Q100 / 125 · BITSAT 2020 · Physics

In an adiabatic process, the pressure is increased by $\frac{2}{3} \% .$ If $\gamma=\frac{3}{2},$ then the volume decreases by nearly

  • Correct answer
    A
    $\frac{4}{9} \%$
  • B
    $\frac{2}{3} \%$
  • C
    $1 \%$
  • D
    $\frac{9}{4} \%$

Solution

$\mathrm{PV}^{3 / 2}=\mathrm{K}$ $\log \mathrm{P}+\frac{3}{2} \log \mathrm{V}=\log \mathrm{K}$ $\frac{\Delta \mathrm{P}}{\mathrm{P}}+\frac{3}{2} \frac{\Delta \mathrm{V}}{\mathrm{V}}=0$ $\frac{\Delta \mathrm{V}}{\mathrm{V}}=-\frac{2}{3} \frac{\Delta \mathrm{P}}{\mathrm{P}}$ or $\frac{\Delta \mathrm{V}}{\mathrm{V}}=\left(-\frac{2}{3}\right)\left(\frac{2}{3}\right)=-\frac{4}{9}$

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

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