Question 1

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average kinetic energy?
A) It is the same for both of the gases because the temperatures are the same.
B) The oxygen molecules do because they are diatomic.
C) The oxygen molecules do because they are more massive.
D) The helium molecules do because they are less massive.
E) The helium molecules do because they are monatomic.

Accepted Answer

At a given temperature, the average kinetic energy of gas molecules is the same regardless of the mass or type of gas. This is a principle of kinetic molecular theory.

Question 2

As a result of any natural process, the total entropy of any system plus that of its environment
A) never decreases.
B) sometimes decreases.
C) never increases.
D) always stays the same.

Accepted Answer

This is a statement of the second law of thermodynamics, which states that the total entropy of a closed system (including the system and its surroundings) will always increase over time. The only way to decrease entropy in one part of the system is to increase entropy elsewhere in the system or its surroundings. Therefore, the total entropy of the system plus its environment can never decrease.

Question 3

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 becomes 4 times as great.
C) It becomes 2 times as great.
D) It becomes 1/2 as great.
E) It becomes 1/4 as great.

Accepted Answer

According to the ideal gas law, PV=nRT, when temperature is constant (as is the case in this scenario), pressure and volume are inversely proportional. This means that as the volume is halved, the pressure will double. However, the average speed of the gas molecules is determined by the temperature of the gas, not the pressure or volume. Since the temperature is held constant, the average speed of the gas molecules will not change.

Question 4

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed (thermal speed) of the gas molecules was V, the new speed is
A) V.
B) 2V.
C)  V.
D) V/2.
E) V/

Accepted Answer

The answer of A sample of an ideal gas is...

Question 5

The entropy of an isolated system must be conserved, so it never changes.
A) True
B) False

Accepted Answer

The entropy of an isolated system never decreases, but it can increase or remain constant. It is not conserved.

Question 6

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that
A) the pressure of the gas will increase.
B) the volume of the gas will increase.
C) the speed of the gas molecules will increase.
D) All of the above statements are correct.

Accepted Answer

The answer of If the temperature of a fixed amount...

Question 7

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average speed?
A) It is the same for both of the gases because the temperatures are the same.
B) The oxygen molecules do because they are diatomic.
C) The oxygen molecules do because they are more massive.
D) The helium molecules do because they are less massive.
E) The helium molecules do because they are monatomic.

Accepted Answer

The average speed of gas molecules is directly proportional to their mass, so lighter molecules will have a greater average speed at the same temperature. Helium is a monatomic gas and has a smaller atomic mass than oxygen, which is a diatomic gas. Therefore, helium molecules have a greater average speed than Oxygen molecules at the same temperature.

Question 8

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?
A) The entropy gained by the ice cube is equal to the entropy lost by the water.
B) The entropy lost by the ice cube is equal to the entropy gained by the water.
C) The net entropy change of the system (ice plus water) is zero because no heat was added to the system.
D) The entropy of the system (ice plus water) increases because the process is irreversible.
E) The entropy of the water does not change because its temperature did not change.

Accepted Answer

The process of melting ice into water is irreversible, and in such processes, the total entropy of the system always increases. This is because the heat transfer from the warmer water to the colder ice cube increases the disorder of the system.

Question 9

The root-mean-square speed (thermal speed) for a certain gas at 100°C is 0.500 km/s. If the temperature of the gas is now increased to 200°C, the root-mean-square (thermal) speed will be closest to
A) 563 m/s.
B) 634 m/s.
C) 707 m/s.
D) 804 m/s.
E) 1000 m/s.

Accepted Answer

The answer of The root-mean-square speed (thermal speed) for a...

Question 10

A 5.0-liter gas tank holds 1.4 moles of helium (He) and 0.70 moles of oxygen (O₂), at a temperature of 260 K. The atomic masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K. The total random translational kinetic energy of the gas in the tank is closest to A) 6.8 kJ. B) 6.1 kJ. C) 7.6 kJ. D) 8.3 kJ. E) 9.1 kJ.

Accepted Answer

The answer of A 5.0-liter gas tank holds 1.4 moles...

Question 11

According to the second law of thermodynamics, the entropy of any system always increases.
A) True
B) False

Accepted Answer

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. However, it can remain constant in ideal cases where the system is in equilibrium or undergoes a reversible process. Therefore, the entropy of a system does not always increase; it can stay the same under certain conditions.

Question 12

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen? A) 1.4 B) 2.0 C) 2.8 D) 4.0 E) 5.6

Accepted Answer

The root-mean-square speed of a gas is given by the equation: 
rms speed = sqrt((3RT)/M), 
where R is the gas constant, T is the temperature, and M is the molar mass of the gas.

For helium: 
rms speed_He = sqrt((3RT)/M_He) 
= sqrt((3*8.31 J/K*mol*260 K)/(4.0 g/mol)) 
= 1,317 m/s

For oxygen: 
rms speed_O2 = sqrt((3RT)/M_O2) 
= sqrt((3*8.31 J/K*mol*260 K)/(32.0 g/mol)) 
= 517 m/s

The ratio of the rms speeds of helium to oxygen is: 
rms speed_He/rms speed_O2 = 1,317 m/s / 517 m/s 
= 2.55

The answer should be rounded to one significant figure, which gives: 
Answer: C

Question 13

A hot piece of iron is thrown into the ocean and its temperature eventually stabilizes. Which of the following statements concerning this process is correct? (There may be more than one correct choice.)
A) The entropy lost by the iron is equal to the entropy gained by the ocean.
B) The entropy gained by the iron is equal to the entropy lost by the ocean.
C) The change in the entropy of the iron-ocean system is zero.
D) The ocean gains more entropy than the iron loses.
E) The ocean gains less entropy than the iron loses.

Accepted Answer

The ocean gains more entropy than the iron loses because when heat is transferred from a hotter object (the iron) to a colder one (the ocean), the increase in entropy of the colder object is greater than the decrease in entropy of the hotter object. This is due to the fact that entropy change is related to the amount of heat transferred divided by the temperature at which the transfer occurs, and the ocean's larger mass and lower temperature mean it can absorb heat with a greater increase in entropy.

Question 14

What is the total translational kinetic energy in a test chamber filled with nitrogen (N₂) at and The dimensions of the chamber are The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

Accepted Answer

The answer of What is the total translational kinetic energy...

Question 15

An ideal gas is kept in a rigid container. When its temperature is 100 K, the mean-free-path of the gas molecules is λ. What will be the mean-free-path of the molecules at 400 K?
A) 4λ
B) 2λ
C) λ
D) λ/2
E) λ/4

Accepted Answer

The mean free path (λ) of gas molecules in a rigid container is independent of temperature because it primarily depends on the density and diameter of the molecules, both of which remain constant in a rigid container. Therefore, changing the temperature does not affect λ.

Question 16

An ideal gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 20.0°C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be double its value at 20.0°C?
A) 40.0°C
B) 141°C
C) 313°C
D) 400°C
E) 899°C

Accepted Answer

The root-mean-square speed of an ideal gas is proportional to the square root of its absolute temperature (in Kelvin). To double the speed, the temperature must be quadrupled. Starting at 20.0°C = 293.15 K, quadrupling this temperature gives 1172.6 K, which is approximately 899.45°C.

Question 17

The second law of thermodynamics leads us to conclude that
A) the total energy of the universe is constant.
B) disorder in the universe is increasing with the passage of time.
C) it is theoretically impossible to convert work into heat with 100% efficiency.
D) the total energy in the universe is increasing with time.
E) the total energy in the universe is decreasing with time.

Accepted Answer

The second law of thermodynamics states that entropy (disorder) in the universe is increasing with time. This means that the energy available to do useful work is decreasing, resulting in decreased efficiency in energy conversions (including work to heat). The total energy of the universe may remain constant, but the available energy for useful work is decreasing.

Question 18

A mole of oxygen (O₂) molecules and a mole of carbon dioxide (CO₂) molecules at the same temperature and pressure have A) the same average molecular speeds. B) the same number of atoms. C) different average kinetic energy per molecule. D) the same number of molecules. E) different volumes.

Accepted Answer

The answer of A mole of oxygen (O₂) molecules and...

Question 19

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then
A) its temperature must increase by a factor of 4.
B) its temperature must increase by a factor of 2.
C) its temperature must increase by a factor of  .
D) its pressure must increase by a factor of 2.
E) its pressure must increase by a factor of 4.

Accepted Answer

The answer of If we double the root-mean-square speed (thermal...

Question 20

The average molecular kinetic energy of a gas can be determined by knowing
A) only the number of molecules in the gas.
B) only the volume of the gas.
C) only the pressure of the gas.
D) only the temperature of the gas.
E) All of the above quantities must be known to determine the average molecular kinetic energy.

Accepted Answer

The average molecular kinetic energy of a gas is directly proportional to its temperature. Therefore, only the temperature of the gas needs to be known to determine its average molecular kinetic energy. The number of molecules, volume, and pressure of the gas may affect other properties of the gas, but they are not directly related to its average molecular kinetic energy.

Quiz 20: The Micromacro Connection

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average kinetic energy?

As a result of any natural process, the total entropy of any system plus that of its environment

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 sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed (thermal speed) of the gas molecules was V, the new speed is

The entropy of an isolated system must be conserved, so it never changes.

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average speed?

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

The root-mean-square speed (thermal speed) for a certain gas at 100°C is 0.500 km/s. If the temperature of the gas is now increased to 200°C, the root-mean-square (thermal) speed will be closest to

According to the second law of thermodynamics, the entropy of any system always increases.

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂) , at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?

A hot piece of iron is thrown into the ocean and its temperature eventually stabilizes. Which of the following statements concerning this process is correct? (There may be more than one correct choice.)

What is the total translational kinetic energy in a test chamber filled with nitrogen (N₂) at and The dimensions of the chamber are The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

An ideal gas is kept in a rigid container. When its temperature is 100 K, the mean-free-path of the gas molecules is λ. What will be the mean-free-path of the molecules at 400 K?

An ideal gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 20.0°C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be double its value at 20.0°C?

The second law of thermodynamics leads us to conclude that

A mole of oxygen (O₂) molecules and a mole of carbon dioxide (CO₂) molecules at the same temperature and pressure have

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

The average molecular kinetic energy of a gas can be determined by knowing

Quiz 20: The Micromacro Connection

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average kinetic energy?

As a result of any natural process, the total entropy of any system plus that of its environment

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 sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed (thermal speed) of the gas molecules was V, the new speed is

The entropy of an isolated system must be conserved, so it never changes.

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average speed?

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

The root-mean-square speed (thermal speed) for a certain gas at 100°C is 0.500 km/s. If the temperature of the gas is now increased to 200°C, the root-mean-square (thermal) speed will be closest to

According to the second law of thermodynamics, the entropy of any system always increases.

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O2) , at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?

A hot piece of iron is thrown into the ocean and its temperature eventually stabilizes. Which of the following statements concerning this process is correct? (There may be more than one correct choice.)

What is the total translational kinetic energy in a test chamber filled with nitrogen (N2) at and The dimensions of the chamber are The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 1023 molecules/mol and the Boltzmann constant is 1.38 × 10-23 J/K.

An ideal gas is kept in a rigid container. When its temperature is 100 K, the mean-free-path of the gas molecules is λ. What will be the mean-free-path of the molecules at 400 K?

An ideal gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 20.0°C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be double its value at 20.0°C?

The second law of thermodynamics leads us to conclude that

A mole of oxygen (O2) molecules and a mole of carbon dioxide (CO2) molecules at the same temperature and pressure have

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

The average molecular kinetic energy of a gas can be determined by knowing

What is the total translational kinetic energy in a test chamber filled with nitrogen (N₂) at and The dimensions of the chamber are The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

A mole of oxygen (O₂) molecules and a mole of carbon dioxide (CO₂) molecules at the same temperature and pressure have