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 V0 while the volume to the right is 3V0. Both compartments contain the same monatomic ideal gas. The initial temperature is T0 on both sides, while the pressure is P0 to the left and 2P0 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

The concrete roof of a house is 10 m by 8 m and 10 cm thick (4").
a. At what rate would the roof absorb energy from the sun if the emissivity of the white roof paint is .08? Does your answer depend upon the time of day?
b. Estimate the total heat the roof would absorb over the 12 day.

Problem #3

Utilizing the answer to the previous problem, estimate the overall or average increase in temperature (?T) of the concrete roof from the energy absorbed from the sun during a 12 hour day. Assume that all of the radiation absorbed goes into heating the roof. The specific heat of concrete is about 900 J/kg, and the density is about 2,300 kg/m3.

Solutions