Chapter 6, Problem 6.43NP

(a)

Interpretation Introduction

Interpretation:

The value of $\Delta U$ per mole of ${\text{N}}_2(g)$ at 1 bar pressure and 298 K should be calculated if the volume is increased by 1.00% at constant T.

Concept Introduction :

The change in internal energy with respect to change in volume at constant temperature for Van der Waals gas can be represented as follows:

  ${\left(\frac{\partial U_m}{\partial V}\right)}_T=\frac{a}{V_m^2}$

Where U is internal energy, V is volume, V_m is molar volume and a is correction for intermolecular forces.

(b)

Interpretation Introduction

Interpretation:

The value of $\Delta U$ per mole of ${\text{N}}_2(g)$ at 1 bar pressure and 298 K should be calculated if the volume is increased by 1.00% at constant T.

Concept Introduction :

The internal energy change at constant volume is represented as follows:

  $\Delta U_V=C_{V,m}.\Delta T$

Here,

  $\begin{array}{l}\Delta U_V\text{ - internal energy change at constant volume}\\ C_{V,m}\text{ - specific heat capacity at constant volume}\\ \Delta T\text{ - temperature change}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The ratio of the results in part (a) and (b) should be calculated.

Concept Introduction :

  $\text{Ratio = }\frac{\Delta U_V}{\Delta U_T}$