Q: Which equation correctly relates the root mean square speed $$v_{\text{rms}} of a $$gas molecule to temperature $$T$$ and molar mass $$M$$?

$$v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$$

Question 1

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

Accepted Answer

The balloon shrinks because the temperature decrease causes the gas molecules to move slower, reducing pressure and volume.

Question 2

Given two cylinders, one containing helium gas and the other containing krypton gas at the same temperature, which statement is TRUE?

Accepted Answer

The average kinetic energy of atoms in both gases is the same.

Question 3

The air inside a hot-air balloon has a temperature of 370 K and a pressure of $$101.3\,	ext{kPa}$$, the same as the air outside. If the air inside is composed of 78% $$	ext{N}_2$$, 21% $$	ext{O}_2$$, and 1% $$	ext{Ar}$$, what is the density of the air inside the balloon?

Accepted Answer

$$\rho = \dfrac{P M}{R T}$$, where $$M is $$the average molar mass of the mixture.

Question 4

An air bubble rises from the bottom to the top of a freshwater lake, and its volume increases by 80%. If the temperatures at the bottom and top are $$4.0\,	ext{°C}$$ and $$10.0\,	ext{°C}$$, respectively, how deep is the lake?

Accepted Answer

Use $$P_1$$ $$V_1$$ / $$T_1$$ = $$P_2$$ $$V_2$$ / $$T_2 to $$solve for the pressure difference, then use $$P = P_0$ + \rho g h to $$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 $$20.0\,	ext{°C}. If $$the gauge pressure inside the bulb when it is hot, assuming its average temperature is $$60.0\,	ext{°C}$$, is measured, what is the expected change in volume due to thermal expansion or gas leaks?

Accepted Answer

The actual final pressure will be less than calculated if gas leaks out as the bulb heats, making the effect significant.

Question 6

Which equation correctly relates the root mean square speed $$v_{	ext{rms}} of a $$gas molecule to temperature $$T$$ and molar mass $$M$$?

Accepted Answer

$$v_{	ext{rms}} = \sqrt{\dfrac{3RT}{M}}$$

Question 7

Consider a sealed empty gas can that expands on a hot day. Which statement best describes the work done?

Accepted Answer

Work is done by the system on the environment as the can expands.

Question 8

During a thermodynamic cycle shown in the $$p$$-$$V$$ diagram, steps AB and BC have $$3600\,	ext{J}$$ and $$2400\,	ext{J} of $$heat added, respectively. If the process is cyclic, what is the total work done over the full cycle?

Accepted Answer

The total work done is equal to the net heat added over the cycle.

Question 9

Which of the following statements about the average kinetic energy of gas molecules is correct?

Accepted Answer

It depends only on the temperature, not on the type of gas.

Question 10

A mixture of gases contains 50% helium and 50% fluorine by mole. If the temperature is the same for both gases, which statement is true about the rms speed of the molecules?

Accepted Answer

Helium atoms have a higher rms speed than fluorine molecules.

Question 11

If the pressure of a gas is doubled while keeping the temperature constant, what happens to the volume?

Accepted Answer

The volume is halved, according to Boyle's Law: $$P_1$$ $$V_1$$ = $$P_2$$ $$V_2.$$

Question 12

Which of the following is the correct expression for the density of an ideal gas?

Accepted Answer

$$\rho = \dfrac{P M}{R T}$$

Question 13

A sealed can of carbonated beverage is opened. What type of work is done and by whom?

Accepted Answer

Work is done by the system (the beverage) on the environment as gas escapes.

Question 14

Which of the following is the correct formula for the most probable speed $$v_{	ext{mp}} of a $$gas molecule?

Accepted Answer

$$v_{	ext{mp}} = \sqrt{\dfrac{2RT}{M}}$$

Question 15

A tire is filled with air at $$25\,	ext{°C}$$ and $$2.0\,	ext{atm}. If $$the temperature increases to $$50\,	ext{°C}$$ and the volume remains constant, what is the new pressure?

Accepted Answer

$$P_2$$ = $$P_1$$ \dfrac{$$T_2$$}{$$T_1$$}$$

Question 16

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

Accepted Answer

Work

Question 17

If the internal energy of 1 mole of gas in two cylinders is the same, what can be said about the temperature of the gases?

Accepted Answer

The temperature of the gases must be the same.

Question 18

A sealed gas can is heated from $$20\,	ext{°C} to$$ $$60\,	ext{°C}. If $$the initial pressure is $$1.0\,	ext{atm}$$, what is the final pressure, assuming the volume is constant?

Accepted Answer

$$P_2$$ = $$P_1$$ \dfrac{$$T_2$$}{$$T_1$$}$$

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