During an adiabatic process, pressure P is found to be proportional to the cube of the temperature T (P ∝ T³). The ratio Cₚ/Cᵥ for the gas is:
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During an adiabatic process, pressure P is found to be proportional to the cube of the temperature T (P ∝ T³). The ratio Cₚ/Cᵥ for the gas is:

G1 Physics · Accepted Answer

Step 1: For an ideal gas undergoing a reversible adiabatic process, PVᵞ = constant, where γ = Cₚ/Cᵥ. Step 2: Substitute V = nRT/P into PVᵞ = constant. Step 3: This gives P(nRT/P)ᵞ = constant, or TᵞP⁽¹⁻ᵞ⁾ = constant (n and R are fixed). Step 4: Rearranging: P ∝ T⁽ᵞ⁄⁽ᵞ⁻¹⁾⁾. Step 5: The question states P ∝ T³, so γ/(γ − 1) = 3. Step 6: Solve: γ = 3γ − 3 ⇒ 2γ = 3 ⇒ γ = 3/2. Final answer: (D) Cₚ/Cᵥ = 3/2.