[1] Consider a high-pressure gas cylinder (made of kryptonite, of course), which contains one mole of H2 gas at a temperature of 7500 Kelvin. The gas is allowed to expand to twice its initial volume by means of a movable piston. The expansion happens slowly enough to be reversible, but quickly enough so that no heat is transferred to the gas during the expansion.
(a) [0.5] What is the final temperature of the gas immediately after the expansion, but before the gas has time to come to thermal equilibrium with the walls of the container?
(b) [0.5] How much heat (in Joules) would you have to add to the gas to get it back to its initial temperature?
Hint: Consult Figure 3.9 in your textbook before you start this problem!
Vibration
2
Rotation
Translation
0 10
25
50 75 100 250 500 1000 Temperature, K
2500 5000
Figure 3.9 Heat capacity at constant volume of one molecule of H2, in the gas phase. The vertical scale is in fundamental units; to obtain a value in conventional units, multiply by k. The contribution from the three translational degrees of freedom is ; the contribution at high temperatures from the two rotational degrees of freedom is , and the contribution from the potential and kinetic energy of the vibrational motion in the high temperature limit is 1. The classical limits are attained when the relevant energy level separation is much greater than kT.
