Q149 / 170 · Manipal (MET) 2021 · Physics

During an adiabatic process, the pressure $P$ of a fixed mass of an ideal gas changes by $\Delta P$ and its volume $V$ changes by $\Delta V$. If $\gamma=C_P / C_V$, then $\Delta V / V$ is given by:

  • A
    $-\Delta p / p$
  • B
    $-\gamma \Delta P / P$
  • Correct answer
    C
    $-\Delta P / \gamma P$
  • D
    $\Delta P / \gamma^2 P$

Solution

$K_{\text {adia }}=\gamma P=-\frac{\Delta P}{\Delta V / V}$ $\therefore \quad \frac{\Delta V}{V}=-\frac{\Delta P}{\gamma P}$

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

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