3 moles of an ideal gas fill a cubical box with a side length of 30cm. If the temperature of the gas is 20°C, what is the pressure inside the container?

A 1.0 m ✕ 1.0 m ✕ 1.0 m cube of nitrogen gas is at 20℃ and 1.0 atm. Estimate the number of molecules in the cube with a speed between 700 m/s and 1000 m/s.

Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean free path of photons through the gas. Photons are not gas molecules, so the mean free path of a photon is not given by Equation 20.3, but its dependence on the number density of the gas and on the molecular radius is the same. Suppose you are in a smoggy city and can barely see buildings 500 m away.b. How far would you be able to see if the temperature suddenly rose from 20°C to a blazing hot 1500°C with the pressure unchanged?

Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H₂). The number density is about 1 atom/cm³ and the temperature is about 3 K.a. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.

Equation 20.3 is the mean free path of a particle through a gas of identical particles of equal radius. An electron can be thought of as a point particle with zero radius.b. Electrons travel 3.0 km through the Stanford Linear Accelerator. In order for scattering losses to be negligible, the pressure inside the accelerator tube must be reduced to the point where the mean free path is at least 50 km. What is the maximum possible pressure inside the accelerator tube, assuming T = 20℃? Give your answer in both Pa and atm.

A sample of gas is heated in a closed container with a volume of $2.2\mathrm{L},$ from an initial temperature and pressure of $20°\text{}\mathrm{C}$ and $1.0\text{atm}$ to a final temperature of $238°\text{}\mathrm{C}$. What is the final pressure?

An ideal gas is in a sealed container. It has a temperature T when it has volume V at pressure P. What is the temperature of the gas when its volume is quadrupled, and the pressure is halved?