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
$\gamma P V^{\gamma-1}+\frac{d P}{d V} V^{\gamma}=0 \text { or } \frac{d P}{d V}=-\frac{\gamma P}{V}$
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.