JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Heat & Thermodynamics

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During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of

\frac{C _{P}}{C _{V}}

for the gas is :

(A) $\frac{5}{3}$
(B) $\frac{9}{7}$
(C) $\frac{3}{2}$ ✓ Correct
(D) $\frac{7}{5}$

Answer: (C)

Solution

P \propto T^{3} \Rightarrow P T^{- 3} = constant

. From the ideal gas law,

T \propto P V

, so

P (P V)^{- 3} = constant ⟹ P^{- 2} V^{- 3} = constant ⟹ P V^{3/2} = constant

Comparing with the adiabatic relation

P V^{γ} = constant

gives

γ = \frac{C _{P}}{C _{V}} = \frac{3}{2}

JEE Main · 2024 · 05 Apr 2024 · Shift 2 · Single correct option

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