An ideal gas is expanding such that PT^2 = co | vedclass

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(C) The given process equation is $PT^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can express pressure as $P = \frac{nRT}{V}$.Substitu

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$\frac{3}{T}$

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(C) The given process equation is $PT^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can express pressure as $P = \frac{nRT}{V}$.Substituting this into the process equation: $\left(\frac{nRT}{V}ight)T^2 = 	ext{constant}$.This simplifies to $\frac{T^3}{V} = 	ext{constant}$, or $V \propto T^3$.Differentiating both sides with respect to $T$: $dV = 3k T^2 dT$, where $k$ is a constant.Since $V = k T^3$, we have $\frac{dV}{dT} = 3k T^2 = \frac{3V}{T}$.The coefficient of volume expansion $\gamma$ is defined as $\gamma = \frac{1}{V} \frac{dV}{dT}$.Substituting the expression for $\frac{dV}{dT}$: $\gamma = \frac{1}{V} \left(\frac{3V}{T}ight) = \frac{3}{T}$.

An ideal gas is expanding such that $PT^2 =$ constant. The coefficient of volume expansion of the gas is

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