Question

First law when expressed in terms of entropy takes the form_____

(a) T ds = de – p dv

(b) T ds = dh – p dv

(c) T ds = de + p dv

(d) T ds = dh + p dv

This question was addressed to me by my school teacher while I was bunking the class.

The doubt is from A Brief Review of Thermodynamics topic in portion Compressible Flow – Preliminary Aspects of Aerodynamics

Answer 1

The correct answer is (c) T ds = de + p dv

The explanation: The first law of thermodynamics when expressed in terms of entropy gives us two alternate equations. These equations are T ds = de + p dv and T ds = dh – v dp. We have used the relation of heat and entropy in the first law equation to get these equations.