An ideal gas expands in such a way that PV^2 | vedclass

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(D) Given the process equation: $PV^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting this into t

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Such an expansion is possible only with cooling.

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(D) Given the process equation: $PV^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting this into the process equation: $\left(\frac{nRT}{V}ight) V^2 = 	ext{constant}$.This simplifies to $nRT \cdot V = 	ext{constant}$.Since $n$ and $R$ are constants, we get $TV = 	ext{constant}$, or $T \propto \frac{1}{V}$.The graph of $T$ versus $V$ is a rectangular hyperbola, not a parabola or a straight line.For an expansion, $V$ increases. Since $T \propto \frac{1}{V}$, as $V$ increases, $T$ must decrease.Therefore, such an expansion is possible only with cooling.

An ideal gas expands in such a way that $PV^2 =$ constant throughout the process.

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