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(B) For an ideal gas,the relationship between molar specific heat at constant pressure $(C_P)$ and molar specific heat at constant volume $(C_V)$ is g

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$C_P - C_V = R$

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(B) For an ideal gas,the relationship between molar specific heat at constant pressure $(C_P)$ and molar specific heat at constant volume $(C_V)$ is given by Mayer's relation.According to the first law of thermodynamics,for $1$ mole of an ideal gas,$dQ = dU + dW$.At constant volume,$dW = 0$,so $dQ = C_V dT = dU$.At constant pressure,$dQ = C_P dT = dU + P dV$.Since $PV = RT$ for $1$ mole,differentiating gives $P dV = R dT$.Substituting $dU = C_V dT$ and $P dV = R dT$ into the constant pressure equation,we get $C_P dT = C_V dT + R dT$.Dividing by $dT$,we obtain $C_P - C_V = R$.

What is the correct relationship between molar specific heat at constant pressure $(C_P)$ and constant volume $(C_V)$? ($R$ is the universal gas constant)

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