Q11 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Chemistry

An air bag on adiabatic expansion undergoes $5 \%$ increase in its volume. The percentage change in pressure is $\left[\gamma_{\mathrm{air}}=1.4\right]$

  • A
    5
  • B
    6
  • Correct answer
    C
    7
  • D
    9

Solution

$\mathrm{Pv}^{\mathrm{r}}=\mathrm{K}$ Differentiate above equation; $$ \begin{aligned} & \mathrm{Pv}^{\mathrm{r}-1} \mathrm{dv}+\mathrm{dPv}^{\mathrm{r}}=0 \\ & \frac{\mathrm{dP}}{\mathrm{P}}=-\mathrm{r} \frac{\mathrm{dv}}{\mathrm{v}} \\ & \frac{\mathrm{dP}}{\mathrm{P}} \times 100=-\mathrm{r}\left(\frac{\mathrm{dv}}{\mathrm{dv}} \times 100\right) \\ & =-1.4 \times 5 \\ & =7 \end{aligned} $$

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

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