STATISTICAL MECHANICS PHYS 222

Fall 2002 Homework #2 Dr. P. Misra

Due 9/13/02

1. One mole of a diatomic gas experiences the following thermodynamic cycle of events. It starts out at an initial pressure P_a and volume V_a. During the first stage, the gas expands isothermally to a state of pressure P_b and volume V_b. In the second stage, the gas contracts at constant pressure to V_a. In the third stage of the cycle, the system returns to its initial state P_a, V_a. (Note: All of the transformations are reversible.)

(a) Draw the PV-diagram of the thermodynamic cycle.

Use P_a, V_a, P_b, and V_b to determine the following:

(b) the work done by the gas in each of the three stages of the cycle.

(c) The change in the internal energy of the gas in each of the three stages.

(d) the net heat exchange with the surroundings in the entire cycle.

2. The tension H in a rubber band stretched at constant length, L, is related to the temperature, T, by H = A (L)T, where A(L) >0 is a function of L only. Also > 0.

(a) Show that the internal energy is a function of T only.

(b) Show that the entropy decreases as the band is stretched isothermally.

(c) Show that T increases for adiabatic stretching.

(d) Show that L decreases for heating at constant tension.