A monoatomic gas is suddenly compressed to $(1 / 8)^{\text {th }}$ of its initial volume adiabatically. The…

A monoatomic gas is suddenly compressed to $(1 / 8)^{\text {th }}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is $(\gamma=5 / 3)$
  1. 32
  2. 8
  3. $\frac{40}{3}$
  4. $\frac{24}{5}$

Solution

$\frac{\mathrm{V}_2}{\mathrm{~V}_1}=\frac{1}{8}, \gamma=\frac{5}{3}$ For adiabatic process, $\mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma$ $\therefore \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)^\gamma=(8)^{5 / 3}=(2)^5=32$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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