Chapter 13: Temperature And Kinetic Theory

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| By Drtaylor

Drtaylor

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Quizzes Created: 57 | Total Attempts: 73,746

Questions: 79 | Attempts: 351 | Updated: Mar 19, 2023

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Questions and Answers

1.

When the engine of your car heats up, the spark plug gap will
- A.
  
  Increase.
- B.
  
  Decrease.
- C.
  
  Remain unchanged.
- D.
  
  Decrease at first and then increase later, so that the two effects cancel once the engine reaches operating temperature.
Correct Answer
A. Increase.

Explanation
When the engine of a car heats up, the metal components expand due to the increase in temperature. This expansion causes the spark plug gap to widen, resulting in an increase in the gap size. As a result, the correct answer is that the spark plug gap will increase when the engine heats up.

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2.

The coefficient of linear expansion for aluminum is 1.8 * 10^(-6) (C°)^(-1). What is its coefficient of volume expansion?
- A.
  
  9.0 * 10^(-6) (C°)^(-1)
- B.
  
  5.8 * 10^(-18) (C°)^(-1)
- C.
  
  5.4 * 10^(-6) (C°)^(-1)
- D.
  
  3.6 * 10^(-6) (C°)^(-1)
Correct Answer
C. 5.4 * 10^(-6) (C°)^(-1)

Explanation
The coefficient of volume expansion is related to the coefficient of linear expansion by the equation: β = 3α, where β is the coefficient of volume expansion and α is the coefficient of linear expansion. Therefore, to find the coefficient of volume expansion, we multiply the coefficient of linear expansion by 3. In this case, 1.8 * 10^(-6) (C°)^(-1) * 3 = 5.4 * 10^(-6) (C°)^(-1).

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3.

The surface water temperature on a large, deep lake is 3°C. A sensitive temperature probe is lowered several meters into the lake. What temperature will the probe record?
- A.
  
  A temperature warmer than 3°C
- B.
  
  A temperature less than 3°C
- C.
  
  A temperature equal to 3°C
- D.
  
  There is not enough information to determine.
Correct Answer
A. A temperature warmer than 3°C

Explanation
When the temperature probe is lowered several meters into the lake, it will record a temperature warmer than 3°C. This is because as you go deeper into the lake, the water temperature tends to decrease. Therefore, the temperature recorded by the probe will be higher than the surface water temperature of 3°C.

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4.

Which temperature scale never gives negative temperatures?
- A.
  
  Kelvin
- B.
  
  Fahrenheit
- C.
  
  Celsius
- D.
  
  All of the above
Correct Answer
A. Kelvin

Explanation
The Kelvin temperature scale is the only scale that never gives negative temperatures. Unlike Fahrenheit and Celsius, which have negative values below freezing, Kelvin starts at absolute zero, the lowest possible temperature. Therefore, Kelvin only measures temperatures above absolute zero, ensuring that it never produces negative values.

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5.

Which two temperature changes are equivalent?
- A.
  
  1 K = 1 F°
- B.
  
  1 F° = 1 C°
- C.
  
  1 C° = 1 K
- D.
  
  None of the above
Correct Answer
C. 1 C° = 1 K

Explanation
The given answer is correct because 1 degree Celsius is equivalent to 1 Kelvin. Both Celsius and Kelvin are temperature scales that have the same size of degree increments, with the only difference being their starting points. In the Kelvin scale, 0 Kelvin is absolute zero, while in the Celsius scale, 0 degrees Celsius is the freezing point of water. Therefore, a change of 1 degree Celsius is equal to a change of 1 Kelvin.

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6.

The temperature in your classroom is approximately
- A.
  
  68 K.
- B.
  
  68°C.
- C.
  
  50°C.
- D.
  
  295 K.
Correct Answer
D. 295 K.

Explanation
The correct answer is 295 K. This is because the temperature in the classroom is given in Kelvin (K), which is the standard unit of temperature in the scientific community. 295 K is equivalent to approximately 22°C, which is a reasonable temperature for a classroom.

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7.

A container of an ideal gas at 1 atm is compressed to one-third its volume, with the temperature held constant. What is its final pressure?
- A.
  
  1/3 atm
- B.
  
  1 atm
- C.
  
  3 atm
- D.
  
  9 atm
Correct Answer
C. 3 atm

Explanation
When a container of an ideal gas is compressed, its volume decreases while the temperature remains constant. According to Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature, the pressure of the gas will increase. In this case, since the volume is compressed to one-third, the pressure will increase by a factor of 3. Therefore, the final pressure of the gas will be 3 atm.

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8.

If the pressure acting on an ideal gas at constant temperature is tripled, its volume is
- A.
  
  Reduced to one-third.
- B.
  
  Increased by a factor of three.
- C.
  
  Increased by a factor of two.
- D.
  
  Reduced to one-half.
Correct Answer
A. Reduced to one-third.

Explanation
When the pressure acting on an ideal gas at constant temperature is tripled, according to Boyle's Law, the volume of the gas will decrease. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature is held constant. Therefore, if the pressure is tripled, the volume will be reduced to one-third of its original value.

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9.

According to the ideal gas Law, PV = constant for a given temperature. As a result, an increase in volume corresponds to a decrease in pressure. This happens because the molecules
- A.
  
  Collide with each other more frequently.
- B.
  
  Move slower on the average.
- C.
  
  Strike the container wall less often.
- D.
  
  Transfer less energy to the walls of the container each time they strike it.
Correct Answer
C. Strike the container wall less often.

Explanation
An increase in volume corresponds to a decrease in pressure because the molecules strike the container wall less often. When the volume increases, the molecules have more space to move around and collide with each other less frequently. As a result, they also strike the container wall less often, leading to a decrease in pressure.

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10.

The number of molecules in one mole of a substance
- A.
  
  Depends on the molecular weight of the substance.
- B.
  
  Depends on the atomic weight of the substance.
- C.
  
  Depends on the density of the substance.
- D.
  
  Is the same for all substances.
Correct Answer
D. Is the same for all substances.

Explanation
The explanation for the given correct answer is that the number of molecules in one mole of a substance is always the same, regardless of the substance. This is known as Avogadro's number, which is approximately 6.022 x 10^23. It is a fundamental constant in chemistry and represents the number of atoms or molecules in one mole of any substance. Therefore, the statement that the number of molecules in one mole of a substance is the same for all substances is accurate.

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11.

A container holds N molecules of an ideal gas at a given temperature. If the number of molecules in the container is increased to 2N with no change in temperature or volume, the pressure in the container
- A.
  
  Doubles.
- B.
  
  Remains constant.
- C.
  
  Is cut in half.
- D.
  
  None of the above
Correct Answer
A. Doubles.

Explanation
When the number of gas molecules in the container is increased to 2N while keeping the temperature and volume constant, according to the ideal gas law, the pressure is directly proportional to the number of molecules. Therefore, if the number of molecules doubles, the pressure will also double.

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12.

Both the pressure and volume of a given sample of an ideal gas double. This means that its temperature in Kelvin must
- A.
  
  Double.
- B.
  
  Quadruple.
- C.
  
  Reduce to one-fourth its original value.
- D.
  
  Remain unchanged.
Correct Answer
B. Quadruple.

Explanation
When the pressure and volume of a gas double, according to the ideal gas law (PV = nRT), the temperature must also double in order to maintain the same value for the product of pressure and volume. Therefore, the temperature in Kelvin must quadruple.

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13.

The temperature of an ideal gas increases from 2°C to 4°C while remaining at constant pressure. What happens to the volume of the gas?
- A.
  
  It decreases slightly.
- B.
  
  It decreases to one-half its original volume.
- C.
  
  It increases slightly.
- D.
  
  It increases to twice as much.
Correct Answer
C. It increases slightly.

Explanation
When the temperature of an ideal gas increases while remaining at constant pressure, according to Charles's Law, the volume of the gas also increases. This is because as the temperature increases, the kinetic energy of the gas molecules increases, causing them to move faster and collide with the walls of the container more frequently and with greater force, leading to an increase in volume. Therefore, the correct answer is that the volume of the gas increases slightly.

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14.

A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules at STP have
- A.
  
  The same average molecular speeds.
- B.
  
  The same number of molecules.
- C.
  
  The same diffusion rates.
- D.
  
  All of the above
Correct Answer
B. The same number of molecules.

Explanation
At STP (Standard Temperature and Pressure), both diatomic oxygen (O2) and diatomic nitrogen (N2) molecules have the same number of molecules in a mole. This is because a mole is a unit that represents a specific number of particles, which is approximately 6.022 x 10^23. Therefore, regardless of the type of molecule, a mole of any substance will always contain the same number of molecules.

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15.

Consider two equal volumes of gas at a given temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules?
- A.
  
  32:28
- B.
  
  28:32
- C.
  
  1:1
- D.
  
  None of the above
Correct Answer
C. 1:1

Explanation
The ratio of the number of oxygen molecules to the number of nitrogen molecules is 1:1 because both gases have equal volumes, temperature, and pressure. The molecular mass of oxygen is 32, while the molecular mass of nitrogen is 28. However, since the question asks for the ratio of molecules, the molecular mass is not relevant. Therefore, the answer is 1:1.

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16.

The average molecular kinetic energy of a gas can be determined by knowing only
- A.
  
  The number of molecules in the gas.
- B.
  
  The volume of the gas.
- C.
  
  The pressure of the gas.
- D.
  
  The temperature of the gas.
Correct Answer
D. The temperature of the gas.

Explanation
The average molecular kinetic energy of a gas can be determined by knowing only the temperature of the gas. This is because temperature is directly proportional to the average kinetic energy of gas molecules. As temperature increases, the kinetic energy of the gas molecules also increases. Therefore, by knowing the temperature, one can determine the average molecular kinetic energy of the gas. The number of molecules, volume, and pressure of the gas do not directly determine the average kinetic energy.

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17.

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample?
- A.
  
  It does not change.
- B.
  
  It doubles.
- C.
  
  It halves.
- D.
  
  None of the above
Correct Answer
A. It does not change.

Explanation
When an ideal gas is compressed, the volume decreases while the temperature remains constant. According to the ideal gas law, PV = nRT, the product of pressure and volume is directly proportional to the number of gas molecules and their average kinetic energy. As the volume is halved, the pressure doubles, but since the temperature remains constant, the average kinetic energy of the gas molecules also remains constant. Therefore, the average speed of the molecules does not change.

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18.

A sample of an ideal gas is heated and its Kelvin temperature doubles. What happens to the average speed of the molecules in the sample?
- A.
  
  It does not change.
- B.
  
  It doubles.
- C.
  
  It halves.
- D.
  
  None of the above
Correct Answer
D. None of the above

Explanation
When the Kelvin temperature of an ideal gas doubles, the average speed of the molecules in the sample does not remain the same nor does it double or halve. The average speed of the molecules is directly proportional to the square root of the Kelvin temperature. Therefore, when the Kelvin temperature doubles, the average speed of the molecules will increase by a factor less than double. Hence, the correct answer is "none of the above".

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19.

The absolute temperature of an ideal gas is directly proportional to which of the following?
- A.
  
  Speed
- B.
  
  Momentum
- C.
  
  Kinetic energy
- D.
  
  Mass
Correct Answer
C. Kinetic energy

Explanation
The absolute temperature of an ideal gas is directly proportional to its kinetic energy. This means that as the temperature of the gas increases, so does its kinetic energy. Kinetic energy is the energy an object possesses due to its motion. In the case of a gas, the temperature is a measure of the average kinetic energy of its particles. Therefore, an increase in the kinetic energy of the gas particles will result in an increase in its absolute temperature.

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20.

In order to double the average speed of the molecules in a given sample of gas, the temperature (measured in Kelvin) must
- A.
  
  Quadruple.
- B.
  
  Double.
- C.
  
  Increase by a factor of square root two of its original value.
- D.
  
  Increase by a factor of square root three of its original value.
Correct Answer
C. Increase by a factor of square root two of its original value.

Explanation
When the temperature of a gas is increased, the average kinetic energy of its molecules also increases. According to the kinetic theory of gases, the average kinetic energy is directly proportional to the temperature. In order to double the average speed of the molecules, the average kinetic energy must also double. Since the average kinetic energy is directly proportional to the temperature, the temperature must also double. Therefore, the temperature must increase by a factor of square root two of its original value.

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21.

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen, compared to hydrogen
- A.
  
  Is greater.
- B.
  
  Is less.
- C.
  
  Is the same.
- D.
  
  Cannot be determined since pressure and volume are not given
Correct Answer
C. Is the same.

Explanation
The average molecular kinetic energy of a gas is directly proportional to its temperature. Since the temperature is given as the only variable, and not the pressure or volume, we can assume that the gases are at the same pressure and volume. Therefore, the average molecular kinetic energy of oxygen and hydrogen would be the same.

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22.

Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving
- A.
  
  4 times faster.
- B.
  
  At 1/4 the speed.
- C.
  
  16 times faster.
- D.
  
  At 1/16 the speed.
Correct Answer
B. At 1/4 the speed.

Explanation
The average molecular speed of gas molecules is directly proportional to the square root of their temperature. Since the temperature is the same for both oxygen and hydrogen molecules, their average molecular speeds will be the same. Therefore, the correct answer is "at 1/4 the speed" which indicates that the oxygen molecules are moving at 1/4 the speed of the hydrogen molecules.

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23.

A fixed container holds oxygen and helium gases at the same temperature. Which one of the following statements is correct?
- A.
  
  The oxygen molecules have the greater kinetic energy.
- B.
  
  The helium molecules have the greater kinetic energy.
- C.
  
  The oxygen molecules have the greater speed.
- D.
  
  The helium molecules have the greater speed.
Correct Answer
D. The helium molecules have the greater speed.

Explanation
At the same temperature, the kinetic energy of gas molecules is directly proportional to their speed. Since helium is lighter than oxygen, helium molecules have a higher average speed compared to oxygen molecules at the same temperature. Therefore, the statement "The helium molecules have the greater speed" is correct.

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24.

A container is filled with a mixture of helium and oxygen gases. A thermometer in the container indicates that the temperature is 22°C. Which gas molecules have the greater average kinetic energy?
- A.
  
  It is the same for both because the temperatures are the same.
- B.
  
  The oxygen molecules do because they are diatomic.
- C.
  
  The helium molecules do because they are less massive.
- D.
  
  The helium molecules do because they are monatomic.
Correct Answer
A. It is the same for both because the temperatures are the same.

Explanation
The correct answer is that the average kinetic energy is the same for both gases because the temperatures are the same. The average kinetic energy of gas molecules is directly proportional to the temperature. Since the temperature is the same for both helium and oxygen gases, their average kinetic energy will also be the same. The other options provided in the question are incorrect explanations for the greater average kinetic energy.

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25.

A container is filled with a mixture of helium and oxygen gases. A thermometer in the container indicates that the temperature is 22°C. Which gas molecules have the greater average speed?
- A.
  
  The helium molecules do because they are monatomic.
- B.
  
  It is the same for both because the temperatures are the same.
- C.
  
  The oxygen molecules do because they are more massive.
- D.
  
  The helium molecules do because they are less massive.
Correct Answer
D. The helium molecules do because they are less massive.

Explanation
The average speed of gas molecules is inversely proportional to their mass. Since helium molecules are less massive than oxygen molecules, they will have a greater average speed at the same temperature.

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26.

The three phases of matter can exist together in equilibrium at the
- A.
  
  Critical point.
- B.
  
  Triple point.
- C.
  
  Melting point.
- D.
  
  Evaporation point.
Correct Answer
B. Triple point.

Explanation
The triple point is the temperature and pressure at which the three phases of matter (solid, liquid, and gas) can coexist in equilibrium. At this point, all three phases have the same energy and can transition into one another without any change in temperature or pressure. Therefore, the correct answer is triple point.

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27.

Supersaturation occurs in air when the
- A.
  
  Relative humidity is 100% and the temperature increases.
- B.
  
  Relative humidity is less than 100% and the temperature increases.
- C.
  
  Relative humidity is less 100% and the temperature decreases.
- D.
  
  Relative humidity is 100% and the temperature decreases.
Correct Answer
D. Relative humidity is 100% and the temperature decreases.

Explanation
Supersaturation occurs in air when the relative humidity is 100% and the temperature decreases. This means that the air is holding more moisture than it can actually contain at that temperature. As the temperature decreases, the air becomes unable to hold the same amount of moisture, causing the excess moisture to condense and form droplets or frost.

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28.

Express your body temperature (98.6°F) in Celsius degrees.
- A.
  
  37.0°C
- B.
  
  45.5°C
- C.
  
  66.6°C
- D.
  
  72.6°C
Correct Answer
A. 37.0°C

Explanation
The correct answer is 37.0°C because to convert from Fahrenheit to Celsius, you subtract 32 from the Fahrenheit temperature and then multiply by 5/9. In this case, 98.6-32 = 66.6 and then 66.6 * 5/9 = 37.0.

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29.

Express 68°F in °C.
- A.
  
  7.0°C
- B.
  
  20°C
- C.
  
  36°C
- D.
  
  181°C
Correct Answer
B. 20°C

Explanation
To convert Fahrenheit to Celsius, you can use the formula: °C = (°F - 32) * 5/9. Plugging in the given temperature of 68°F into the formula, we get: (68 - 32) * 5/9 = 36 * 5/9 = 20°C. Therefore, the correct answer is 20°C.

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30.

Express -40°C in °F.
- A.
  
  -72°F
- B.
  
  -54°F
- C.
  
  -40°F
- D.
  
  4.4°F
Correct Answer
C. -40°F

Explanation
To convert Celsius to Fahrenheit, you can use the formula: °F = (°C × 9/5) + 32. In this case, if we substitute -40°C into the formula, we get (-40 × 9/5) + 32 = -40°F. Therefore, the correct answer is -40°F.

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31.

The temperature changes from 35°F during the night to 75°F during the day. What is the temperature change on the Celsius scale?
- A.
  
  72 C°
- B.
  
  40 C°
- C.
  
  32 C°
- D.
  
  22 C°
Correct Answer
D. 22 C°

Explanation
The temperature change from 35°F to 75°F is a difference of 40 degrees on the Fahrenheit scale. To convert this to Celsius, we can use the formula (F - 32) x 5/9. Plugging in the values, we get (75 - 32) x 5/9 = 43 x 5/9 = 215/9 = 23.89°C. However, since we are looking for the temperature change and not the final temperature, we need to subtract the initial temperature in Celsius. 23.89°C - 1°C (35°F converted to Celsius) = 22.89°C. Rounding to the nearest whole number, the temperature change on the Celsius scale is 22°C.

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32.

A temperature change of 20°C corresponds to a temperature change of
- A.
  
  68°F.
- B.
  
  11°F.
- C.
  
  36°F.
- D.
  
  None of the above
Correct Answer
C. 36°F.

Explanation
A temperature change of 20°C corresponds to a temperature change of 36°F because the conversion formula from Celsius to Fahrenheit is F = (C * 9/5) + 32. Therefore, when we substitute C = 20 into the formula, we get F = (20 * 9/5) + 32 = 36°F.

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33.

At what temperature are the numerical readings on the Fahrenheit and Celsius scales the same?
- A.
  
  -30°
- B.
  
  -40°
- C.
  
  -50°
- D.
  
  -60°
Correct Answer
B. -40°

Explanation
The numerical readings on the Fahrenheit and Celsius scales are the same at -40°. This is because -40° Fahrenheit is equal to -40° Celsius.

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34.

A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? (The average coefficient of linear expansion of steel is 11 * 10^(-6) /C°.)
- A.
  
  0.33 m
- B.
  
  0.44 m
- C.
  
  0.55 m
- D.
  
  0.66 m
Correct Answer
D. 0.66 m

Explanation
When the temperature rises from -20°C to 40°C, there is a change in temperature of 60°C. The change in length can be calculated using the formula: ΔL = L0 * α * ΔT, where ΔL is the change in length, L0 is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature. Plugging in the given values, we get ΔL = 1000 * 11 * 10^(-6) * 60 = 0.66 m. Therefore, the change in length when the temperature rises to 40°C is 0.66 m.

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35.

An aluminum rod 17.4 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 * 10^(-6) /C°.
- A.
  
  17.435 cm
- B.
  
  17.365 cm
- C.
  
  0.348 cm
- D.
  
  0.0348 cm
Correct Answer
A. 17.435 cm

Explanation
When a material is heated, it expands due to thermal expansion. The change in length can be calculated using the formula: ΔL = α * L * ΔT, where ΔL is the change in length, α is the linear expansion coefficient, L is the original length, and ΔT is the change in temperature. In this case, the original length is 17.4 cm, the linear expansion coefficient is 25 * 10^(-6) /C°, and the change in temperature is 100°C - 20°C = 80°C. Plugging these values into the formula, we get ΔL = (25 * 10^(-6) /C°) * (17.4 cm) * (80°C) = 0.0348 cm. Therefore, the new length of the aluminum rod is 17.4 cm + 0.0348 cm = 17.435 cm.

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36.

By how much will a slab of concrete 18 m long contract when the temperature drops from 24°C to -16°C? (The coefficient of linear thermal expansion for concrete is 10^(-5) /C°.)
- A.
  
  0.50 cm
- B.
  
  0.72 cm
- C.
  
  1.2 cm
- D.
  
  1.5 cm
Correct Answer
B. 0.72 cm

Explanation
Concrete contracts when the temperature decreases. The amount of contraction can be calculated using the formula: ΔL = L * α * ΔT, where ΔL is the change in length, L is the original length, α is the coefficient of linear thermal expansion, and ΔT is the change in temperature. In this case, the original length is 18 m, the coefficient of linear thermal expansion is 10^(-5) /C°, and the change in temperature is 24°C - (-16°C) = 40°C. Plugging these values into the formula, we get ΔL = 18 m * 10^(-5) /C° * 40°C = 0.72 cm. Therefore, the slab of concrete will contract by 0.72 cm.

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37.

A bolt hole in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? (The coefficient of linear thermal expansion for brass is 19 * 10^(-6) /C°.)
- A.
  
  1.205 cm
- B.
  
  1.195 cm
- C.
  
  1.200 cm
- D.
  
  1.210 cm
Correct Answer
A. 1.205 cm

Explanation
When the brass plate is heated, it expands due to the increase in temperature. The coefficient of linear thermal expansion for brass is given as 19 * 10^(-6) /C°. To find the change in diameter of the hole, we can use the formula: ΔL = α * L * ΔT, where ΔL is the change in length, α is the coefficient of linear thermal expansion, L is the original length, and ΔT is the change in temperature. In this case, the change in temperature is 220°C - 20°C = 200°C. The original diameter is 1.200 cm, so the original radius is 0.600 cm. Using the formula for diameter, ΔD = 2 * α * L * ΔT, we can calculate the change in diameter as 2 * (19 * 10^(-6) /C°) * (0.600 cm) * (200°C) = 0.00228 cm. Adding the change to the original diameter, we get 1.200 cm + 0.00228 cm = 1.20228 cm, which rounds to 1.205 cm. Therefore, the diameter of the hole when the plate is heated to 220°C is 1.205 cm.

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38.

20.00 cm of space is available. How long a piece of brass at 20°C can be put there and still fit at 200°C? Brass has a linear expansion coefficient of 19 *10^(-6) /C°.
- A.
  
  19.93 cm
- B.
  
  19.69 cm
- C.
  
  19.50 cm
- D.
  
  19.09 cm
Correct Answer
A. 19.93 cm

Explanation
The piece of brass will expand when heated from 20°C to 200°C due to its linear expansion coefficient. To calculate the final length of the brass, we can use the formula:

Final length = Initial length + (Initial length * linear expansion coefficient * change in temperature)

Substituting the given values:

Final length = 20.00 cm + (20.00 cm * 19 * 10^(-6) /°C * (200°C - 20°C))

Calculating this expression, we find that the final length of the brass is approximately 19.93 cm. Therefore, a piece of brass at 20°C can be put in the 20.00 cm space and still fit at 200°C.

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39.

A 5.0-cm diameter steel shaft has 0.10 mm clearance all around its bushing at 20°C. If the bushing temperature remains constant, at what temperature will the shaft begin to bind? Steel has a linear expansion coefficient of 12 * 10^(-6) /C°.
- A.
  
  353°C
- B.
  
  333°C
- C.
  
  53°C
- D.
  
  680°C
Correct Answer
A. 353°C

Explanation
The clearance between the shaft and the bushing is given as 0.10 mm at 20°C. The clearance is due to the difference in thermal expansion between the steel shaft and the bushing. As the temperature increases, both the shaft and the bushing will expand. The shaft will start to bind with the bushing when the expansion of the shaft closes the initial clearance of 0.10 mm. To find the temperature at which this occurs, we can use the linear expansion coefficient of steel. By calculating the expansion of the shaft from 20°C to the unknown temperature, we can determine when the clearance is reduced to zero. The correct answer is 353°C.

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40.

400 cm3 of mercury at 0°C will expand to what volume at 50°C? Mercury has a volume expansion coefficient of 180 * 10^(-6) /C°.
- A.
  
  450 cm^3
- B.
  
  409.7 cm^3
- C.
  
  403.6 cm^3
- D.
  
  401.8 cm^3
Correct Answer
C. 403.6 cm^3

Explanation
The volume expansion coefficient of a substance measures how much its volume changes with a change in temperature. In this question, we are given the initial volume of mercury at 0°C (400 cm^3) and the volume expansion coefficient of mercury (180 * 10^(-6) /C°). We need to find the final volume at 50°C. To do this, we can use the formula: final volume = initial volume * (1 + volume expansion coefficient * change in temperature). Plugging in the values, we get: final volume = 400 cm^3 * (1 + 180 * 10^(-6) /C° * 50°C) = 403.6 cm^3. Therefore, the correct answer is 403.6 cm^3.

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41.

1 L of water at 20°C will occupy what volume at 80°C? Water has a volume expansion coefficient of 210 * 10^(-6)/C°.
- A.
  
  1.6 L
- B.
  
  1.013 L
- C.
  
  0.987 L
- D.
  
  0.9987 L
Correct Answer
B. 1.013 L

Explanation
When the temperature of water increases, its volume also increases due to thermal expansion. The volume expansion coefficient of water is given as 210 * 10^(-6)/C°. This means that for every 1°C increase in temperature, the volume of water increases by 210 * 10^(-6) times its original volume. In this case, the temperature is increasing from 20°C to 80°C, which is a difference of 60°C. Therefore, the volume of water at 80°C will be 1 + (60 * 210 * 10^(-6)) times the original volume of 1 L. Simplifying this calculation gives us 1.013 L, which is the answer.

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42.

The volume coefficient of thermal expansion for gasoline is 950 * 10^(-6) /C°. By how much does the volume of 1.0 L of gasoline change when the temperature rises from 20°C to 40°C?
- A.
  
  6.0 cm^3
- B.
  
  12 cm^3
- C.
  
  19 cm^3
- D.
  
  37 cm^3
Correct Answer
C. 19 cm^3

Explanation
The volume coefficient of thermal expansion for gasoline is given as 950 * 10^(-6) /C°. This coefficient represents the change in volume per degree Celsius change in temperature. To find the change in volume when the temperature rises from 20°C to 40°C, we can use the formula:

Change in volume = (volume coefficient) * (initial volume) * (change in temperature)

Plugging in the values, we get:

Change in volume = (950 * 10^(-6) /C°) * (1.0 L) * (40°C - 20°C)
Change in volume = (950 * 10^(-6) /C°) * (1.0 L) * (20°C)
Change in volume = 0.019 L

Converting liters to cm^3, we get:

Change in volume = 0.019 L * 1000 cm^3/L
Change in volume = 19 cm^3

Therefore, the volume of 1.0 L of gasoline changes by 19 cm^3 when the temperature rises from 20°C to 40°C.

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43.

A 500-mL glass beaker of water is filled to the rim at a temperature of 0°C. How much water will overflow if the water is heated to a temperature of 95°C? (Ignore the expansion of the glass and the coefficient of volume expansion of water is 2.1 * 10^(-4) /C°.)
- A.
  
  3.3 mL
- B.
  
  10 mL
- C.
  
  33 mL
- D.
  
  100 mL
Correct Answer
B. 10 mL

Explanation
When the water is heated from 0°C to 95°C, it will expand due to the increase in temperature. The coefficient of volume expansion of water is given as 2.1 * 10^(-4) /°C. To calculate the amount of water that will overflow, we can use the formula:

ΔV = V * β * ΔT

Where:
ΔV is the change in volume
V is the initial volume of water (500 mL)
β is the coefficient of volume expansion of water (2.1 * 10^(-4) /°C)
ΔT is the change in temperature (95°C - 0°C = 95°C)

Plugging in the values, we get:
ΔV = 500 mL * 2.1 * 10^(-4) /°C * 95°C = 10 mL

Therefore, 10 mL of water will overflow when heated from 0°C to 95°C.

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44.

For mercury to expand from 4.0 cm^3 to 4.1 cm^3, what change in temperature is necessary? Mercury has a volume expansion coefficient of 180 * 10^(-6) /C°.
- A.
  
  400°C
- B.
  
  139°C
- C.
  
  14°C
- D.
  
  8.2°C
Correct Answer
B. 139°C

Explanation
The correct answer is 139°C. This can be determined using the formula for volume expansion:

ΔV = V0 * β * ΔT

where ΔV is the change in volume, V0 is the initial volume, β is the volume expansion coefficient, and ΔT is the change in temperature.

In this case, ΔV is 0.1 cm^3 (4.1 cm^3 - 4.0 cm^3), V0 is 4.0 cm^3, and β is 180 * 10^(-6) /°C. Plugging these values into the formula, we can solve for ΔT:

0.1 cm^3 = 4.0 cm^3 * 180 * 10^(-6) /°C * ΔT

ΔT = 0.1 cm^3 / (4.0 cm^3 * 180 * 10^(-6) /°C)

ΔT = 139°C

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45.

A mercury thermometer has a bulb of volume 0.100 cm^3 at 10°C. The capillary tube above the bulb has a cross-sectional area of 0.012 mm^2. The volume thermal expansion coefficient of mercury is 1.8 * 10^(-4) (C°)^(-1). How much will the mercury rise when the temperature rises by 30°C?
- A.
  
  0.45 mm
- B.
  
  4.5 mm
- C.
  
  45 mm
- D.
  
  45 cm
Correct Answer
C. 45 mm

Explanation
The volume of the mercury in the bulb can be calculated using the formula V = A * h, where V is the volume, A is the cross-sectional area, and h is the height. The initial height of the mercury can be calculated by dividing the volume of the bulb by the cross-sectional area of the capillary tube. The change in temperature can be used to calculate the change in volume using the formula ΔV = V * α * ΔT, where ΔV is the change in volume, α is the volume thermal expansion coefficient, and ΔT is the change in temperature. Since the volume of the bulb is constant, the change in volume is equal to the change in height. Therefore, the change in height can be calculated by dividing the change in volume by the cross-sectional area of the capillary tube. Multiplying the change in height by 10 will give the answer in millimeters. In this case, the change in height is 45 mm.

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46.

Convert 14°C to K.
- A.
  
  46 K
- B.
  
  100 K
- C.
  
  287 K
- D.
  
  474 K
Correct Answer
C. 287 K

Explanation
To convert Celsius to Kelvin, you need to add 273. So, to convert 14°C to K, you add 273 to 14, which equals 287 K.

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47.

Convert 14°F to K.
- A.
  
  263 K
- B.
  
  287 K
- C.
  
  -10 K
- D.
  
  474 K
Correct Answer
A. 263 K

Explanation
To convert Fahrenheit to Kelvin, we need to use the formula: K = (°F + 459.67) × 5/9. Plugging in 14 for °F, we get K = (14 + 459.67) × 5/9, which simplifies to K = 473.67 × 5/9 = 263 K. Therefore, the correct answer is 263 K.

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48.

Convert 14 K to °C.
- A.
  
  46°C
- B.
  
  287°C
- C.
  
  25°C
- D.
  
  -259°C
Correct Answer
D. -259°C

Explanation
To convert from Kelvin to Celsius, we need to subtract 273.15 from the given value. In this case, subtracting 273.15 from 14 K gives us -259°C.

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49.

Convert 14 K to °F.
- A.
  
  287°F
- B.
  
  -434°F
- C.
  
  -259°F
- D.
  
  474°F
Correct Answer
B. -434°F
50.

Oxygen condenses into a liquid at approximately 90 K. What temperature, in degrees Fahrenheit, does this correspond to?
- A.
  
  -193°F
- B.
  
  -217°F
- C.
  
  -265°F
- D.
  
  -297°F
Correct Answer
D. -297°F

Explanation
Oxygen condenses into a liquid at approximately 90 K, which is equivalent to -297°F.

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Mar 19, 2023

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Sep 27, 2012

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