For an adiabatic expansion of an ideal gas,th | vedclass

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(A) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Differentiating both sides w

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$-\gamma \frac{ dV }{ V }$

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(A) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Differentiating both sides with respect to $V$:$P(\gamma V^{\gamma-1}) + V^{\gamma} \frac{dP}{dV} = 0$Rearranging the terms to find the derivative:$V^{\gamma} \frac{dP}{dV} = -\gamma P V^{\gamma-1}$$\frac{dP}{dV} = -\frac{\gamma P V^{\gamma-1}}{V^{\gamma}}$$\frac{dP}{dV} = -\frac{\gamma P}{V}$Multiplying both sides by $dV$ and dividing by $P$ gives the fractional change in pressure:$\frac{dP}{P} = -\gamma \frac{dV}{V}$

For an adiabatic expansion of an ideal gas,the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

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