Chapter 3, Problem 3.25NP

Interpretation Introduction

Interpretation:

This is to be proved that $d\rho /\rho =-\beta dT+kdP$ where $\rho$ is the density $\rho =m/V$ , assuming mass m as constant.

Concept Introduction :

The equation for the isobaric volumetric expansion coefficient and isothermal compressibility are as follows:

$\begin{array}{l}\beta =\frac{1}{V}{\left(\frac{\partial V}{\partial T}\right)}_P\\ k=-\frac{1}{V}{\left(\frac{\partial V}{\partial P}\right)}_T\end{array}$

Here,

$\beta$ = isobaric volumetric expansion coefficient

k = isothermal compressibility

$\partial V$ = change in volume

$\partial P$ = change in pressure