Solids and liquids resist being compressed. They are not totally incompressible, but it takes large forces to compress them even slightly. If it is true that matter consists of atoms, what can you infer about the microscopic nature of solids and liquids from their incompressibility?

Gases, in contrast with solids and liquids, are very compressible. What can you infer from this observation about the microscopic nature of gases?

The density of air at STP is about $\frac{1}{1000}$ the density of water. How does the average distance between air molecules compare to the average distance between water molecules? Explain.

The mean free path of molecules in a gas is 200 nm.

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

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

If the pressure of a gas is really due to the random collisions of molecules with the walls of the container, why do pressure gauges—even very sensitive ones—give perfectly steady readings? Shouldn’t the gauge be continually jiggling and fluctuating? Explain.

Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2.

1. Would the rms speed of the molecules increase by a factor of $2^{1\text{/}2}$, 2, or $2^2?$ Explain.

2. Would the gas pressure increase by a factor of $2^{1\text{/}2}$, 2, or $2^2?$ Explain.

Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2.

1. Would the temperature of the gas increase by a factor of $2^{1\text{/}2}$, 2, or $2^2?$ Explain.

2. Would the molar specific heat at constant volume change? If so, by what factor? If not, why not?

The two containers of gas in FIGURE Q20.8 are in good thermal contact with each other but well insulated from the environment. They have been in contact for a long time and are in thermal equilibrium.

FIGURE Q20.8

1. Is $v_{\text{rms}}$ of helium greater than, less than, or equal to $v_{\text{rms}}$ of argon? Explain.

2. Does the helium have more thermal energy, less thermal energy, or the same amount of thermal energy as the argon? Explain.

Suppose you place an ice cube in a beaker of room-temperature water, then seal them in a rigid, well-insulated container. No energy can enter or leave the container.

1. If you open the container an hour later, will you find a beaker of water slightly cooler than room temperature, or a large ice cube and some $100\text{°C}$ steam?

2. Finding a large ice cube and some $100\text{°C}$ steam would not violate the first law of thermodynamics. $W=0\text{J}$ and $Q=0\text{J}$ because the container is sealed, and $\text{Δ}{E}_{\text{th}}=0\text{J}$ because the increase in thermal energy of the water molecules that became steam is offset by the decrease in thermal energy of the water molecules that turned to ice. Energy would be conserved, yet we never see an outcome like this. Why not?