Question 1

A balloon is inflated at room temperature and then placed in a refrigerator overnight. What happens to the volume of the balloon, and why?

Accepted Answer

The volume decreases because, according to the ideal gas law $$PV = nRT$$, lowering the temperature $$T at $$constant pressure $$P$$ causes the volume $$V to $$decrease.

Question 2

A cylinder contains helium gas and another contains krypton gas at the same temperature. Which statement is TRUE?

Accepted Answer

The average kinetic energy of atoms in both gases is the same, given by $$\frac{3}{2}k_B T.$$

Question 3

The air inside a hot-air balloon has a temperature of 370 K and a pressure of 101.3 kPa, the same as the air outside. If the air inside is composed of 78% $$N_2$$, 21% $$O_2$$, and 1% $$H_2O$$, what is the density of the air inside the balloon?

Accepted Answer

Use $$\rho = \frac{P M}{R T}$$, where $$M is $$the average molar mass. The density is less than outside air because the temperature is higher.

Question 4

An air bubble rises from the bottom to the top of a freshwater lake. Its volume increases by 80%. If the temperatures at the bottom and top of the lake are 4.0°C and 10°C, respectively, how deep is the lake?

Accepted Answer

Use the combined gas law $$\frac{P_1$ V_1$}{T_1$} = \frac{P_2$ V_2$}{T_2$}$$, and solve for the pressure difference to find the depth.

Question 5

A gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has been heated to a temperature of 20°C. If the gauge pressure inside the bulb when it is hot, assuming its average temperature is 60°C, is measured to be 0.06 atm, what is the actual final pressure inside the bulb?

Accepted Answer

The final pressure is $$P = P_0$ + 0.06$$ atm, where $$P_0 is $$atmospheric pressure.

Question 6

Which of the following best explains why the pressure inside a sealed empty gas can expands on a hot day, possibly blowing out the walls?

Accepted Answer

As temperature increases, the pressure increases according to $$P = \frac{nRT}{V}$$, which can exceed the structural limits of the can.

Question 7

During a thermodynamic cycle shown on a $$P$$-$$V$$ diagram, the system undergoes the following steps: AB and BC, 3600 J and 2400 J of heat, respectively, are added to the system. If the work done during AB is 600 J and during BC is 800 J, what is the change in internal energy during AB and BC?

Accepted Answer

Use $$\Delta U = Q - W$$ for each step: $$\Delta U_{AB} = 3600 - 600 = 3000 J$$, $$\Delta U_{BC} = 2400 - 800 = 1600 J.$$

Question 8

Which of the following scenarios involves work being done BY the system ON the environment?

Accepted Answer

Opening a carbonated beverage, as the gas expands against atmospheric pressure.

Question 9

For a monoatomic ideal gas, the root mean square speed $$v_{rms} is $$given by which formula?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$

Question 10

A sealed container of gas is heated from 20°C to 100°C at constant volume. What happens to the pressure inside the container?

Accepted Answer

The pressure increases proportionally to the absolute temperature, $$P_2$$ = $$P_1$$ \frac{$$T_2$$}{$$T_1$$}$$.

Question 11

If the internal energy of 1 mole of an ideal monoatomic gas is $$U = \frac{3}{2}RT$$, what is the internal energy of 2 moles at the same temperature?

Accepted Answer

$$U = 3RT$$

Question 12

A gas sample at 1 atm and 273 K occupies 22.4 L. If the pressure is increased to 2 atm at constant temperature, what is the new volume?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{1 	imes 22.4}{2} = 11.2$$ L

Question 13

Which of the following is NOT an assumption of the kinetic molecular theory of gases?

Accepted Answer

Gas molecules exert attractive forces on each other.

Question 14

A mixture of gases contains 2 moles of $$N_2$$, 1 mole of $$O_2$$, and 1 mole of $$CO_2. $$What is the mole fraction of $$O_2$$?

Accepted Answer

$$X_{O_2$} = \frac{1}{4}$$

Question 15

A gas sample is compressed isothermally from 5.0 L to 2.0 L at 300 K. If the initial pressure is 1.0 atm, what is the final pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$V_1$$}{$$V_2$$} = 1.0 	imes \frac{5.0}{2.0} = 2.5$$ atm

Question 16

Which of the following best describes the work done by a gas during an isobaric expansion from volume $$V_1 to$$ $$V_2 at $$pressure $$P$$?

Accepted Answer

$$W = P(V_2$ - V_1$)$$

Question 17

A sealed flask contains a mixture of gases at 1 atm and 25°C. If the partial pressure of $$O_2 is 0.21 $$atm, what is the mole fraction of $$O_2$$?

Accepted Answer

$$X_{O_2$} = \frac{P_{O_2$}}{P_{total}} = \frac{0.21}{1.00} = 0.21$$

Question 18

Which of the following is a state variable in thermodynamics?

Accepted Answer

Internal energy

Question 19

A sample of gas at 300 K has an average kinetic energy per molecule of $$\frac{3}{2}k_B T. If $$the temperature is doubled, what happens to the average kinetic energy?

Accepted Answer

It doubles, $$\frac{3}{2}k_B (2T) = 3k_B T$$

Thermodynamics and Kinetic Theory: Study Notes and Problem Analysis

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