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.

On earth, STP is based on the average atmospheric pressure at the surface and on a phase change of water that occurs at an easily produced temperature, being only slightly cooler than the average air temperature. The atmosphere of Venus is almost entirely carbon dioxide (CO₂), the pressure at the surface is a staggering 93 atm, and the average temperature is 470℃. Venusian scientists, if they existed, would certainly use the surface pressure as part of their definition of STP. To complete the definition, they would seek a phase change that occurs near the average temperature. Conveniently, the melting point of the element tellurium is 450℃. What are (a) the rms speed and (b) the mean free path of carbon dioxide molecules at Venusian STP based on this phase change in tellurium? The radius of a CO₂ molecule is 1.5 x 10^-10 m.

Uranium has two naturally occurring isotopes. ${}^{238}\text{U}$ has a natural abundance of $99.3\%$ and ${}^{235}\text{U}$ has an abundance of $0.7\%$. It is the rarer ${}^{235}\text{U}$ that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, ${\text{UF}}_6$, which is a gas, then allowing it to diffuse through a series of porous membranes. ${}^{235}U{F}_6$ has a slightly larger rms speed than ${}^{238}U{F}_6$ and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of ${}^{235}U{F}_6$ to that of ${}^{238}U{F}_6$?

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. 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 P_a and atm.

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?

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?