[UPSC CSE 1998] Thermodynamics (Q159, 20M)

Prove that \int_A^B \delta Q / T evaluated along a reversible path joining the states A and B does not depend on the path chosen. Hence define the entropy function S. Calculate the entropy change in an ideal gas undergoing a state change from (V, P) to (2V, P/2) for three suitably chosen different paths and show that the result turns out to be the same all the cases.