Calculate the mass density of air at a temperature of $24^{\circ} \mathrm{C}$ and a pressure of $1 \mathrm{~atm}\left(1.01 \times 10^5 \mathrm{~N} / \mathrm{m}^2\right)$ using the ideal-gas law. Air is roughly 74 percent $\mathrm{N}_2$ and 26 percent $\mathrm{O}_2$.

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?

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 $(b)$ $293 \text{~K}$?

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 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?

You copy the following paragraph from a Martian physics textbook: "$1$ snorf of an ideal gas occupies a volume of $1.35$ zaks. At a temperature of $22$ glips, the gas has a pressure of $12.5 \text{klads}$. At a temperature of $-10$ glips, the same gas now has a pressure of $8.7$ klads Determine the temperature of absolute zero in glips.

A pressure as low as $1.00 \times 10^{-8}$ torr can be achieved using an oil diffusion pump. How many molecules are there in $1.00 \text{~cm}^3$ of gas at this pressure if its temperature is $300 \text{~K}$?

A $10.0\text{-L}$ vessel contains gas at a temperature of $0.00^{\circ} \text{C}$ and a pressure of $4.00 \text{~atm}$. How many moles of gas are in the vessel? How many molecules?

An ideal gas in a cylinder fitted with a piston is held at a fixed pressure. If the temperature of the gas increases from $50^{\circ}$ to $100^{\circ} \text{C}$, by what factor does the volume change?

A thermistor is a solid-state device widely used in a variety of engineering applications. Its primary characteristic is that its electrical resistance varies greatly with temperature. Its temperature dependence is given approximately by $R=R_0 e^{B / T}$, where $R$ is in ohms $(\Omega), T$ is in kelvins, and $R_0$ and $B$ are constants that can be determined by measuring $R$ at calibration points such as the ice point and the steam point. $(d)$ At which temperature is the thermistor most sensitive?

A thermistor is a solid-state device widely used in a variety of engineering applications. Its primary characteristic is that its electrical resistance varies greatly with temperature. Its temperature dependence is given approximately by $R=R_0 e^{B / T}$, where $R$ is in ohms $(\Omega), T$ is in kelvins, and $R_0$ and $B$ are constants that can be determined by measuring $R$ at calibration points such as the ice point and the steam point. $(c)$ What is the rate of change of the resistance with temperature $(d R / d T)$ at the ice point and the steam point?