Chapter 3, Problem 3.35NP

Interpretation Introduction

Interpretation: The following equation needs to be derived:

  ${\left(\frac{\partial \text{H}}{\partial \text{T}}\right)}_{\text{V}}{\text{ = C}}_{\text{V}}\text{ + V}\left(\frac{\beta }{\text{k}}\right)$

Concept Introduction: The relations of thermodynamics used to derive given equations are coefficient of isothermal compressibility, $\text{k}$ and coefficient of thermal expansion, $\beta$ . The expressions of both the coefficients are:

  $\text{k}=-\frac{1}{\text{V}}{\left(\frac{\partial \text{V}}{\partial P}\right)}_{\text{T}}$ and $\beta =\frac{1}{\text{V}}{\left(\frac{\partial \text{V}}{\partial \text{T}}\right)}_{\text{P}}$

Where $\partial$ represents change, $\text{V}$ represents volume, $\text{T}$ represents temperature, and $\text{P}$ represents pressure.