Chapter 3, Problem 3.18NP

Interpretation Introduction

Interpretation:

This is to be shown that expression ${(\partial U/\partial T)}_T=T{(\partial P/\partial T)}_V-P$ could be written in the form of ${(\partial U/\partial T)}_T=T^2{\left(\partial \left[\frac{P}{T}\right]/\partial T\right)}_V=-\left(\partial \left[\frac{P}{T}\right]/\partial {\left[\frac{1}{T}\right]}_V\right)$ .

Concept Introduction :

The first thermodynamics state is given as below:

  ${(\partial U/\partial T)}_T=T{(\partial P/\partial T)}_V-P$

Here,

U = internal energy

P = pressure

V= volume

T = temperature.