The specific heat of a gas at constant pressu | vedclass

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(A) By the first law of thermodynamics,$dQ = dU + dW$.For a gas at constant volume,the volume change $dV = 0$,so the work done $dW = P dV = 0$. Thus,a

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work is done in the expansion of the gas at constant pressure

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(A) By the first law of thermodynamics,$dQ = dU + dW$.For a gas at constant volume,the volume change $dV = 0$,so the work done $dW = P dV = 0$. Thus,all heat supplied goes into increasing the internal energy $(dQ = dU = C_v dT)$.For a gas at constant pressure,when heat is supplied,the gas expands to maintain constant pressure. This expansion requires the gas to do work against the external pressure $(dW = P dV > 0)$.Therefore,to achieve the same rise in temperature $(dT)$,more heat must be supplied at constant pressure to account for both the increase in internal energy and the work done during expansion $(C_p dT = dU + P dV)$.Since $C_p dT > C_v dT$,it follows that $C_p > C_v$.

The specific heat of a gas at constant pressure $(C_p)$ is more than that of the same gas at constant volume $(C_v)$ because

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