During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of Cₚ/Cᵥ for the gas is :
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During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of Cₚ/Cᵥ for the gas is :

G1 Physics · Accepted Answer

P ∝ T³ ⇒ PT⁻³ = constant PVᵞ = constant Using PV = nRT: P(nRT/P)ᵞ = constant ⇒ P¹⁻ᵞ Tᵞ = constant ⇒ PTᵞ/(1-ᵞ) = constant Comparing with PT⁻³ = constant: γ/(1 - γ) = -3 ⇒ 3 - 3γ = -γ ⇒ γ = 3/2