Question

One mole of an ideal monatomic gas is taken along the process in which $P{V}^x=\text{constant}$. The graph shown represents the variation of molar heat capacity of such a gas with respect to $x$ . Find the values of $C^{\prime }$ and $x^{\prime }$ indicated in the diagram.

• A. $\frac{5}{2}R,\frac{5}{3}$
• B. $\frac{3R}{2},\frac{7}{5}$
• C. $\frac{3R}{2},\frac{5}{3}$
• D. $\frac{5R}{2},\frac{7}{5}$

Answer 1

The correct option is A $\frac{5}{2}R,\frac{5}{3}$

For polytropic process $P{V}^x=\text{constant}$
$C=\frac{R}{\gamma -1}-\frac{R}{x-1}(\text{for monoatomic gas}\gamma =\frac{5}{3})$
$C^{\prime }$ corresponds to $x=0$
$\Rightarrow C^{\prime }=C_p=\frac{R}{\frac{5}{3}-1}+R=\frac{5}{2}R$
$x^{\prime }$ corresponds to $C=0$ [i.e adiabatic]
$\Rightarrow x^{\prime }=\gamma =\frac{5}{3}$