Question 1

Eleven molecules have speeds 16, 17, 18, . . . , 26 m/s. Calculate the root-mean-square of this group of molecules.

Accepted Answer

A)  21.2 m/s 
B)  21.0 m/s 
C)  21.5 m/s 
D)  21.7 m/s 
A)  21.2 m/s 
B)  21.0 m/s 
C)  21.5 m/s 
D)  21.7 m/s A

Question 2

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

Accepted Answer

A)  6.8 kJ. 
B)  6.1 kJ. 
C)  7.6 kJ. 
D)  8.3 kJ. 
E)  9.1 kJ. 
A)  6.8 kJ. 
B)  6.1 kJ. 
C)  7.6 kJ. 
D)  8.3 kJ. 
E)  9.1 kJ. A

Question 3

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to

Accepted Answer

A)  160 m/s 
B)  330 m/s 
C)  260 m/s 
D)  630 m/s 
E)  2000 m/s 
A)  160 m/s 
B)  330 m/s 
C)  260 m/s 
D)  630 m/s 
E)  2000 m/s C

Question 4

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?

Accepted Answer

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. 
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.

Question 5

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

Accepted Answer

A)  never decreases. 
B)  sometimes decreases. 
C)  never increases. 
D)  always stays the same. 
A)  never decreases. 
B)  sometimes decreases. 
C)  never increases. 
D)  always stays the same.

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

A cubic box with sides of 20.0 cm contains 2.00 × 1023 molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10-27 kg. What is the average pressure exerted by the molecules on the walls of the container? The Boltzmann constant is 1.38 × 10-23 J/K and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

Accepted Answer

A)  3.39 kPa 
B)  1.13 kPa 
C)  570 Pa 
D)  2.26 kPa 
E)  9.10 Pa 
A)  3.39 kPa 
B)  1.13 kPa 
C)  570 Pa 
D)  2.26 kPa 
E)  9.10 Pa

Question 8

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

Accepted Answer

A)  563 m/s. 
B)  634 m/s. 
C)  707 m/s. 
D)  804 m/s. 
E)  1000 m/s. 
A)  563 m/s. 
B)  634 m/s. 
C)  707 m/s. 
D)  804 m/s. 
E)  1000 m/s.

Question 9

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?

Accepted Answer

A)  4λ 
B)  2λ 
C)  λ 
D)  λ/2 
E)  λ/4 
A)  4λ 
B)  2λ 
C)  λ 
D)  λ/2 
E)  λ/4

Question 10

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?

Accepted Answer

A)  40.0°C 
B)  141°C 
C)  313°C 
D)  400°C 
E)  899°C 
A)  40.0°C 
B)  141°C 
C)  313°C 
D)  400°C 
E)  899°C

Question 11

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

Accepted Answer

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. 
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.

Question 12

A 0.10-   gas tank holds 5.0 moles of nitrogen gas (N2), at a temperature of 370 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10-10 m, and the Boltzmann constant is 1.38 × 10-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to

Accepted Answer

A)  570 m/s. 
B)  810 m/s. 
C)  410 m/s. 
D)  22 m/s. 
E)  99 m/s. 
A)  570 m/s. 
B)  810 m/s. 
C)  410 m/s. 
D)  22 m/s. 
E)  99 m/s.

Question 13

Dust particles are pulverized rock, which has density 2500 kg/m3. They are approximately spheres 20 μm in diameter. Treating dust as an ideal gas, what is the root-mean-square speed (thermal speed) of a dust particle at 400°C? (The Boltzmann constant is 1.38 × 10-23 J/K.)

Accepted Answer

A)  5.2 × 10-5 m/s 
B)  1.7 × 10-5 m/s 
C)  3.0 × 10-5 m/s 
D)  7.3 × 10-5 m/s 
A)  5.2 × 10-5 m/s 
B)  1.7 × 10-5 m/s 
C)  3.0 × 10-5 m/s 
D)  7.3 × 10-5 m/s

Question 14

Assuming the radius of diatomic molecules is approximately 1.0 × 10-10 m, for what pressure will the mean free path in room-temperature (20°C) nitrogen be 4.6 m? The Boltzmann constant is 1.38 × 10-23 J/K, Avogadro's number is 6.02 × 1023 molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

Accepted Answer

A)  4.9 × 10-8 atm 
B)  6.9 × 10-8 atm 
C)  1.5 × 10-7 atm 
D)  2.2 × 10-7 atm 
A)  4.9 × 10-8 atm 
B)  6.9 × 10-8 atm 
C)  1.5 × 10-7 atm 
D)  2.2 × 10-7 atm

Question 15

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at a temperature 23.0°C. What is the mass of the individual molecules? The Boltzmann constant is 1.38 × 10-23 J/K.

Accepted Answer

A)  2.13 × 10-25 kg 
B)  2.45 × 10-25 kg 
C)  5.66 × 10-25 kg 
D)  1.78 × 10-25 kg 
E)  3.11 × 10-25 kg 
A)  2.13 × 10-25 kg 
B)  2.45 × 10-25 kg 
C)  5.66 × 10-25 kg 
D)  1.78 × 10-25 kg 
E)  3.11 × 10-25 kg

Question 16

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

Accepted Answer

A)  V. 
B)  2V. 
C)    V. 
D)  V/2. 
E)  V/   
A)  V. 
B)  2V. 
C)    V. 
D)  V/2. 
E)  V/

Question 17

The mean free path of an oxygen molecule is 2.0 × 10-5 m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The molecular mass of oxygen is 32.0 g/mol and the Boltzmann constant is 1.38 × 10-23 J/K, Avogadro's number is 6.02 × 1023 molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. Assuming that the molecules are moving at their root-mean-square speeds, the average time interval between collisions of an oxygen molecule is closest to

Accepted Answer

A)  20 ns. 
B)  43 ns. 
C)  95 ns. 
D)  200 ns. 
E)  420 ns. 
A)  20 ns. 
B)  43 ns. 
C)  95 ns. 
D)  200 ns. 
E)  420 ns.

Question 18

What is the mean free path of molecules in an ideal gas in which the mean collision time is 3.00 × 10-10 s, the temperature is 300 K, and the mass of the molecules is 6.00 × 10-25 kg? Assume that the molecules are moving at their root-mean-square speeds. The Boltzmann constant is 1.38 × 10-23 J/K.

Accepted Answer

A)  7.22 × 10-8 m 
B)  4.32 × 10-8 m 
C)  9.19 × 10-8 m 
D)  1.39 × 10-8 m 
E)  6.71 × 10-8 m 
A)  7.22 × 10-8 m 
B)  4.32 × 10-8 m 
C)  9.19 × 10-8 m 
D)  1.39 × 10-8 m 
E)  6.71 × 10-8 m

Question 19

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?

Accepted Answer

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. 
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.

Question 20

The second law of thermodynamics leads us to conclude that

Accepted Answer

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. 
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.

Exam 18: The Micromacro Connection

Eleven molecules have speeds 16, 17, 18, . . . , 26 m/s. Calculate the root-mean-square of this group of molecules.

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to

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

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

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

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?

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

A 0.10- gas tank holds 5.0 moles of nitrogen gas (N2), at a temperature of 370 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10-10 m, and the Boltzmann constant is 1.38 × 10-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to

Dust particles are pulverized rock, which has density 2500 kg/m3. They are approximately spheres 20 μm in diameter. Treating dust as an ideal gas, what is the root-mean-square speed (thermal speed) of a dust particle at 400°C? (The Boltzmann constant is 1.38 × 10-23 J/K.)

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at a temperature 23.0°C. What is the mass of the individual molecules? The Boltzmann constant is 1.38 × 10-23 J/K.

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 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?

The second law of thermodynamics leads us to conclude that

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

A 0.10- gas tank holds 5.0 moles of nitrogen gas (N₂), at a temperature of 370 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10^-10 m, and the Boltzmann constant is 1.38 × 10^-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to

Dust particles are pulverized rock, which has density 2500 kg/m³. They are approximately spheres 20 μm in diameter. Treating dust as an ideal gas, what is the root-mean-square speed (thermal speed) of a dust particle at 400°C? (The Boltzmann constant is 1.38 × 10^-23 J/K.)

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at a temperature 23.0°C. What is the mass of the individual molecules? The Boltzmann constant is 1.38 × 10^-23 J/K.