P-V plots for two gases during an adiabatic p | vedclass

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(B) For an adiabatic process, the equation is $PV^{\gamma} = 	ext{constant}$.Differentiating with respect to $V$, we get $\frac{dP}{dV} = -\gamma \fr

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$O_2$ and $He$

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(B) For an adiabatic process, the equation is $PV^{\gamma} = 	ext{constant}$.Differentiating with respect to $V$, we get $\frac{dP}{dV} = -\gamma \frac{P}{V}$.The magnitude of the slope is $|	ext{slope}| = \gamma \frac{P}{V}$.Thus, the slope is directly proportional to the adiabatic index $\gamma$.From the given graph, the magnitude of the slope of curve $(2)$ is greater than the magnitude of the slope of curve $(1)$.Therefore, $\gamma_2 > \gamma_1$.For a monoatomic gas (like $He$), $\gamma = \frac{5}{3} \approx 1.67$.For a diatomic gas (like $O_2$), $\gamma = \frac{7}{5} = 1.4$.Since $\gamma_{	ext{mono}} > \gamma_{	ext{dia}}$, curve $(2)$ corresponds to the monoatomic gas $(He)$ and curve $(1)$ corresponds to the diatomic gas $(O_2)$.Thus, plots $(1)$ and $(2)$ correspond to $O_2$ and $He$ respectively.

$P-V$ plots for two gases during an adiabatic process are shown in the figure. Plots $(1)$ and $(2)$ correspond respectively to

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