Question 1

Which of the following statements best describes the conditions under which the ideal gas law is a good approximation for real gases?

Accepted Answer

Low density, temperature well above the condensation point, and absence of chemical reactions.

Question 2

A 100 g sample of O$$_2$$ gas is placed in a 600 cm$$^3$$ container at 150$$^	ext{o}C. $$What is the pressure inside the container? (Molar mass of O$$_2 = 32 g/$$mol, $$R = 8.31 J/$$mol$$ulletK)$$

Accepted Answer

$$p = 1.83 	imes 10^7$ Pa

Question 3

Which equation represents the ideal gas law in terms of the number of molecules $$N$$?

Accepted Answer

$$pV = Nk_B T$$

Question 4

What is the value of the Boltzmann constant $$k_B in $$terms of the universal gas constant $$R$$ and Avogadro’s number $$N_A$$?

Accepted Answer

$$k_B = \frac{R}{N_A}$$

Question 5

If the temperature of a gas in a constant-volume container is increased, what happens to the pressure?

Accepted Answer

The pressure increases.

Question 6

For a constant-pressure process, what is the work done by the gas as it expands from $$V_i to$$ $$V_f$$?

Accepted Answer

$$W = p(V_f - V_i)$$

Question 7

Which process is represented by a vertical line on a $$pV$$ diagram?

Accepted Answer

Constant-volume process

Question 8

During an adiabatic expansion of an ideal gas, what happens to the temperature of the gas?

Accepted Answer

The temperature decreases.

Question 9

Which equation correctly expresses the change in thermal energy for any process undergone by an ideal gas?

Accepted Answer

$$\Delta E_{th} = W + Q$$

Question 10

A monatomic ideal gas has three degrees of freedom. According to the equipartition theorem, what is its thermal energy?

Accepted Answer

$$E_{th} = \frac{3}{2} Nk_B T$$

Question 11

Which of the following statements about the specific heat of gases is correct?

Accepted Answer

The specific heat at constant pressure ($$C_P) is $$always greater than the specific heat at constant volume ($$C_V).$$

Question 12

For a diatomic ideal gas at room temperature, how many degrees of freedom are typically active?

Accepted Answer

Five

Question 13

Which process is characterized by $$Q = 0$$ and all energy transfer is due to work?

Accepted Answer

Adiabatic process

Question 14

What is the molar specific heat at constant volume ($$C_V) $$for a monatomic ideal gas?

Accepted Answer

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

Question 15

A gas undergoes a constant-temperature (isothermal) expansion from $$V_i to$$ $$V_f. $$What is the work done by the gas?

Accepted Answer

$$W = nRT \ln \left( \frac{V_f}{V_i} \right)$$

Question 16

Which of the following is NOT a state variable in thermodynamics?

Accepted Answer

Work ($$W)$$

Question 17

In a $$pV$$ diagram, what does the area under the curve between two volumes represent?

Accepted Answer

The work done by the gas during the process.

Question 18

Which law states that the thermal energy of a system of particles is equally divided among all possible degrees of freedom?

Accepted Answer

Equipartition theorem

Question 19

What is the enthalpy $$H of a $$system defined as?

Accepted Answer

$$H = E_{int} + pV$$

Question 20

A solid has six degrees of freedom. What is its average thermal energy?

Accepted Answer

$$E_{avg} = 3 Nk_B T$$

Thermodynamics and the Ideal Gas Law: Study Notes

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