Question

P-V plots for two gases during an adiabatic process are given in the figure.
Plot A and Plot B can correspond to: (assume ideal behaviour)

• A. $\text{He and}{O}_2$
• B. $S{O}_2\text{and Ar}$
• C. $O_2\text{and He}$
• D. $\text{Ar and}{O}_2$

Answer 1

Answer: (B), (C)

$O_2\text{and He}$

$P{V}^{\gamma }$ = constant (in ~adiabatic)
$\therefore$ differentiating,
$dp.V^{\gamma }+\gamma P{V}^{\gamma -1}dV=0$
$\Rightarrow \frac{dp}{dV}=-\gamma \frac{P}{V}$
Hence, from same starting point, slope is greates for gas with higher value of $\gamma .$ Now, $\gamma =1+\frac{2}{f}$ where f : degress of freedom. Higher the vlaue of f, lower is $\gamma$ So, 'A' has higher 'f'' compared to 'B' $\therefore (S{O}_2,Ar)and(O_2,He)$ both are possible