Chapter 3, Problem 3.30NP

Interpretation Introduction

Interpretation:

Starting with $\beta$ = (1/V) ${(\partial V/\partial T)}_P$ , this is to be proved that $\beta$ = - $(1/\rho ){(\partial P/\partial T)}_P$ , where $\rho$ is the density.

Concept Introduction :

Specific heat could be explained as the quantity of heat needed in order to increase the temperature by 1⁰C. From the given relation $\beta$ = (1/V) ${(\partial V/\partial T)}_P$ , this is to be proved that,

  $\beta$ = - $(1/\rho ){(\partial P/\partial T)}_P\mathrm{.....}(1)$ ,

Here,

  $\beta$ = isobaric volumetric thermal expansion coefficient.

  $\partial V$ = change in volume

  $\partial T$ = change in temperature