Chapter 20: The Micro/Macro Connection

$2.0$mol of monatomic gas $A$initially has role="math" localid="1648440865095" $5000J$of thermal energy. It interacts with $3.0$mol of monatomic gas $B$, which initially has $8000J$ of thermal energy.
a. Which gas has the higher initial temperature?
b. What is the final thermal energy of each gas?

$4.0$mol of monatomic gas $A$interacts with $3.0$mol of monatomic gas $B$. Gas $A$initially has $9000J$of thermal energy, but in the process of coming to thermal equilibrium it transfers $1000J$of heat energy to gas $B$. How much thermal energy did gas $B$have initially?

Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each container every second. In $10,000s$, you find $80$times when all the balls were in one container (either one) and the other container was empty.

a. How many balls are there?

b. What is the most likely number of balls to be found in one of the containers?

The pressure inside a tank of neon is $150atm$. The temperature is $25°C$. On average, how many atomic diameters does a neon atom move between collisions?

From what height must an oxygen molecule fall in a vacuum so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at $300K$?

Dust particles are$10\mathrm{\mu m}$in diameter. They are pulverized rock, with $\mathrm{\rho }\approx 2500\mathrm{kg}/{\mathrm{m}}^3$. If you treat dust as an ideal gas, what is the rms speed of a dust particle at$20°\mathrm{C}$$?$

Integrated circuits are manufactured in vacuum chambers in which the air pressure is $1.0\times {10}^{-10}\mathrm{mm}$ of $\mathrm{Hg}$. What are (a) the number density and (b) the mean free path of a molecule? Assume $T=20°\mathrm{C}$.

4. The mean free path of molecules in a gas is $200\mathrm{nm}$.

a. What will be the mean free path if the pressure is doubled while the temperature is held constant?

b. What will be the mean free path if the absolute temperature is doubled while the pressure is held constant?

A mad engineer builds a cube,$2.5\mathrm{m}$on a side, in which $6.2-\mathrm{cm}$diameterrubber 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 $6.2-\mathrm{cm}$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 $1.8\mathrm{m}$. How many rubber balls do you think are in the cube?

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 buildingslocalid="1648634576764" role="math" $500$away.

a. How far would you be able to see if all the molecules around you suddenly doubled in volumelocalid="1648634590441" $?$

b. How far would you be able to see if the temperature suddenly rose from ${20}^{°}\mathrm{C}$to a blazing hot${500}^{°}\mathrm{C}$with the pressure unchanged?