The adiabatic elasticity of a gas is equal to

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(C) 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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$\gamma 	imes 	ext{pressure}$

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(C) 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 $V$,we get $P(\gamma V^{\gamma-1}) + V^{\gamma} \frac{dP}{dV} = 0$.Dividing by $V^{\gamma-1}$,we get $P\gamma + V \frac{dP}{dV} = 0$.Rearranging the terms,we find $-V \frac{dP}{dV} = \gamma P$.The adiabatic elasticity $K_a$ is defined as the bulk modulus for an adiabatic process,given by $K_a = -V \frac{dP}{dV}$.Therefore,$K_a = \gamma P$.

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