AP EAMCET · PHYSICS · Thermodynamics
The ratio of specific heats of a gas is \(\gamma\). The change in internal energy of one mole of the gas, when the volume changes from \(V\) to \(2 V\) at constant pressure \(p\) is
- A \(\frac{\gamma-1}{p V}\)
- B \(p V\)
- C \(\frac{p V}{\gamma-1}\)
- D \(\frac{p V}{\gamma}\)
Answer & Solution
Correct Answer
(C) \(\frac{p V}{\gamma-1}\)
Step-by-step Solution
Detailed explanation
Change in internal energy, \(d U=d Q-d W\) At constant pressure, \(\begin{aligned} d U & =C_p d T-p d V \\ & =C_p d T-R d T \\ & =\left(C_p-R\right) d T=C_V d T \\ & =\frac{R}{\gamma-1} d T \\ & =\frac{R}{\gamma-1} \times \frac{p V}{R} \\ & =\frac{p V}{\gamma-1} \end{aligned}\)
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