An adiabatic cylinder, closed at both ends, is fitted with a frictionless adiabatic piston that divides the cylinder into two parts. Initially the pressure, volume, and temperature are the same on both sides of the piston (Po, Vo, and To). The gas is ideal with Cv independent of temperature and, ϒ = 1.5. By means of a heating coil in the gas on the left side, heat is slowly supplied to the gas on the left until the pressure reaches 27 Po/8. In terms of nR, Vo, and To:
(a) What is the final volume on the right side?
(b) What is the final temperature on the right side?
(c) What is the final temperature on the left side?
(d) How much heat must be supplied to the gas on the left side? (Note: Ignore the coil!)
(e) How much work is done on the gas on the right side?
(f) What is the entropy change of the gas on the right side?
(g) What is the entropy change of the gas on the left side?
(h) What is the entropy change of the universe?