Question 1

According to the kinetic theory, what is the average translational kinetic energy per molecule in an ideal gas at temperature $$T$$?

Accepted Answer

$$\frac{3}{2}kT$$

Question 2

For a monatomic ideal gas, what is the theoretical molar heat capacity at constant volume ($$C_V$$)?

Accepted Answer

$$\frac{3}{2}R$$

Question 3

Why does the molar heat capacity at constant volume ($$C_V) $$for diatomic gases exceed that of monatomic gases?

Accepted Answer

Diatomic molecules possess additional rotational degrees of freedom.

Question 4

Which of the following best describes the degrees of freedom for a diatomic molecule at low-to-moderate temperatures?

Accepted Answer

3 translational and 2 rotational

Question 5

According to the principle of equipartition of energy, how much energy is associated with each degree of freedom?

Accepted Answer

$$\frac{1}{2}kT$$

Question 6

A sample of hydrogen gas ($$\mathrm{H}_2) is $$heated from 40 K to 1000 K. Which type of motion becomes appreciable above 50 K, according to the graph?

Accepted Answer

Rotational motion

Question 7

For a polyatomic molecule with $$N$$ atoms, how many vibrational degrees of freedom does it have?

Accepted Answer

$$3N - 6$$

Question 8

Which gas listed in Table 18.1 has the highest molar heat capacity at constant volume ($$C_V$$)?

Accepted Answer

SO$$_2$$

Question 9

A monatomic gas is heated at constant volume. Which equation gives the change in internal energy per mole for a temperature increase $$\Delta T$$?

Accepted Answer

$$\Delta U = \frac{3}{2}R \Delta T$$

Question 10

Which statement best explains why vibrational motion is 'switched off' at low-to-moderate temperatures for diatomic molecules?

Accepted Answer

The energy required to excite vibrational modes is much higher than the available thermal energy.

Question 11

If a diatomic gas has 5 degrees of freedom, what is its theoretical molar heat capacity at constant volume ($$C_V$$)?

Accepted Answer

$$\frac{5}{2}R$$

Question 12

Which real-world scenario would most likely cause the heat capacity of a gas to increase beyond the value predicted for translational motion only?

Accepted Answer

Heating a polyatomic gas to a high temperature where vibrational modes are excited

Question 13

Which of the following is NOT a plausible reason for the discrepancy between theoretical and experimental values of $$C_V$$ for polyatomic gases?

Accepted Answer

Polyatomic molecules are ideal and have no internal structure.

Question 14

A gas sample contains molecules that can rotate about two independent axes but not vibrate at low temperature. What type of gas is this most likely?

Accepted Answer

Diatomic gas

Question 15

If the molar heat capacity at constant volume ($$C_V) $$for a gas is measured to be close to $$12.47 \ \mathrm{J \ $$mol^{-1}$$ \ K$$^{-1}$$}$$, what can you infer about the gas?

Accepted Answer

It is likely a monatomic ideal gas.

Question 16

Which equation correctly relates the root-mean-square speed ($$v_{rms}) of $$molecules in an ideal gas to temperature $$T$$?

Accepted Answer

$$\frac{1}{2}m v_{rms}^2 = \frac{3}{2}kT$$

Question 17

A polyatomic molecule with 4 atoms is heated to a temperature where all degrees of freedom are active. How many vibrational degrees of freedom does it have?

Accepted Answer

6

Question 18

Which of the following gases would you expect to have the lowest molar heat capacity at constant volume ($$C_V$$)?

Accepted Answer

He

Question 19

At what temperature does appreciable vibrational motion begin to occur for hydrogen gas ($$\mathrm{H}_2$$), according to the graph?

Accepted Answer

Above 600 K

Question 20

Which statement best describes the relationship between the number of degrees of freedom and the molar heat capacity of a gas?

Accepted Answer

The molar heat capacity increases as the number of active degrees of freedom increases.

Kinetic Theory and Heat Capacities of Gases

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