Chapter 3, Problem 3.16P

(a)

Interpretation Introduction

Interpretation:

It is to be showed that the path of the process of a substance with isothermal compressibility $\kappa$ constant undergoes an isothermal, mechanically reversible process from initial state $(P_1,V_1)$ to final state $(P_2,V_2)$ is:

  $V=A(T)\exp (-\kappa P)$

Concept Introduction:

The volume expansitivity $\beta$ and with isothermal compressibility $\kappa$ is given by:

  $\beta =\frac{1}{V}{(\frac{\partial V}{\partial T})}_P$

  $\kappa =-\frac{1}{V}{(\frac{\partial V}{\partial P})}_T$

After combining both above equations

  $\frac{dV}{V}=\beta dT-\kappa dP$.......(a)

(b)

Interpretation Introduction

Interpretation:

Derive the express for work done having same conditions of part (a) of question for 1 mol of a substance.

Concept Introduction:

The work done on any substance is given by

  $W=-{\displaystyle \underset{V_1}{\overset{V_2}{\int }}PdV}$.......(b)