C_P is always greater than C_V for an ideal g | vedclass

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(B) For an ideal gas,the relationship between molar heat capacities is given by Mayer's relation: $C_P - C_V = R$. At constant volume,the work done by

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No work is done by a gas at constant volume.

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(B) For an ideal gas,the relationship between molar heat capacities is given by Mayer's relation: $C_P - C_V = R$. At constant volume,the work done by the gas is zero $(w = 0)$ because there is no change in volume $(dV = 0)$. Therefore,all the heat supplied at constant volume is used to increase the internal energy of the system $(q_V = \Delta U)$. At constant pressure,some heat is used to increase the internal energy and some is used to perform work of expansion $(q_P = \Delta U + P\Delta V)$. Since the internal energy change $(\Delta U)$ depends only on temperature for an ideal gas,it is the same for both processes for the same temperature change. Thus,$C_P$ must be greater than $C_V$ because additional heat is required to perform work at constant pressure.

$C_P$ is always greater than $C_V$ for an ideal gas. Choose the correct option.

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