A cylindrical piston-chamber contains an ideal gas in equilibrium with the surroundings at a temperature of 293 K, a pressure of 1 bar and a volume of 5 x 10^-3 m3. The piston-chamber is idealized because it has no mass and can slide without friction. The gas has a ratio of specific heats y = 1.4 and the universal gas constant is R = 8.314 J/(K.mol).
1. Assume the chamber walls are diathermal. The operator slowly pushes on the piston and increases the pressure to 10 bars. What is the new equilibrium pressure volume and temperature ?
2. What are the expressions for the variation in internal energy , the variation in enthalpy , the heat transferred Q and the work exchanged Wwith the surroundings. What are the signs of Q and W?
3. What is the change in entropy of the gas?
4. Defining F ? U - TS and G ? H - TS, give the relation between the variation of free enthalpy ?G and the variation of free energy ?F of the ideal gas.
5. In the next experiment, starting from the same initial conditions, the operator places a mass M = [(P2-P1)A]/g, where P2 is the final pressure of 10 bar, P1 is the initial pressure of 1 bar, is the piston-chamber cross-sectional area and the gravitational acceleration. What are the new final equilibrium volumes and
temperatures ?
6. What is the change of entropy of the the surroundings ?Ssurr?
7. What does Ssurr + Sgas represent? What does the sign mean ?