Question

$P-V$ plots for two gases during adiabatic processes are shown in Fig. Plots 1 and 2 should correspond respectively to

• A. $He$ and $O_2$
• B. $O_2$ and $He$
• C. $He$ and $Ar$
• D. $O_2$ and $N_2$

Answer 1

The correct option is B $O_2$ and $He$

For an adiabatic process, $P{V}^{\gamma }=\text{constant}$,
Differentiating, we have
$\gamma P{V}^{\gamma -1}+\frac{dP}{dV}{V}^{\gamma }=0$ or

$\frac{dP}{dV}=-\frac{\gamma P}{V}$
Thus, the slope of $P-V$ curve is proportional to $\gamma$. Now, for a diatomic gas, $\gamma (=7/5)$ is less than that for a monoatomic gas for which $\gamma =5/3$. Therefore, the slope of the $P-V$ curve is less for a diatomic gas than for a monoatomic gas. Hence curve 1 corresponds to diatomic gas and curve 2 to monoatomic gas. Thus, the correct choice is (b).