Chapter 5, Problem 5.20NP

Interpretation Introduction

Interpretation: The value of heat, work done, change in internal energy, change in enthalpy and entropy needs to be determined for the given process in case of Van der Waals gas.

Concept introduction:

The Van der Waals equation of gas is represented as follows:

  $P=\frac{nRT}{V-nb}-\frac{n^{2}a}{V^2}$

Here, n is number of moles, R is Universal gas constant, T is temperature, V is volume, a and b are Van der Waals constants.

The change in enthalpy can be calculated as follows:

  $\Delta H=\Delta U+\Delta PV$

Here, $\Delta U$ is change in internal energy, P is pressure and V is volume.

The work done can be calculated as follows:

  $w=-{\displaystyle \underset{V_i}{\overset{V_f}{\int }}PdV}$

Here, P is pressure, $V_f$ is final volume and $V_i$ is initial volume.

According to first law of thermodynamics,

  $\Delta U=q+w$

Here, q is heat and w is work done.

Also, the change in entropy can be calculated as follows:

  $\Delta S=\frac{q}{T}$

Here, q is heat and T is temperature.