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. How far would you be able to see if all the molecules around you suddenly doubled in volume?

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. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.

A gas cylinder has a piston at one end that is moving outward at speed v_piston during an isobaric expansion of the gas. Find an expression for the rate at which v_rms is changing in terms of v_piston, the instantaneous value of v_rms, and the instantaneous value L of the length of the cylinder.

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. What is the edge length L of an L ✕ L ✕ L cube of gas with 1.0 J of thermal energy?

A mad engineer builds a cube, 2.5 m on a side, in which 6.2-cm-diameter rubber balls are constantly sent flying in random directions by vibrating walls. He will award a prize to anyone who can figure out how many balls are in the cube without entering it or taking out any of the balls. You decide to shoot 6.2-cm-diameter plastic balls into the cube, through a small hole, to see how far they get before colliding with a rubber ball. After many shots, you find they travel an average distance of 1.8 m. How many rubber balls do you think are in the cube?

You are watching a science fiction movie in which the hero shrinks down to the size of an atom and fights villains while jumping from air molecule to air molecule. In one scene, the hero's molecule is about to crash head-on into the molecule on which a villain is riding. The villain's molecule is initially 50 molecular radii away and, in the movie, it takes 3.5 s for the molecules to collide. Estimate the air temperature required for this to be possible. Assume the molecules are nitrogen molecules, each traveling at the rms speed. Is this a plausible temperature for air?

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. 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?