Volume of an ideal gas (gamma=1.5) is changed adiabatically from 5 litres to 4 litres. ratio of init

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11.Thermodynamics

hard

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5$ litres to $4$ litres. The ratio of initial pressure to final pressure is:

A

$\frac{4}{5}$

B

$\frac{16}{25}$

C

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

D

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

(JEE MAIN-2024)

Solution

For Adiabatic process

$P_i V_i=P_f V_f^\gamma$

$P_i(5)^{1.5}=P_f(4)^{1.5}$

$\frac{P_i}{P_f}=\left(\frac{4}{5}\right)^{\frac{3}{2}}=\frac{4}{5} \cdot\left(\frac{4}{5}\right)^{\frac{1}{2}} \Rightarrow \frac{8}{5 \sqrt{5}}$

Standard 11

Physics

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