Q138 / 160 · AP EAMCET 2005 · Physics

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
    $p V$
  • Correct answer
    C
    $\frac{p V}{\gamma-1}$
  • D
    $\frac{p V}{\gamma}$

Solution

Change in internal energy, $d U=d Q-d W$ At constant pressure, $\begin{aligned} d U & =C_p d T-p d V \\ & =C_p d T-R d T \\ & =\left(C_p-R\right) d T=C_V d T \\ & =\frac{R}{\gamma-1} d T \\ & =\frac{R}{\gamma-1} \times \frac{p V}{R} \\ & =\frac{p V}{\gamma-1} \end{aligned}$

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

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