PHYSICS 313
Problem set 1 2003
Given September 12 2003
Due September 22 2003

Problem 1: A thermally insulated cylinder is closed at both ends. The cylinder contains two chambers which are separated by an airtight frictionless piston, Initially the piston is clamped in a position where the volume to the left is $V_0$ while the volume to the right is 3 $V_0$. Both compartments contain the same monatomic ideal gas. The initial temperature is $T_0$ on both sides, while the pressure is $P_0$ to the left and 2 $P_0$ to the right. The piston is then released and after some motion back and forth comes to rest. What is the final temperature, volume and pressure on each side if the piston is a thermal conductor (so that the temperature ends up the same on both sides).
Problem 2: An ideal gas of volume 1 liter and pressure 10 bar undergoes a quasistatic adiabatic expansion until the pressure drops to 1 bar. Assume $\gamma$ to be 1.4
a: What is the final volume?
b: If the initial temperature was 300 K what is the final temperature?
Problem 3: Two glass bulbs of the same volume contains dry air. They are connected by a thin tube of negligible volume. Initially the temperature $T$ is the same on both sides. The left bulb is then kept at temperature $T$ while the right bulb is heated. Assume that since the bulbs are connected the two sides always have the same pressure. To what temperature must the temperature on the right side be increased for the pressure inside the assembly to double.