Solve the following problem:
A vessel contains 10-3 m3 of helium gas at 3 K and 103 Pa. Take the zero of internal energy of helium to be at this state.
(a) The temperature is raised at constant volume to 300 K. Assuming helium to behave like an ideal monatomic gas, how much heat is absorbed, and what is the internal energy of the helium? Can this energy be regarded as the result of heating or working?
(b) The helium is now expanded adiabatically to 3 K. How much work is done, and what is the new internal energy? Has heat been converted to work without compensation, thus violating the second law?
(c) The helium is now compressed isothermally to its original volume. What are the quantities of heat and work in this process? What is the thermal efficiency of the cycle? Plot the cycle on a PV diagram.