Question 1

If the rms speed of helium atoms is vrms,He at temperature T, what is the rms speed of CO2 at the same temperature?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 2

The average translational speed of a nitrogen molecule at room temperature (20°C) is approximately (in m/s)

Accepted Answer

A)  100. 
B)  500. 
C)  300. 
D)  700. 
E)  200. 
A)  100. 
B)  500. 
C)  300. 
D)  700. 
E)  200.

Question 3

The average molecular translational kinetic energy of a molecule in an ideal gas is

Accepted Answer

A) 
  kBT. 
B) 
  RT. 
C) 
  kBT. 
D) 
  RT. 
E) 
  kBT, where n = number of internal degrees of freedom. 
A) 
  kBT. 
B) 
  RT. 
C) 
  kBT. 
D) 
  RT. 
E) 
  kBT, where n = number of internal degrees of freedom.

Question 4

During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with γ = 1.4.)

Accepted Answer

A)  7.0 atm 
B)  5.6 atm 
C)  3.5 atm 
D)  2.2 atm 
E)  0.14 atm 
A)  7.0 atm 
B)  5.6 atm 
C)  3.5 atm 
D)  2.2 atm 
E)  0.14 atm

Question 5

A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the total energy of the system is

Accepted Answer

A)  2.0 × 104 J. 
B)  2.5 × 104 J. 
C)  1.7 × 103 J. 
D)  1.5 × 103 J. 
E)  4.0 × 104 J. 
A)  2.0 × 104 J. 
B)  2.5 × 104 J. 
C)  1.7 × 103 J. 
D)  1.5 × 103 J. 
E)  4.0 × 104 J.

Question 6

The internal energy of n moles of an ideal gas depends on

Accepted Answer

A)  one state variable T. 
B)  two state variables T and V. 
C)  two state variables T and P. 
D)  three state variables T, P and V. 
E)  four variables R, T, P and V. 
A)  one state variable T. 
B)  two state variables T and V. 
C)  two state variables T and P. 
D)  three state variables T, P and V. 
E)  four variables R, T, P and V.

Question 7

Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion?

Accepted Answer

A)  The total internal energy of the hydrogen is the same as that of the helium. 
B)  The total internal energy of the hydrogen is 167 times that of the helium. 
C)  The total internal energy of the helium is 1.67 times that of the hydrogen. 
D)  The total internal energy of the hydrogen is 3.33 times that of the helium. 
E)  The total internal energy of the helium is 3.33 times that of the hydrogen. 
A)  The total internal energy of the hydrogen is the same as that of the helium. 
B)  The total internal energy of the hydrogen is 167 times that of the helium. 
C)  The total internal energy of the helium is 1.67 times that of the hydrogen. 
D)  The total internal energy of the hydrogen is 3.33 times that of the helium. 
E)  The total internal energy of the helium is 3.33 times that of the hydrogen.

Question 8

The molar specific heat at constant pressure at 0°C of an ideal monatomic gas is

Accepted Answer

A) 
  . 
B)  R. 
C) 
  . 
D)  2R. 
E) 
  . 
A) 
  . 
B)  R. 
C) 
  . 
D)  2R. 
E) 
  .

Question 9

If the total translational kinetic energy of the molecules of oxygen in a container is 15 J at room temperature, what is the total rotational kinetic energy of these molecules?

Accepted Answer

A)  5 J 
B)  10 J 
C)  20 J 
D)  25 J 
E)  0 J 
A)  5 J 
B)  10 J 
C)  20 J 
D)  25 J 
E)  0 J

Question 10

A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the average kinetic energy per molecule is

Accepted Answer

A)  6.7 × 10−20 J. 
B)  1.0 × 10−21 J. 
C)  1.0 × 10−20 J. 
D)  6.7 × 10−21 J. 
E)  1.3 × 10−20 J. 
A)  6.7 × 10−20 J. 
B)  1.0 × 10−21 J. 
C)  1.0 × 10−20 J. 
D)  6.7 × 10−21 J. 
E)  1.3 × 10−20 J.

Question 11

An ideal gas is allowed to expand adiabatically until its volume increases by 50%. By approximately what factor is the pressure reduced? (γ = 5/3.)

Accepted Answer

A)  1.5 
B)  2.0 
C)  2.5 
D)  3.0 
E)  3.5 
A)  1.5 
B)  2.0 
C)  2.5 
D)  3.0 
E)  3.5

Question 12

One mole of helium gas expands adiabatically from 2 atm pressure to 1 atm pressure. If the original temperature of the gas is 20°C, what is the final temperature of the gas? (γ = 1.67)

Accepted Answer

The answer of One mole of helium gas expands adiabatically...

Question 13

Which statement below is NOT an assumption made in the molecular model of an ideal gas?

Accepted Answer

A)  The average separation between molecules is large compared with the dimensions of the molecules. 
B)  The molecules undergo inelastic collisions with one another. 
C)  The forces between molecules are short range. 
D)  The molecules obey Newton's laws of motion. 
E)  Any molecule can move in any direction with equal probability. 
A)  The average separation between molecules is large compared with the dimensions of the molecules. 
B)  The molecules undergo inelastic collisions with one another. 
C)  The forces between molecules are short range. 
D)  The molecules obey Newton's laws of motion. 
E)  Any molecule can move in any direction with equal probability.

Question 14

A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than

Accepted Answer

A)  one radius away from its center. 
B)  one diameter away from its center. 
C)  two diameters away from its center. 
D)  twice the cube root of volume away from its center. 
E) 
  diameters away from its center. 
A)  one radius away from its center. 
B)  one diameter away from its center. 
C)  two diameters away from its center. 
D)  twice the cube root of volume away from its center. 
E) 
  diameters away from its center.

Question 15

The average kinetic energy of a nitrogen molecule at room temperature (20°C) is

Accepted Answer

A)  2 × 10−21 J. 
B)  4 × 10−21 J. 
C)  6 × 10−21 J. 
D)  8 × 10−21 J. 
E)  1 × 10−20 J. 
A)  2 × 10−21 J. 
B)  4 × 10−21 J. 
C)  6 × 10−21 J. 
D)  8 × 10−21 J. 
E)  1 × 10−20 J.

Question 16

Assume molecules have an average diameter of 3.00 × 10−10 m. How many times larger is the mean free path than the diameter at one atmosphere and 0°C?

Accepted Answer

A)  500 
B)  300 
C)  700 
D)  1 000 
E)  2 500 
A)  500 
B)  300 
C)  700 
D)  1 000 
E)  2 500

Question 17

Five gas molecules are found to have speeds of 100, 200, 300, 400, and 500 m/s. The rms speed (in m/s) is

Accepted Answer

A)  390. 
B)  300. 
C)  360. 
D)  330. 
E)  320. 
A)  390. 
B)  300. 
C)  360. 
D)  330. 
E)  320.

Question 18

The theorem of equipartition of energy states that the energy each degree of freedom contributes to each molecule in the system (an ideal gas) is

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  . 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  .

Exam 21: The Kinetic Theory of Gases

If the rms speed of helium atoms is vrms,He at temperature T, what is the rms speed of CO2 at the same temperature?

The average translational speed of a nitrogen molecule at room temperature (20°C) is approximately (in m/s)

The average molecular translational kinetic energy of a molecule in an ideal gas is

During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with γ = 1.4.)

A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the total energy of the system is

The internal energy of n moles of an ideal gas depends on

Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion?

The molar specific heat at constant pressure at 0°C of an ideal monatomic gas is

If the total translational kinetic energy of the molecules of oxygen in a container is 15 J at room temperature, what is the total rotational kinetic energy of these molecules?

A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the average kinetic energy per molecule is

An ideal gas is allowed to expand adiabatically until its volume increases by 50%. By approximately what factor is the pressure reduced? (γ = 5/3.)

One mole of helium gas expands adiabatically from 2 atm pressure to 1 atm pressure. If the original temperature of the gas is 20°C, what is the final temperature of the gas? (γ = 1.67)

Which statement below is NOT an assumption made in the molecular model of an ideal gas?

A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than

The average kinetic energy of a nitrogen molecule at room temperature (20°C) is

Assume molecules have an average diameter of 3.00 × 10−10 m. How many times larger is the mean free path than the diameter at one atmosphere and 0°C?

Five gas molecules are found to have speeds of 100, 200, 300, 400, and 500 m/s. The rms speed (in m/s) is

The theorem of equipartition of energy states that the energy each degree of freedom contributes to each molecule in the system (an ideal gas) is

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If the rms speed of helium atoms is v_rms,He at temperature T, what is the rms speed of CO₂ at the same temperature?

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the total energy of the system is

Two tanks of gas, one of hydrogen, H₂, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H₂. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion?

A container having a volume of 1.0 m³ holds 5.0 moles of helium gas at 50°C. If the helium behaves like an ideal gas, the average kinetic energy per molecule is

Assume molecules have an average diameter of 3.00 × 10−¹⁰ m. How many times larger is the mean free path than the diameter at one atmosphere and 0°C?