Chapter 20: The Micro/Macro Connection

FIGURE $P20.50$shows the thermal energy of$0.14mol$of gas as a function of temperature. What is$C_v$ for this gas?

A $100c{m}^3$box contains helium at a pressure of $2.0atm$and a temperature of $100°C$. It is placed in thermal contact with a$200c{m}^3$box containing argon at a pressure of$4.0atm$and a temperature of $400°C$.

a. What is the initial thermal energy of each gas?

b. What is the final thermal energy of each gas?

c. How much heat energy is transferred, and in which direction?

d. What is the final temperature?

e. What is the final pressure in each box?

$2.0g$of helium at an initial temperature of $300K$interacts thermally with $8.0g$of oxygen at an initial temperature of $600K$.

a. What is the initial thermal energy of each gas?

b. What is the final thermal energy of each gas?

c. How much heat energy is transferred, and in which direction?

d. What is the final temperature?

A gas of $1.0\times {10}^{20}$atoms or molecules has $1.0J$ of thermal energy. Its molar specific heat at constant pressure is $20.8J/molK$. What is the temperature of the gas?

Scientists studying the behavior of hydrogen at low temperatures need to lower the temperature of $0.50mol$of hydrogen gas from $300K$ to $30K$. How much thermal energy must they remove from the gas?

A water molecule has its three atoms arranged in a "$V$" shape, so it has rotational kinetic energy around any of three mutually perpendicular axes. However, like diatomic molecules, its vibrational modes are not active at temperatures below $1000K$. What is the thermal energy of $2.0mol$ of steam at a temperature of $160°C$?

A monatomic gas and a diatomic gas have equal numbers of moles and equal temperatures. Both are heated at constant pressure until their volume doubles. What is the ratio $Q_{diatomic}/Q_{monatomic}$?

In the discussion following Equation $20.43$ it was said that $Q_1=-Q_2$. Prove that this is so.

A monatomic gas is adiabatically compressed to $\frac{1}{8}$of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not?

a. The $rms$speed.

b. The mean free path.

c. The thermal energy of the gas.

d. The molar specific heat at constant volume.

$n$moles of a diatomic gas with $C_v=\frac{5}{2}R$has initial pressure $p_1$and volume $V_i$. The gas undergoes a process in which the pressure is directly proportional to the volume until the $rms$speed of the molecules has doubled.

a. Show this process on a $pV$diagram.

b. How much heat does this process require? Give your answer in terms of $n$, $p_1$, and $v_i$.