Which statement is correct?

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(C) For an ideal gas,the enthalpy change with respect to temperature at constant pressure is given by $(\frac{dH}{dT})_p = C_p$. Similarly,the interna

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$(\frac{dE}{dV})_T$ for ideal gas is zero

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(C) For an ideal gas,the enthalpy change with respect to temperature at constant pressure is given by $(\frac{dH}{dT})_p = C_p$. Similarly,the internal energy change with respect to temperature at constant volume is given by $(\frac{dE}{dT})_v = C_v$. We know that for an ideal gas,$C_p - C_v = R$. Therefore,$C_p = C_v + R$. Since $R > 0$,it follows that $C_p > C_v$,which means $(\frac{dH}{dT})_p > (\frac{dE}{dT})_v$. Thus,option $A$ is incorrect. Option $B$ is incorrect because $C_p + C_v$ is not equal to $\frac{R}{2}$. For an ideal gas,internal energy $E$ depends only on temperature,so $(\frac{dE}{dV})_T = 0$. Therefore,option $C$ is the correct statement.

List-$I$ (Process)	List-$II$ (Conditions)
$A$. Isothermal process	$I$. No heat exchange
$B$. Isochoric process	$II$. Carried out at constant temperature
$C$. Isobaric process	$III$. Carried out at constant volume
$D$. Adiabatic process	$IV$. Carried out at constant pressure

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