A scuba diver is $40 \text{~m}$ below the surface of a lake, where the temperature is $5.0^{\circ} \text{C}$. He releases an air bubble that has a volume of $15 \text{~cm}^3$. The bubble rises to the surface, where the temperature is $25^{\circ} \text{C}$. Assume that the air in the bubble is always in thermal equilibrium with the surrounding water, and assume that there is no exchange of molecules between the bubble and the surrounding water. What is the volume of the bubble right before it breaks the surface? Hint: Remember that the pressure also changes.

After nitrogen $\left(\text{N}_2\right)$ and oxygen $\left(\text{O}_2\right)$, the most abundant molecule in Earth's atmosphere is water, $\text{H}_2 \text{O}$. However, the fraction of $\text{H}_2 \text{O}$ molecules in a given volume of air varies dramatically, from practically zero percent under the driest conditions to a high of $4$ percent where it is very humid. $(a)$ At a given temperature and pressure, would air be denser when its water vapor content is large or small?

An automobile tire is filled to a gauge pressure of $200 \text{kPa}$ when its temperature is $20^{\circ} \text{C}$. (Gauge pressure is the difference between the actual pressure and atmospheric pressure.) After the car has been driven at high speeds, the tire temperature increases to $50^{\circ} \text{C}$. $(b)$ Calculate the gauge pressure if the tire expands so the volume of the enclosed air increases by 10 percent.

An automobile tire is filled to a gauge pressure of $200 \text{kPa}$ when its temperature is $20^{\circ} \text{C}$. (Gauge pressure is the difference between the actual pressure and atmospheric pressure.) After the car has been driven at high speeds, the tire temperature increases to $50^{\circ} \text{C}$. $(a)$ Assuming that the volume of the tire does not change and that air behaves as an ideal gas, find the gauge pressure of the air in the tire.

A container with a volume of $6.0 \mathrm{~L}$ holds $10 \mathrm{~g}$ of liquid helium. As the container warms to room temperature, what is the pressure exerted by the gas on its walls?

A closed container with a volume of $6.00 \text{~L}$ holds $10.0 \text{~g}$ of liquid helium at $25.0 \text{~K}$ and enough air to fill the rest of its volume at a pressure of $1.00 \text{~atm}$. The helium then evaporates and the container warms to room temperature $(293 \text{~K})$. What is the final pressure inside the container?

Imagine that $10.0 \text{~g}$ of liquid helium, initially at $4.20 \text{~K}$, evaporate into an empty balloon that is kept at $1.00$-atm pressure. What is the volume of the balloon at $(b)$ $293 \text{~K}$?

Imagine that $10.0 \text{~g}$ of liquid helium, initially at $4.20 \text{~K}$, evaporate into an empty balloon that is kept at $1.00$-atm pressure. What is the volume of the balloon at $(a)$ $25.0 \text{~K}$?

The boiling point of helium at $1 \mathrm{~atm}$ is $4.2 \mathrm{~K}$. What is the volume occupied by helium gas due to evaporation of $10 \mathrm{~g}$ of liquid helium at $1 \mathrm{~atm}$ pressure and a temperature of $($ a $) 4.2 \mathrm{~K}$ and $($ b $) 293 \mathrm{~K}$ ? temperature of $(a) 4.2 \mathrm{~K}$

A room is $6.0 \text{~m}$ by $5.0 \text{~m}$ by $3.0 \text{~m}$. $(b)$ If the temperature increases by $5.0 \text{~K}$ and the pressure remains constant, how many moles of air leave the room?

A room is $6.0 \text{~m}$ by $5.0 \text{~m}$ by $3.0 \text{~m}$. $(a)$ If the air pressure in the room is $1.0 \text{~atm}$ and the temperature is $300 \text{~K}$, find the number of moles of air in the room?

A plot of volume V versus absolute temperature T for a process that takes a fixed amount of an ideal gas from point A to point B. What happens to the pressure of the gas during this process?

A motorist inflates the tires of her car to a gauge pressure of $180 \text{kPa}$ on a day when the temperature is $-8.0^{\circ} \text{C}$. When she arrives at her destination, the tire pressure has increased to $245 \text{kPa}$. What is the temperature of the tires if we assume that $(b)$ that the tires expand so the volume of the enclosed air increases by $7$ percent?

A motorist inflates the tires of her car to a gauge pressure of $180 \text{kPa}$ on a day when the temperature is $-8.0^{\circ} \text{C}$. When she arrives at her destination, the tire pressure has increased to $245 \text{kPa}$. What is the temperature of the tires if we assume that $(a)$ the tires do not expand?