ExamBro
ExamBro
TS 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

  1. A \(\frac{\gamma-1}{p V}\)
  2. B \(p V\)
  3. C \(\frac{p V}{\gamma-1}\)
  4. D \(\frac{p V}{\gamma}\)
Verified Solution

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, \(\begin{aligned} d U & =C_p d T-p d V \\ & =C_p d T-R d T \\ & =\left(C_p-R\right) d T=C_V d T \\ & =\frac{R}{\gamma-1} d T \\ & =\frac{R}{\gamma-1} \times \frac{p V}{R} \\ & =\frac{p V}{\gamma-1} \end{aligned}\)