P-V plots for two gases during adiabatic proc | 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} V^{\gamma} +

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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 $\frac{dP}{dV} V^{\gamma} + P \gamma V^{\gamma-1} = 0$.Thus, the slope of the $P-V$ curve is $\frac{dP}{dV} = -\gamma \frac{P}{V}$.The magnitude of the slope is proportional to the adiabatic index $\gamma$ (i.e., $|	ext{slope}| \propto \gamma$).From the figure, the slope of curve $2$ is greater than the slope of curve $1$ (at any given $V$).Therefore, $\gamma_2 > \gamma_1$.For a monoatomic gas like $He$, $\gamma = 1.67$, and for a diatomic gas like $O_2$, $\gamma = 1.4$.Since $\gamma_{mono} > \gamma_{dia}$, curve $2$ corresponds to a monoatomic gas $(He)$ and curve $1$ corresponds to a diatomic gas $(O_2)$.Thus, plots $1$ and $2$ correspond to $O_2$ and $He$ respectively.

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

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