Derive an expression for the change in entropy of the universe. What is a temperature-entropy…

Derive an expression for the change in entropy of the universe.

What is a temperature-entropy diagram ?

Derive expressions for entropy changes for a closed system in the following cases :

(i) General case for change of entropy of a gas

(ii) Heating a gas at constant volume

(iii) Heating a gas at constant pressure

(iv) Polytropic process.