The volume of an ideal gas is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

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Solution

Q.
The volume of an ideal gas $(γ = 1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is: [2024]

1 $\frac{4}{5}$

2 $\frac{16}{25}$

3 $\frac{8}{5 \sqrt{5}}$

4 $\frac{2}{\sqrt{5}}$

Ans.
(3)

For adiabatic process, $P V^{γ} = k$

$P_{1} V_{1}^{3 / 2} = P_{2} V_{2}^{3 / 2}$

$P_{1} \times {(5)}^{3 / 2} = P_{2} \times {(4)}^{3 / 2}$

$\frac{P_{1}}{P_{2}} = {(\frac{4}{5})}^{3 / 2} = \frac{{(2)}^{3}}{{(125)}^{1 / 2}} = \frac{8}{5 \sqrt{5}}$

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