A hypothetical gas expands adiabatically such that its volume changes… | JEE Main 2023 (31 Jan, Shift 2)

Q155JEE Main 2023 · 31 JAN · SHIFT 2Medium

Thermodynamic Processes

A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$ . Then the ratio of $\frac{C_p}{C_v}$ will be.

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Answer: (b)

Adiabatic: $PV^{\gamma} =$ const, so $\frac{P_2}{P_1} = \left(\frac{V_1}{V_2}\right)^{\gamma}$ .
$\frac{16}{81} = \left(\frac{8}{27}\right)^{\gamma} = \left(\frac{2}{3}\right)^{3\gamma}$ and $\frac{16}{81} = \left(\frac{2}{3}\right)^{4}$ .
$3\gamma = 4 \Rightarrow \gamma = \frac{4}{3}$
So the answer is (b) $\frac{4}{3}$ .

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