Question

P-V plots for two gases during adiabatic processes are shown in figure. 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

Answer: (B)

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