AP EAMCET · PHYSICS · Kinetic Theory of Gases
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 \(\frac{d U}{d T}\)
- C \(\frac{d U}{d T}+R\)
- D \(U \times T\)
Answer & Solution
Correct Answer
(C) \(\frac{d U}{d T}+R\)
Step-by-step Solution
Detailed explanation
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, \(C_p=\frac{d U}{d T}+R\)
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