Chapter 2, Problem 2.7IA

(a)

Interpretation Introduction

Interpretation: The work of the given isothermal reversible expansion of $1.0\text{mol}$ ${\text{CO}}_{\text{2}}$ at $298\text{K}$ on the basis of Van der Waals equation of state has to be calculated.

Concept introduction: The process in which the temperature of the system does not change and remains constant is known as isothermal process.

Van der Waals states that real gases are more compressible as compared to ideal gases.  Thus, the van der Waal’s gas equation with respect to pressure of a gas is given as,

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

(b)

Interpretation Introduction

Interpretation: The affect of the parameter $\gamma$ over the dependence of the pressure on the volume if the expansion is reversible, adiabatic and the gas is perfect has to be stated.  The validation corresponding to the fact that pressure-volume dependence whether becomes stronger or weaker if volume increases has to be stated.

Concept introduction: The perfect gas equation of state is consistent with Boyle’s law, Charles’s law and also with Avogadro’s law.  The perfect gas law is also known as ideal gas equation.  The expression that is used to show the perfect gas equation of state is given as,

    $pV=nRT$

The final volume of any perfect gas for the adiabatic expansion is calculated by the expression,

    $V_{\text{f}}=V_{\text{i}}{\left(\frac{p_{\text{i}}}{p_{\text{f}}}\right)}^{1/\gamma }$