rpp=20&pos=10 .
[10] Hodge, M.G., Hector N., Blackman, M. J., Minc, L. D., Latin American Antiquity , Black-on-Orange Ceramic Production in the Aztec Empire’s Heartland, June, 1993, 4(2), p. 134.
[11] Retrieved from. https://www.metmuseum.org/art/collection/search/314365?searchField=All&sortBy=relevance&ft=aztec+ceramic&offset=0&rpp=20&pos=5 .


6: Astronomical Instruments
If you look at the sky when you are far away from city lights, there seem to be an overwhelming number of stars up there. In reality, only about 9000 stars are visible to the unaided eye (from both hemispheres of our planet). The light from most stars is so weak that by the time it reaches Earth, it cannot be detected by the human eye. How can we learn about the vast majority of objects in the universe that our unaided eyes simply cannot see?
In this chapter, we describe the tools astronomers use to extend their vision into space. We have learned almost everything we know about the universe from studying electromagnetic radiation, as discussed in the chapter on Radiation and Spectra. In the twentieth century, our exploration of space made it possible to detect electromagnetic radiation at all wavelengths, from gamma rays to radio waves. The different wavelengths carry different kinds of information, and the appearance of any given object often depends on the wavelength at which the observations are made.
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- 6.2: Telescopes
- A telescope collects the faint light from astronomical sources and brings it to a focus. Light is then directed to a detector, where a permanent record is made. The light-gathering power of a telescope is determined by the diameter of its aperture, or opening—that is, by the area of its largest or primary lens or mirror. The primary optical element in a telescope is either a convex lens (in a refracting telescope) or a concave mirror (in a reflector) that brings the light to a focus.
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- 6.3: Telescopes Today
- New technologies for creating and supporting lightweight mirrors have led to the construction of a number of large telescopes since 1990. The site for an astronomical observatory must be carefully chosen for clear weather, dark skies, low water vapor, and excellent atmospheric seeing (low atmospheric turbulence). The resolution of a visible-light or infrared telescope is degraded by turbulence in Earth’s atmosphere. The technique of adaptive optics can make corrections for this turbulence.
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- 6.4: Visible-Light Detectors and Instruments
- Visible-light detectors include the human eye, photographic film, and charge-coupled devices (CCDs). Detectors that are sensitive to infrared radiation must be cooled to very low temperatures since everything in and near the telescope gives off infrared waves. A spectrometer disperses the light into a spectrum to be recorded for detailed analysis.
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- 6.5: Radio Telescopes
- A radio telescope is basically a radio antenna connected to a receiver. Significantly enhanced resolution can be obtained with interferometers, including interferometer arrays like the 27-element VLA and the 66-element ALMA. Expanding to very long baseline interferometers, radio astronomers can achieve resolutions as precise as 0.0001 arcsecond. Radar astronomy involves transmitting as well as receiving. The largest radar telescope currently in operation is a 305-meter bowl at Arecibo.
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- 6.6: Observations outside Earth's Atmosphere
- Infrared observations are made with telescopes aboard aircraft and in space and from ground-based facilities on dry mountain peaks. Ultraviolet, X-ray, and gamma-ray observations must be made from above the atmosphere. Orbiting observatories have been flown to observe in these bands of the spectrum. The largest-aperture telescope in space is the Hubble Space telescope, the most significant infrared telescope is Spitzer.
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- 6.7: The Future of Large Telescopes
- New and even larger telescopes are on the drawing boards. The James Webb Space Telescope, a 6-meter successor to Hubble, is currently scheduled for launch in 2018. Gamma-ray astronomers are planning to build the CTA to measure very energetic gamma rays. Astronomers are building the LSST to observe with an unprecedented field of view and a new generation of visible-light/infrared telescopes with apertures of 24.5 to 39 meters in diameter.
Thumbnail: This artist’s impression shows the Hubble above Earth, with the rectangular solar panels that provide it with power seen to the left and right.


1.14.17: Energy and Entropy
This Topic takes a rather different approach from the other Topics in this Notebook. Across the galaxy of terms used in thermodynamics, two terms stand out, namely Energy and Entropy . With respect to a given closed system, both terms describe extensive properties, using the letter \(\mathrm{U}\) to identify energy and the letter \(\mathrm{S}\) to identify entropy.
The term ‘energy’ is used quite generally in everyday life. One dictionary [1] describes energy as ‘the power and ability to be physically active’. Perhaps we might not be too happy at the use of the term ‘power’ in this context on the grounds that this term is normally linked to the rate at which energy is supplied [2]. Indeed in every day life we refer to powerful engines in, for example, fast sports cars. Nevertheless in a thermodynamic context the concepts of energy and energy change are part of the language of chemistry; e.g. bond energy, energy of activation, radiant energy… The First Law of Thermodynamics formalises the concept of energy change using the following ostensibly simple equation.
\[\Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \nonumber \]
Here \(\mathrm{U}\) is the thermodynamic energy, a function of state; \(\Delta \mathrm{U}\) describes the increase in thermodynamic energy of a closed system when heat \(\mathrm{q}\) flows from the surroundings into a given system and work w is done by the surroundings on that system.
The distinction between heat and work is crucial. There are many ways in which the surroundings can do work on a system. Caldin [3] lists many examples in which work is given by the product of Intensity and Capacity Factors; e.g. intensity factor pressure, \(\mathrm{p}\) and capacity factor volume, \(\mathrm{V}\) such that \(\mathrm{w}=\mathrm{p} \, \mathrm{dV}\).
In the context of energy, chemical thermodynamics quite generally describes quite modest changes in energy. Even in the case of an explosion involving, for example, ignition of a mixture of hydrogen and oxygen gases, the energy change turns out to involve transitions between electronic energy levels in atoms and molecules. Much more dramatic are nuclear reactions which involve the conversion of mass, \(\mathrm{m}\) into energy \(\mathrm{E}\) as described by Einstein’s famous equation.
\[\mathrm{E}=\mathrm{m} \, \mathrm{c}^{2} \nonumber \]
Here \(\mathrm{c}\) is the speed of light, \(3.00 \times 10^{8} \mathrm{~m s}^{-1}\). In nuclear fission the nucleus of an atom breaks into two smaller nuclei of similar mass [4]. Thus \(\text{uranium}^{235}\) nuclei bombarded by neutrons split into barium-142 and krypton-92 nuclei. Einstein’s equation shows that \(1.0 \mathrm{~g}\) of this uranium isotope undergoes fission with the release of \(7.5 \times 10^{10} \mathrm{~J}\) [5], an awesome amount of energy.
Here we return to the domain of chemical properties and chemical reactions where nuclei of atoms are not destroyed. Our interest centres on the thermodynamic variable, entropy \(\mathrm{S}\), an extensive function of state. However in every day conversation and in articles in newspapers and magazines the term ‘entropy’ is rarely used suggesting that it is not important. This conclusion is incorrect and the message quite misleading.
In these Topics we describe the Second Law using an equation based on the formulation given by Clausius as follows.
\[\mathrm{T} \, \mathrm{dS}=\mathrm{q}+\mathrm{A} \, \mathrm{d} \xi \nonumber \]
Here a positive \(\mathrm{q}\) describes heat passing from the surroundings into a closed system; \(\mathrm{A}\) is the affinity for spontaneous change, the change being described by the property \(\xi\). Following De Donder [6] as discussed by Prigogine and Defay [7] the Second Law is simply stated as follows.
\[A \, d \xi \geq 0 \nonumber \]
For a system moving between equilibrium states (i.e. the system and surroundings are at all stages at equilibrium where \(\mathrm{A}\) is zero),
\[\mathrm{T} \, \mathrm{dS}=\mathrm{q} \nonumber \]
Hence \(\mathrm{q}\), measured using a calorimeter, is a direct measure of the change in entropy accompanying a change where the system is always in equilibrium with the surroundings. In fact this statement provides a useful answer to the question ‘what is entropy?’. There is therefore a fundamental link between the two quantities \(\mathrm{dS}\) and heat \(\mathrm{q}\). Indeed we understand immediately the importance of calorimeters in thermodynamics. At the same time we understand the importance of chemical kinetics because this subject is built around equation (d) which in the basis of the Law of Mass Action.
In summary we see how the two foundation stones of thermodynamics, namely energy and entropy, are formalised in two laws for which there are no exceptions. So we can end the Topics here. But chemists do not although there are new hazards.
It follows from equation (d) that for a process where \(\mathrm{q} < 0\), the entropy of the system decreases. [It is interesting to note that the unit of entropy \(\mathm{J K}^{-1}\) is the same as that for heat capacity.] At this point we review the arguments advanced by Lewis and Randall [8].
An important reference system in thermodynamics is the perfect gas. No such gas is actually known in the real world but the concept is very valuable. The properties of a perfect gas conform to the two laws [7b].
We envisage a closed system, volume \(\mathrm{V}\) containing n moles of a perfect gas. The first condition states that the thermodynamic energy \(\mathrm{U}\) is only a function of temperature. Thus,
\[\left(\frac{\partial \mathrm{U}}{\partial \mathrm{V}}\right)_{\mathrm{T}}=0 \nonumber \]
The second condition states that the following equation relates the pressure, volume and temperature of \(\mathrm{n}\) moles of a perfect gas.
\[\mathrm{p} \, \mathrm{V}=\mathrm{n} \, \mathrm{R} \, \mathrm{T} \nonumber \]
Thus for one mole of a perfect gas, having molar volume \(\mathrm{V}_{\mathrm{m}}\),
\[\mathrm{p} \, \mathrm{V}_{\mathrm{m}}=\mathrm{R} \, \mathrm{T} \nonumber \]
A key equation (Topic 2500) relates the change in thermodynamic energy \(\mathrm{U}\) to the changes in entropy, volume and composition. Thus
\[\mathrm{dU}=\mathrm{T} \, \mathrm{dS}-\mathrm{p} \, \mathrm{dV}-\mathrm{A} \, \mathrm{d} \xi \nonumber \]
For an equilibrium transformation, the affinity of spontaneous change is zero. Hence for an equilibrium process,
\[\mathrm{dU}=\mathrm{T} \, \mathrm{dS}-\mathrm{p} \, \mathrm{dV} \nonumber \]
For 1 mole of an ideal gas,
\[\mathrm{dU}_{\mathrm{m}}=\mathrm{T} \, \mathrm{dS}_{\mathrm{m}}-\mathrm{p} \, \mathrm{dV}_{\mathrm{m}} \nonumber \]
Or,
\[\mathrm{dS}_{\mathrm{m}}=\frac{1}{\mathrm{~T}} \, \mathrm{dU}_{\mathrm{m}}+\frac{\mathrm{P}}{\mathrm{T}} \, \mathrm{dV} \mathrm{m}_{\mathrm{m}} \nonumber \]
Molar isochoric heat capacity \(\mathrm{C}_{\mathrm{Vm}}\) is related to \(\mathrm{dU}_{\mathrm{m}}\) by equation (m).
\[\mathrm{C}_{\mathrm{V}_{\mathrm{m}}}=\left(\partial \mathrm{U}_{\mathrm{m}} / \partial \mathrm{T}\right)_{\mathrm{V}(\mathrm{m})} \nonumber \]
Then,
\[\mathrm{dS}_{\mathrm{m}}=\frac{\mathrm{C}_{\mathrm{Vm}^{\mathrm{m}}}}{\mathrm{T}} \, \mathrm{dT}+\frac{\mathrm{p}}{\mathrm{T}} \, \mathrm{dV} \mathrm{V}_{\mathrm{m}} \nonumber \]
We define the molar entropy of an ideal gas using equation (o).
\[\mathrm{S}_{\mathrm{m}}=\mathrm{S}_{\mathrm{m}}\left[\mathrm{T}, \mathrm{V}_{\mathrm{m}}\right] \nonumber \]
The total differential of equation (o) takes the following form.
\[\mathrm{dS}_{\mathrm{m}}=\left(\frac{\partial \mathrm{S}_{\mathrm{m}}}{\partial \mathrm{T}}\right)_{\mathrm{V}(\mathrm{m})} \mathrm{dT}+\left(\frac{\partial \mathrm{S}_{\mathrm{m}}}{\partial \mathrm{V}_{\mathrm{m}}}\right)_{\mathrm{T}} \mathrm{dV} \mathrm{V}_{\mathrm{m}} \nonumber \]
Comparison of equations (n) and (p) reveals the following relation.
\[\left(\frac{\partial S_{m}}{\partial V_{m}}\right)_{T}=\frac{p}{T} \nonumber \]
Hence using equation h),
\[\left(\frac{\partial S_{m}}{\partial V_{m}}\right)_{T}=\frac{R}{V_{m}} \nonumber \]
Thus at constant temperature,
\[\mathrm{dS}_{\mathrm{m}}=\mathrm{T} \, \mathrm{d} \ln \left(\mathrm{V}_{\mathrm{m}}\right) \nonumber \]
Hence the change in entropy for the isothermal expansion of an ideal gas between states where the volumes are \(\mathrm{V}_{\mathrm{m}}(\mathrm{B})\) and \(\mathrm{V}_{\mathrm{m}}(\mathrm{A})\) is given by equation (t).
\[S_{m}(B)-S_{m}(A)=R \, \ln \left[\frac{V_{m}(B)}{V_{m}(A)}\right] \nonumber \]
We turn now to a consideration of changes in entropy from a statistical point of view.
A given experiment [8] uses two glass flasks of equal volumes connected by a glass tube which includes a tap, all at the same temperature \(\mathrm{T}\). The system contains \(\mathrm{N}\) gas molecules; e.g. oxygen. The gas molecules pass freely between the two flasks through the open tap. On examining the contents of the two flasks we would not be surprised to discover that there are equal numbers of the gas molecules in the two flasks. The probability of this results from experiment A is expressed by stating that \(\mathrm{P}_{\mathrm{y}}^{\mathrm{A}}\) is unity.
We return to the two flasks and close the tap. The probability that all the oxygen molecules are to be found in one flask is \({(1/2)}^{\mathrm{N}}\); i.e. a very low probability. If the total system contained only 20 molecules this probability signals a chance of 1 in \(2^{20}\). Thus the probability \(\mathrm{P}_{\mathrm{y}}^{\mathrm{B}}\) for experiment B is very small; effectively zero.
An interesting exercise characterises these probabilities by a property \(\sigma\). Then,
\[\sigma=\frac{R}{N} \, \ln \left(P_{Y}\right) \nonumber \]
Note that the auxiliary property \(\sigma\) is generally negative because statistical probabilities vary between zero and unity. For the two experiments,
\[\sigma_{B}-\sigma_{A}=\frac{R}{N} \, \ln \left(\frac{P_{Y}^{B}}{P_{Y}^{A}}\right) \nonumber \]
Hence,
\[\sigma_{B}-\sigma_{A}=\frac{R}{N} \, \ln \left(\frac{(1 / 2)^{N}}{1}\right) \nonumber \]
Or,
\[\sigma_{\mathrm{B}}-\sigma_{\mathrm{A}}=-\mathrm{R} \, \ln (2) \nonumber \]
We can express this result in general terms describing the expansions of one mole of gas from volume \(\mathrm{V}_{\mathrm{A}}\) to \(\mathrm{V}_{\mathrm{B}}\). Then,
\[\sigma_{B}-\sigma_{A}=R \, \ln \left[V_{m}(B) / V_{m}(A)\right] \nonumber \]
At this point comparison between equations (t) and (y) is rewarding. Thus we may write the following equation.
\[\mathrm{S}_{\mathrm{m}}(\mathrm{B})-\mathrm{S}_{\mathrm{m}}(\mathrm{A})=\frac{\mathrm{R}}{\mathrm{N}} \,\left[\ln \left(\mathrm{P}_{\mathrm{Y}}^{\mathrm{B}}\right)-\ln \left(\mathrm{P}_{\mathrm{Y}}^{\wedge}\right)\right] \nonumber \]
In other words the difference between the entropies in the ideal gas state is related to a probability. Thus we might conclude that \(\mathrm{S}_{\mathrm{m}}(\mathrm{B})\) is larger that \(\mathrm{S}_{\mathrm{m}}(\mathrm{A})\) because there are more ways of arranging molecules in system B than in system A. The state with the more ordered arrangement is the state with the lower entropy. It is a small step (but a very dangerous step) to draw comparison between entropy and (if there is such a word) the muddled-up-ness of a given system. But these are treacherous waters and outside the province of the classic thermodynamics which form the basis of the Topics. Indeed strong feelings are aroused. McGlashan [9,10], for example, takes to task chemists who assume that an increase in entropy implies an increase of disorder or of randomness or of ‘mixed-upness’. We leave the debate here except to note that both authors of these Topics favour the view advanced by McGlashan [9,10] although this view would not a win a popularity contest. But ‘popularity’ is not an acceptable criterion in thermodynamics.
Footnotes
[1] Cambridge International Dictionary of English, Cambridge University Press, Cambridge, 1995.
[2] P. W. Atkins, Concepts in Physical Chemistry, Oxford University Press, Oxford, 1995.
[3] E. F. Caldin, An Introduction to Chemical Thermodynamics, Oxford University Press, Oxford, 1958.
[4] S. Glasstone, Sourcebook of Atomic Energy, MacMillan, London, 1954.
[5] P. W. Atkins and L. Jones, Chemistry: Molecules, Matter and Change, W H Freeman, New York, 3rd edition, 1997, p.875.
[6] Th. de Donder, Bull. Acad. Roy. Belg. (Cl.Sc), 1922, 7, 197, 205.
[7] I. Prigogine and R. Defay, Chemical Thermodynamics, transl. D. H. Everett, Longmans Green, London, 1954, (a) chapter 3; (b) chapter 4.
[8] G. N. Lewis and M. Randall, Thermodynamics , McGraw-Hill, New York, 1923, chapter VI.
[9] M. L. McGlashan, Chemical Thermodynamics, Academic Press, London, 1979,pages 112-113;
[10] M.L. McGlashan, J. Chem. Educ.,1966, 43 ,226.


6.2: Lewis Structures of Ionic Compounds- Electrons Transferred
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Learning Objectives
- State the octet rule.
- Define ionic bond .
- Draw Lewis structures for ionic compounds.
In Section 4.7, we demonstrated that ions are formed by losing electrons to make cations, or by gaining electrons to form anions. The astute reader may have noticed something: many of the ions that form have eight electrons in their valence shell. Either atoms gain enough electrons to have eight electrons in the valence shell and become the appropriately charged anion, or they lose the electrons in their original valence shell; the lower shell, now the valence shell, has eight electrons in it, so the atom becomes positively charged. For whatever reason, having eight electrons in a valence shell is a particularly energetically stable arrangement of electrons. The octet rule explains the favorable trend of atoms having eight electrons in their valence shell. When atoms form compounds, the octet rule is not always satisfied for all atoms at all times, but it is a very good rule of thumb for understanding the kinds of bonding arrangements that atoms can make.
It is not impossible to violate the octet rule. Consider sodium: in its elemental form, it has one valence electron and is stable. It is rather reactive, however, and does not require a lot of energy to remove that electron to make the Na + ion. We could remove another electron by adding even more energy to the ion, to make the Na 2 + ion. However, that requires much more energy than is normally available in chemical reactions, so sodium stops at a 1+ charge after losing a single electron. It turns out that the Na + ion has a complete octet in its new valence shell, the n = 2 shell, which satisfies the octet rule. The octet rule is a result of trends in energies and is useful in explaining why atoms form the ions that they do.
Now consider an Na atom in the presence of a Cl atom. The two atoms have these Lewis electron dot diagrams and electron configurations:
\[\mathbf{Na\, \cdot }\; \; \; \; \; \; \; \; \; \; \mathbf{\cdot }\mathbf{\ddot{\underset{.\: .}Cl}}\mathbf{\: :} \nonumber \]
\[\left [ Ne \right ]3s^{1}\; \; \; \; \left [ Ne \right ]3s^{2}3p^{5} \nonumber \]
For the Na atom to obtain an octet, it must lose an electron; for the Cl atom to gain an octet, it must gain an electron. An electron transfers from the Na atom to the Cl atom:
\[\mathbf{Na\, \cdot }\curvearrowright \mathbf{\cdot }\mathbf{\ddot{\underset{.\: .}Cl}}\mathbf{\: :} \nonumber \]
resulting in two ions—the Na + ion and the Cl − ion:
\[\mathbf{Na}^{+}\; \; \; \; \; \; \; \; \mathbf{:}\mathbf{\ddot{\underset{.\: .}Cl}}\mathbf{\: :}^{-} \nonumber \]
\[\left [ Ne \right ]\; \; \; \; \; \left [ Ne \right ]3s^{2}3p^{6} \nonumber \]
Both species now have complete octets, and the electron shells are energetically stable. From basic physics, we know that opposite charges attract. This is what happens to the Na + and Cl − ions:
\[\mathbf{Na}^{+}\; + \; \mathbf{:}\mathbf{\ddot{\underset{.\: .}Cl}}\mathbf{\: :}^{-}\rightarrow Na^{+}Cl^{-}\; \; or\; \; NaCl \nonumber \]
where we have written the final formula (the formula for sodium chloride) as per the convention for ionic compounds, without listing the charges explicitly. The attraction between oppositely charged ions is called an ionic bond, and it is one of the main types of chemical bonds in chemistry. Ionic bonds are caused by electrons transferring from one atom to another.
In electron transfer, the number of electrons lost must equal the number of electrons gained. We saw this in the formation of NaCl. A similar process occurs between Mg atoms and O atoms, except in this case two electrons are transferred:
The two ions each have octets as their valence shell, and the two oppositely charged particles attract, making an ionic bond:
\[\mathbf{Mg\,}^{2+}\; + \; \left[\mathbf{:}\mathbf{\ddot{\underset{.\: .}O}}\mathbf{\: :}\right]^{2-}\; \; \; \; \; Mg^{2+}O^{2-}\; or\; MgO \nonumber \]
Remember, in the final formula for the ionic compound, we do not write the charges on the ions.
What about when an Na atom interacts with an O atom? The O atom needs two electrons to complete its valence octet, but the Na atom supplies only one electron:
\[\mathbf{Na\, \cdot }\curvearrowright \mathbf{\cdot }\mathbf{\ddot{\underset{.}O}}\mathbf{\: :} \nonumber \]
The O atom still does not have an octet of electrons. What we need is a second Na atom to donate a second electron to the O atom:
These three ions attract each other to give an overall neutral-charged ionic compound, which we write as Na 2 O. The need for the number of electrons lost being equal to the number of electrons gained explains why ionic compounds have the ratio of cations to anions that they do. This is required by the law of conservation of matter as well.
Example \(\PageIndex{1}\): Synthesis of Calcium Chloride from Elements
With arrows, illustrate the transfer of electrons to form calcium chloride from \(Ca\) atoms and \(Cl\) atoms.
Solution
A \(Ca\) atom has two valence electrons, while a \(Cl\) atom has seven electrons. A \(Cl\) atom needs only one more to complete its octet, while \(Ca\) atoms have two electrons to lose. Thus we need two \(Cl\) atoms to accept the two electrons from one \(Ca\) atom. The transfer process looks as follows:
The oppositely charged ions attract each other to make CaCl 2 .
Exercise \(\PageIndex{1}\)
With arrows, illustrate the transfer of electrons to form potassium sulfide from \(K\) atoms and \(S\) atoms.
- Answer
Summary
- The tendency to form species that have eight electrons in the valence shell is called the octet rule.
- The attraction of oppositely charged ions caused by electron transfer is called an ionic bond.
- The strength of ionic bonding depends on the magnitude of the charges and the sizes of the ions.


5.4: Differentiation Between Sex and Gender
Gender is a complex subject, but could be better understood when we learn to differentiate biology from gender expression. Nevertheless, while gender may begin with the assignment of our sex, it doesn’t end there. According to Understanding Gender, n.d., a person’s gender is the complex interrelationship between three dimensions: body, identity, and social gender.
Body : Our body, our experience of our own body, how society genders bodies, and how others interact with us based on our body.
Identity : The name we use to convey our gender based on our deeply held, internal sense of self. Identities typically fall into binary (e.g. man, woman), nonbinary (e.g., genderqueer, genderfluid, etc.), or ungendered (e.g., agender, genderless) categories. The meaning associated with a particular identity can vary among individuals using the same term. A person’s gender identity can correspond to or differ from the sex they were assigned at birth.
Social gender : How we present our gender in the world and how individuals, society, culture, and community perceive, interact with, and try to shape our gender. Social gender includes roles and expectations and how society uses those to try to enforce conformity to current gender norms (Understanding gender, n.d.).
The connection between one’s gender and physical appearance extends beyond reproductive functions. Gender experience is based on a broader scientific basis, according to research in Neurology, hormones, and Cellular Biology. Indeed, research is increasingly pointing to our brains as a crucial factor in how we uniquely experience gender (Understanding gender, n.d.). Given the fact that gender identity is separate from sex, not everyone identifies within the binary (male or female). For a broader analysis of gender beyond the binary, let’s look at gender as a spectrum.


5.9: Research Starts with a Thesis Statement
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- Cheryl E. Ball & Drew M. Loewe ed.
- West Virginia University via Digital Publishing Institute and West Virginia University Libraries
Aujthor: Emily Wierszewski, Seton Hill University, Pittsburgh, PA
Our collective belief in the importance of definite answers impacts many areas of our lives, including how we understand the process and purpose of research. Specifically, it leads to a thesis-first research model in which research is only used to verify our existing ideas or theses. (Alison Witte discusses this bad idea in a previous chapter.) In this model, there is no room for doubt or ambiguity. We assume we need to know the answers to our problems or questions before the process gets underway, before we consult and evaluate what others have said.
Research can be productively used in this way to verify assumptions and arguments. Sometimes what we need is just a little support for an idea, a confirmation of the best approach to a problem, or the answer to simple questions. For example, we might believe the new iPhone is the best smartphone on the market, and use research on the phone’s specs to prove we’re right. This kind of thesis-first approach to research becomes harmful, however, when we assume that it is the only or the most valuable way to conduct research. Evidence of this widespread assumption is easy to find. A simple search for the research process on Google will yield multiple hits hosted by academic institutions that suggest a researcher needs a thesis early in the research process. For instance, the University of Maryland University College’s Online Guide to Writing and Research suggests that a thesis should be developed as soon as source collection gets underway, though that thesis may change over time. In the book, A Writing Process , author Vinetta Bell suggests that the thesis-writing process begins during the “preliminary research” stage. This strategy is endorsed by multiple research library websites, such as the University of Minnesota.
And yet, genuine inquiry—the kind of research that often leads to new ideas and important choices—tends to begin with unsettled problems and questions, rather than with thesis statements and predetermined answers. Wernher von Braun, an engineer whose inventions advanced the U.S. space program in the mid-21st century, famously describes research as, “What I’m doing when I don’t know what I’m doing.” The understanding of research as discovery is echoed in the recent “Framework for Information Literacy in Higher Education,” a document authored by the Association of College and Research Librarians (ACRL). They write that research often begins with open-ended questions that are “based on information gaps or reexamination of existing, possibly conflicting, information.” In other words, research isn’t just for backing up our hunches. It can, and should, also be used as a method of investigating areas of uncertainty, curiosity, conflict, and multiple perspectives.
As the ACRL’s framework also emphasizes, when researchers review published source material around their topic, points of disagreement will be discovered; these points are expected as scholars propose ideas to address complicated issues. When we are open to selecting and engaging with these multiple published perspectives in our research, we’re also forced to consider how they extend or challenge our beliefs and ideas about a topic. Considering all sides, we can then make a more informed decision about our questions or topics.
Another potential harm of the thesis-first model of research is the attendant assumption that the research process is linear. In a thesis-guided research process, a question is posed, an answer is generated, and sources are found that match up with that answer. Truthfully, research rarely progresses on an uncluttered path toward a clear solution. Instead, research is a recursive process that involves many diversions, bumps, and missteps. Clark College’s library website describes the research process as a daisy, rather than a line. Like a daisy’s petals, research is described as cyclical and fluid. As we research, we may find ourselves returning to and changing our question, or we may near the end of a project and think we’re done but discover we need to go back to find more or better sources. The messiness of research requires us to be flexible, often modifying our approaches along the way. When we enter the research process with a narrow and rigid focus on our thesis, we can become discouraged and inclined to abandon our ideas when the research process does not unfold neatly.
In place of a thesis-first model, we would be better served to begin research with a question or a statement of a problem. We should conduct research not just to back up our pre-existing assumptions and prove we’re right about something, but also when we feel curious or confused and do not have answers. Why is something the way it is? Why doesn’t the data quite add up? How could something be changed for the better?
When we understand research as a process of discovery rather than a process of proof, we open ourselves up to be changed by our research—to better our lives, our decisions, and our world. We acknowledge that we do not have the only or the best answer to every question, and that we might learn something from considering the ideas of others. While research definitely has the power to impact our lives and beliefs, research doesn’t always have to be life altering. But in a thesis-first model where our only goal is just to prove we’re right, there is no possibility of being changed by our research. Here’s a practical example of the difference. Just imagine the results of a research process beginning with a thesis like “Human trafficking should have harsher legal penalties” versus one that starts with an open-ended question like “Why does human trafficking persist in the democratic nation of the United States?” In the thesis-first model, a researcher would likely only encounter sources that argue for her pre-existing belief: that harsher penalties are needed. She would probably never be exposed to multiple perspectives on this complex issue, and the result would just be confirmation of her earlier beliefs. However, a researcher who begins with an open-ended question motivated by curiosity, whose goal is not to prove anything, but to discover salient ideas about a human rights issue, has the chance to explore different thoughts about human trafficking and come to her own conclusions as she researches why it’s a problem and what ought to be done to stop it, not just create stronger consequences for it.
Viewing research as a process of discovery allows us to accept that not every question is answerable and that questions sometimes lead only to more questions. For instance, the researcher in the previous paragraph exploring the issue of human trafficking might find that there is no clear, single explanation for the prevalence of this human rights violation, and that she’s interested to know more about the role of immigration laws and human trafficking—something she never even thought of before she did her research. When researchers do discover answers, they may find those answers are fluid and debatable. What we have at any 234 Bad Ideas time is only a consensus between informed parties, and at any time, new research or insights can cause that agreement to shift. Kenneth Burke, a philosopher and literary critic, explains the constructed nature of knowledge in his unending conversation metaphor. According to Burke, the moment in which a researcher reads and participates in scholarship around the research topic or problem is just a speck on a continuum of conversation that has been ongoing well before the researcher thought of the question, and will continue long after the researcher has walked away from it. As Burke writes, “The discussion is interminable.”
So how can we move toward embracing uncertainty? In his book, A More Beautiful Question , Warren Berger suggests that parents and those who work with young children can foster curiosity by welcoming questions. Parents also need to learn to be comfortable with saying “I don’t know” in response, rather than searching for a simple answer. Berger also recommends that as children go through school, parents and educators can work together to support children’s questioning nature, rather than always privileging definite answers. When students graduate and move into the working world, employers can encourage them to ask questions about policies, practices, and workplace content; employees should be given freedom to explore those questions with research, which can potentially lead to more sustainable and current policies, practices, and content. The same goes for civic and community life, where any form of questioning or inquiry is often misconstrued as a challenge to authority. To value questions more than answers in our personal and professional lives requires a cultural shift.
Although our culture would tell us that we have to know everything, and that we should even begin a research project by knowing the answer to our question, there is obvious value in using research as a tool to engage our curiosity and sense of wonder as human beings—perhaps even to improve our lives or the lives of others. If all researchers started the process with preconceived answers, no new findings would ever come to be. In order to truly learn about a topic or issue, especially when it involves important decision making, we need to learn to embrace uncertainty and feel comfortable knowing we might not always have an answer when we begin a research project.
Further Reading
For additional information about the power and purpose of inquiry in our everyday lives, consult Warren Berger’s book, A More About Genres 235 Beautiful Question (Bloomsbury), which provides an overview of how to engage in authentic inquiry in a variety of settings. Berger offers practical advice for learning to develop research questions that are driven by discovery and innovation. Robert Davis and Mark Shadle also provide a defense of inquiry in their article, “‘Building a Mystery’: Alternative Research Writing and the Academic Art of Seeking” (College Composition and Communication).
For more specific information about all of the stages of the research process including formulating a question, Bruce Ballenger’s classic guide to research, The Curious Researcher (Longman) and Ken Macrorie’s canonical text I Search (Boynton/Cook), which focuses on research with personal value, may both be useful. Clark College Libraries’ website also provides a quick reference chart outlining the research process entitled “The Research Process Daisy.” Finally, Wendy Bishop and Pavel Zemliansky’s edited collection, The Subject Is Research: Processes and Practices (Boynton/Cook), provides perspectives from multiple authors about various research techniques such as interviewing and observation that can be used to engage in the inquiry process.
Keywords
discovery, process, research, thesis, thesis-first research model
Author Bio
Emily Wierszewski has been teaching writing for over ten years, most recently at Seton Hill University outside of Pittsburgh, PA. Her graduate work focused on nonfiction writing, including the study of what makes writing persuasive, as well as how people learn to read and write. As a professor, she’s very interested in how her college students understand and have used the research process before coming to her class, including how their preconceptions about the purpose and process of research impact their attitudes toward and proficiency with college-level inquiry. She recently wrote a book chapter about how comics can help students more effectively engage with research in the writing classroom. Her Twitter handle is @ewazoo23.


9.5: Sell a Product or Process Further
A manufactured item may be produced in various stages or processes. In some cases, the initial production yields one finished product and processing it further results in a different product. In other cases, there may be a market for a partially completed manufactured good, where the buyer ultimately completes the product to its own specifications. A manufacturer may have to decide whether to sell a product at an initial stage or process it further. The preferred choice is the one that is more financially beneficial.
Morning Roast Coffee, Inc. produces dark roast coffee in batches of 5,000 pounds. Materials cost is $5.80 per pound. The dark roast coffee can be sold without further processing for $9.70 per pound or may be processed further to yield dark roast decaf, which can be sold for $12.10 per pound. The processing into decaf requires additional costs of $7,480 per batch. The additional processing will also cause a 4% loss of product due to evaporation.
|
Sell |
Process |
Difference |
|
|
Revenue 1 |
$48,500 |
$60,500 |
|
|
Costs: |
|||
|
\(\ \quad \quad\)Materials cost 2 |
29,000 |
36,480 |
|
|
\(\ \quad \quad\)Evaporation 3 |
2,420 |
||
|
Income |
$19,500 |
$9,800 |
$2,100 |
1 5,000 x $9.70 \(\ \quad \quad\)5,000 x $12.10
2 5,000 x $5.80 \(\ \quad \quad\)5,000 x $5.80 + $7,480
3 $60,500 x 4%
The differential analysis first considers the different revenues from each alternative and then the respective costs. Even with the 4% product loss from processing further, the decaf coffee results in higher income. The company shouldprocess the batch further.


7.1: Limblessness as a discrete trait
R markdown to recreate analyses
Squamates, the clade that includes all living species of lizards, are well known for their diversity. From the gigantic Komodo dragon of Indonesia (Figure 7.1A, Varanus komodoensis ) to tiny leaf chameleons of Madagascar (Figure 7.1B, Brookesia ), squamates span an impressive range of form and ecological niche use (Vitt et al. 2003; Pianka et al. 2017) . Even the snakes (Figure 7.1C and D), extraordinarily diverse in their own right (~3,500 species), are actually a clade that is nested within squamates (Streicher and Wiens 2017) . The squamate lineage that is ancestral to snakes became limbless about 170 million years ago (see Hedges et al. 2006) – and also underwent a suite of changes to their head shape, digestive tract, and other traits associated with their limbless lifestyle. In other words, snakes are lizards – highly modified lizards, but lizards nonetheless. And snakes are not the only limbless lineage of squamates. In fact, lineages within squamates have lost their limbs over and over again through their history (e.g. Figure 7.1E and F), with some estimates that squamates have lost their limbs at least 26 times in the past 240 million years (Brandley et al. 2008) .
Limblessness is an example of a discrete trait – a trait that can occupy one of a set of distinct character states. Analyzing the evolution of discrete traits requires a different modeling approach than what we used for continuous traits. In this chapter, I will discuss the Mk model (Lewis 2001) , which is a general approach to modeling the evolution of discrete traits on trees. Fitting this model to comparative data will help us understand the evolution of traits like limblessness where species can be placed into one of a number of discrete character states.