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 Cₚ/Cᵥ for the gas is :
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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 Cₚ/Cᵥ for the gas is :

G1 Physics · Accepted Answer

Given: P ∝ T³ Therefore: PT⁻³ = constant Using ideal-gas relation: T = PV/(nR) Substituting: P(PV)⁻³ = constant So: P⁻²V⁻³ = constant Equivalently: P²V³ = constant Taking square root: PV³ᐟ² = constant For an adiabatic process: PVᵞ = constant Therefore: γ = 3/2 Since: γ = Cₚ/Cᵥ we get: Cₚ/Cᵥ = 3/2