Q145 / 160 · AP EAMCET 2021 (25 Aug Shift 1) · Physics

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

  • A
    $\frac{U}{T}$
  • B
    $\frac{d U}{d T}$
  • Correct answer
    C
    $\frac{d U}{d T}+R$
  • D
    $U \times T$

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, $C_p=\frac{d U}{d T}+R$

Hence, the correct answer is option: 'C'.

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