Question 1

The specific heat Cv at constant volume of a monatomic gas at low pressure is proportional to Tn where the exponent n is:

Accepted Answer

A)  -1 
B)  0 
C)  1 
D)  1/2 
E)  2 
A)  -1 
B)  0 
C)  1 
D)  1/2 
E)  2

Question 2

Use R = 8.2 *10-5 m3 . atm/mol . K and NA = 6.02 * 1023 mol-1. The approximate number of air molecules in a 1 m3 volume at room temperature (300 K) and atomospheric pressure is:

Accepted Answer

A)  41 
B)  450 
C)  2.5 * 1025 
D)  2.7 *1026 
E)  5.4 *1026 
A)  41 
B)  450 
C)  2.5 * 1025 
D)  2.7 *1026 
E)  5.4 *1026

Question 3

According to the Maxwellian speed distribution, as the temperature increases the number of molecules with speeds within a small interval near the most probable speed:

Accepted Answer

A)  increases 
B)  decreases 
C)  increases at high temperatures and decreases at low 
D)  decreases at high temperatures and increases at low 
E)  stays the same 
A)  increases 
B)  decreases 
C)  increases at high temperatures and decreases at low 
D)  decreases at high temperatures and increases at low 
E)  stays the same

Question 4

An isothermal process for an ideal gas is represented on a p-V diagram by:

Accepted Answer

A)  a horizontal line 
B)  a vertical line 
C)  a portion of an ellipse 
D)  a portion of a parabola 
E)  a hyperbola 
A)  a horizontal line 
B)  a vertical line 
C)  a portion of an ellipse 
D)  a portion of a parabola 
E)  a hyperbola

Question 5

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$C, 1 atm). The volume occupied by 42 grams of this gas at standard conditions is:

Accepted Answer

A)  14.9 liters 
B)  22.4 liters 
C)  33.6 liters 
D)  42 liters 
E)  more data are needed 
A)  14.9 liters 
B)  22.4 liters 
C)  33.6 liters 
D)  42 liters 
E)  more data are needed

Question 6

TV  $\gamma$ is constant for an ideal gas undergoing an adiabatic process, where $\gamma$ is the ratio of heat capacities Cp/Cv. This is a direct consequence of:

Accepted Answer

A)  the zeroth law of thermodynamics alone 
B)  the zeroth law and the ideal gas equation of state 
C)  the first law of thermodynamics alone 
D)  the ideal gas equation of state alone 
E)  the first law and the equation of state 
A)  the zeroth law of thermodynamics alone 
B)  the zeroth law and the ideal gas equation of state 
C)  the first law of thermodynamics alone 
D)  the ideal gas equation of state alone 
E)  the first law and the equation of state

Question 7

If the temperature T of an ideal gas is increased at constant pressure the mean free path:

Accepted Answer

A)  decreases in proportion to 1/T 
B)  decreases in proportion to 1/T2 
C)  increases in proportion to T 
D)  decreases in proportion to T2 
E)  does not change 
A)  decreases in proportion to 1/T 
B)  decreases in proportion to 1/T2 
C)  increases in proportion to T 
D)  decreases in proportion to T2 
E)  does not change

Question 8

The difference between the molar specific heat at constant pressure and the molar specific heat at constant volume for an ideal gas is:

Accepted Answer

A)  the Boltzmann constant k 
B)  the universal gas constant R 
C)  the Avogadro number NA 
D)  kT 
E)  RT 
A)  the Boltzmann constant k 
B)  the universal gas constant R 
C)  the Avogadro number NA 
D)  kT 
E)  RT

Question 9

The ratio of the specific heat of a gas at constant volume to its specific heat at constant pressure is:

Accepted Answer

A)  1 
B)  less than 1 
C)  more than 1 
D)  has units of pressure/volume 
E)  has units of volume/pressure 
A)  1 
B)  less than 1 
C)  more than 1 
D)  has units of pressure/volume 
E)  has units of volume/pressure

Question 10

The pressure of an ideal gas of diatomic molecules is doubled by halving the volume. The ratio of the new internal energy to the old, both measured relative to the internal energy at 0 K, is:

Accepted Answer

A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4 
A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4

Question 11

The mean free path of a gas molecule is:

Accepted Answer

A)  the shortest dimension of the containing vessel 
B)  the cube root of the volume of the containing vessel 
C)  approximately the diameter of a molecule 
D)  average distance between adjacent molecules 
E)  average distance a molecule travels between intermolecular collisions 
A)  the shortest dimension of the containing vessel 
B)  the cube root of the volume of the containing vessel 
C)  approximately the diameter of a molecule 
D)  average distance between adjacent molecules 
E)  average distance a molecule travels between intermolecular collisions

Question 12

In order that a single process be both isothermal and isobaric:

Accepted Answer

A)  one must use an ideal gas 
B)  such a process is impossible 
C)  a change of phase is essential 
D)  one may use any real gas such as N2 
E)  one must use a solid 
A)  one must use an ideal gas 
B)  such a process is impossible 
C)  a change of phase is essential 
D)  one may use any real gas such as N2 
E)  one must use a solid

Question 13

According to the Maxwellian speed distribution, as the temperature increases the most probable speed:

Accepted Answer

A)  increases 
B)  decreases 
C)  increases at high temperatures and decreases at low 
D)  decreases at high temperatures and increases at low 
E)  stays the same 
A)  increases 
B)  decreases 
C)  increases at high temperatures and decreases at low 
D)  decreases at high temperatures and increases at low 
E)  stays the same

Question 14

Three gases, one consisting of monatomic molecules, the second consisting of diatomic molecules, and the third consisting of polyatomic molecules, are in thermal equilibrium with each other and remains in thermal equilibrium as the temperature is raised. All have the same number of molecules. The gases with the least and greatest internal energy are respectively:

Accepted Answer

A)  polyatomic, monatomic 
B)  monatomic, polyatomic 
C)  diatomic, monatomic 
D)  polyatomic, diatomic 
E)  monatomic, diatomic 
A)  polyatomic, monatomic 
B)  monatomic, polyatomic 
C)  diatomic, monatomic 
D)  polyatomic, diatomic 
E)  monatomic, diatomic

Question 15

Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased. A molecule of the first gas has mass m and a molecule of the second has mass 4m. The ratio of the internal energies E4m/Em is:

Accepted Answer

A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4 
A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4

Question 16

Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is composed of molecules with mass 4m. The average molecular speeds are the same if the ratio of the temperatures TA/TB is:

Accepted Answer

A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4 
A)  1/4 
B)  1/2 
C)  1 
D)  2 
E)  4

Question 17

For a gas at thermal equilibrium the average speed v, the most probable speed vp, and the root-mean-square speed vrms are in the order:

Accepted Answer

A)  vp rms rms p rms p 
D)  vp rms 
E)  v p rms 
A)  vp rms rms p rms p 
D)  vp rms 
E)  v p rms

Question 18

The average speeds v and molecular diameters d of five ideal gases are given below. The number of molecules per unit volume is the same for all of them. For which is the collision rate the greatest?

Accepted Answer

A)  v = v0 and d = d0 
B)  v = 2v0 and d = d0/2 
C)  v = 3v0 and d = d0 
D)  v = v0 and d = 2d0 
E)  v = 4v0 and d = d0/2 
A)  v = v0 and d = d0 
B)  v = 2v0 and d = d0/2 
C)  v = 3v0 and d = d0 
D)  v = v0 and d = 2d0 
E)  v = 4v0 and d = d0/2

Question 19

When an ideal gas undergoes a slow isothermal expansion:

Accepted Answer

A)  the work done by the gas is the same as the energy absorbed as heat 
B)  the work done by the environment is the same as the energy absorbed as heat 
C)  the increase in internal energy is the same as the heat absorbed 
D)  the increase in internal energy is the same as the work done by the gas 
E)  the increase in internal energy is the same as the work done by the environment 
A)  the work done by the gas is the same as the energy absorbed as heat 
B)  the work done by the environment is the same as the energy absorbed as heat 
C)  the increase in internal energy is the same as the heat absorbed 
D)  the increase in internal energy is the same as the work done by the gas 
E)  the increase in internal energy is the same as the work done by the environment

Question 20

An ideal diatomic gas has a molar specific heat at constant pressure, Cp, of:

Accepted Answer

A)  R 
B)  3R/2 
C)  5R/2 
D)  7R/2 
E)  9R/2 
A)  R 
B)  3R/2 
C)  5R/2 
D)  7R/2 
E)  9R/2

Exam 19: The Kinetic Theory of Gases

The specific heat Cv at constant volume of a monatomic gas at low pressure is proportional to Tn where the exponent n is:

Use R = 8.2 *10-5 m3 . atm/mol . K and NA = 6.02 * 1023 mol-1. The approximate number of air molecules in a 1 m3 volume at room temperature (300 K) and atomospheric pressure is:

According to the Maxwellian speed distribution, as the temperature increases the number of molecules with speeds within a small interval near the most probable speed:

An isothermal process for an ideal gas is represented on a p-V diagram by:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 °\degree° C, 1 atm). The volume occupied by 42 grams of this gas at standard conditions is:

TV γ\gammaγ is constant for an ideal gas undergoing an adiabatic process, where γ\gammaγ is the ratio of heat capacities Cp/Cv. This is a direct consequence of:

If the temperature T of an ideal gas is increased at constant pressure the mean free path:

The difference between the molar specific heat at constant pressure and the molar specific heat at constant volume for an ideal gas is:

The ratio of the specific heat of a gas at constant volume to its specific heat at constant pressure is:

The pressure of an ideal gas of diatomic molecules is doubled by halving the volume. The ratio of the new internal energy to the old, both measured relative to the internal energy at 0 K, is:

The mean free path of a gas molecule is:

In order that a single process be both isothermal and isobaric:

According to the Maxwellian speed distribution, as the temperature increases the most probable speed:

Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased. A molecule of the first gas has mass m and a molecule of the second has mass 4m. The ratio of the internal energies E4m/Em is:

Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is composed of molecules with mass 4m. The average molecular speeds are the same if the ratio of the temperatures TA/TB is:

For a gas at thermal equilibrium the average speed v, the most probable speed vp, and the root-mean-square speed vrms are in the order:

The average speeds v and molecular diameters d of five ideal gases are given below. The number of molecules per unit volume is the same for all of them. For which is the collision rate the greatest?

When an ideal gas undergoes a slow isothermal expansion:

An ideal diatomic gas has a molar specific heat at constant pressure, Cp, of:

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The specific heat C_v at constant volume of a monatomic gas at low pressure is proportional to Tⁿ where the exponent n is:

Use R = 8.2 10^-⁵ m³ . atm/mol . K and N_A = 6.02 10²³ mol^-¹. The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atomospheric pressure is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 1 atm). The volume occupied by 42 grams of this gas at standard conditions is:

TV ^$\gamma$ is constant for an ideal gas undergoing an adiabatic process, where $\gamma$ is the ratio of heat capacities C_p/C_v. This is a direct consequence of:

Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased. A molecule of the first gas has mass m and a molecule of the second has mass 4m. The ratio of the internal energies E₄_m/E_m is:

Ideal monatomic gas A is composed of molecules with mass m while ideal monatomic gas B is composed of molecules with mass 4m. The average molecular speeds are the same if the ratio of the temperatures T_A/T_B is:

For a gas at thermal equilibrium the average speed v, the most probable speed v_p, and the root-mean-square speed v_rms are in the order:

An ideal diatomic gas has a molar specific heat at constant pressure, C_p, of: