Question

# It is possible to go from a given initial equilibrium state of a system to a...

It is possible to go from a given initial equilibrium state of a system to a given final equilibrium state by a number of different paths, involving different intermediate states and different amounts of heat and work. Since the internal energy of a system is a state function, its change between any two states must be independent of the path chosen. The heat and work flows are, however, path-dependent quantities and can differ on different paths between given initial and final states. This assertion is established here by example. One mole of a gas at a temperature of 25oC and a pressure of 1 bar (the initial state) is to be heated and compressed in a frictionless piston and cylinder to 300oC and 10 bar (the final state). Compute the entropy change (?S) along each of the following paths.

Path A: Isothermal (constant temperature) compression to 10 bar, and then isobaric (constant pressure) heating to 300 oC
Path B: Isobaric heating to 300 oC followed by isothermal compression to 10 bar

Path C: A compression in which Cp = (PV)^gamma , where gamma = Cp/Cv , followed by an isobaric colloing or heating, if necessary, to 300oC

Cp = 38 J/(mol K)