Chapter 2, Problem 2D.3P

(a)

Interpretation Introduction

Interpretation: The expression for $dV$ and $dp$ has to be stated using the relation that $V$ is a function of $p$ and $T$ and $p$ is a function of $V$ and $T$.

Concept introduction: The expansion coefficient is defined as the fraction change in volume with respect to change in temperature.  Thus, it defines the change in size on changing temperature.  This is represented by the formula given below as,

  $\alpha =\frac{1}{V}{\left(\frac{\partial V}{\partial T}\right)}_p$

The isothermal compressibility is defined as the fraction change in volume with respect to change in pressure.  This is represented by the formula given below as,

  ${\kappa }_T=-\frac{1}{V}{\left(\frac{\partial V}{\partial p}\right)}_T$

(b)

Interpretation Introduction

Interpretation: The expression for $d\ln V$ and $d\ln p$ in terms of expansion coefficient and isothermal compressibility has to be stated.

Concept introduction: The expansion coefficient is defined as the fraction change in volume with respect to change in temperature.  Thus, it defines the change in size on changing temperature.  This is represented by the formula given below as,

  $\alpha =\frac{1}{V}{\left(\frac{\partial V}{\partial T}\right)}_p$

The isothermal compressibility is defined as the fraction change in volume with respect to change in pressure.  This is represented by the formula given below as,

  ${\kappa }_T=-\frac{1}{V}{\left(\frac{\partial V}{\partial p}\right)}_T$