Chapter 20: The Micro/Macro Connection

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

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

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

For a monatomic gas, what is the ratio of the volume per atom $(V/N)$to the volume of an atom when the mean free path is ten times the atomic diameter?

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.

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

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

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.

a. Is vrms of helium greater than, less than, or equal to vrms of

argon? Explain.

b. Does the helium have more thermal energy, less thermal

energy, or the same amount of thermal energy as the argon?

Explain.

9. 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.

a. 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 $100°\mathrm{C}$steam?

b. Finding a large ice cube and some $100°\mathrm{C}$steam would not violate the first law of thermodynamics. $W=0\mathrm{J}$and $Q=0\mathrm{J}$because the container is sealed, and $\Delta E_{\text{th}}=0\mathrm{J}$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?

Eleven molecules have speeds $15,16,17,\dots ,25m/s$. Calculate

(a) $v_{avg}$and

(b) $v_{rms}$.