JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Heat & Thermodynamics

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A hypothetical gas expands adiabatically such that its volume changes from 08 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.

(A) $\frac{4}{3}$ ✓ Correct
(B) $\frac{3}{1}$
(C) $\frac{1}{2}$
(D) $\frac{3}{2}$

Answer: (A)

Solution

An adiabatic change obeys

P V^{γ} = constant

, so

\frac{P _{2}}{P _{1}} = (\frac{V _{1}}{V _{2}})^{γ}

. Here

\frac{V _{1}}{V _{2}} = \frac{8}{27} = (\frac{2}{3})^{3}

and

\frac{P _{2}}{P _{1}} = \frac{16}{81} = (\frac{2}{3})^{4}

. Equating

(\frac{2}{3})^{4} = (\frac{2}{3})^{3 γ}

forces

3 γ = 4

, so the ratio of the specific heats is

\frac{4}{3}

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Single correct option

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