Thermodynamic entropy — UPSC CSE 1993 Physics PYQ

Define entropy. Write a general expression for the elemental entropy change dS for 1 mole of an ideal gas. How would this become for cases where the change is (i) isothermal, (ii) isochoric, (iii) isobaric? Deduce expression for S_2 - S_1 for each of these cases, where (i) and (ii) refer to the initial and final stage entropies respectively. Constants C_p, C_v, R may be used, as needed, to express the results.