Molar specific heat at constant pressure $C_p$ is related to internal energy $U$ and absolute temperature…

Molar specific heat at constant pressure $C_p$ is related to internal energy $U$ and absolute temperature $T$ as $C_p$ is equal to
  1. $\frac{U}{T}$
  2. $\frac{d U}{d T}$
  3. $\frac{d U}{d T}+R$
  4. $U \times T$

Solution

From Mayer's formula, $ C_p-C_V=R \Rightarrow C_p=C_V+R $ At constant volume, heat capacity, $ \begin{aligned} \frac{d Q}{d T} & =\frac{d U}{d T} \\ \Rightarrow \quad C_V & =\frac{d U}{d T} \end{aligned} \quad(\because \Delta Q=\Delta U) $ Hence, $C_p=\frac{d U}{d T}+R$

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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