Which of the following relations does NOT give the equation of an adiabatic process, where γ = Cₚ/Cᵥ?
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Question

Which of the following relations does NOT give the equation of an adiabatic process, where γ = Cₚ/Cᵥ?

G1 Physics · Accepted Answer

Step 1: The standard equation for a reversible adiabatic process of an ideal gas is PVᵞ = constant. Step 2: Using PV = nRT gives TV⁽ᵞ⁻¹⁾ = constant. Step 3: From V = nRT/P, substitute into PVᵞ = constant: P(nRT/P)ᵞ = constant. Step 4: Simplifying gives P⁽¹⁻ᵞ⁾Tᵞ = constant. Step 5: Therefore options A, B and C describe equivalent adiabatic laws. Step 6: The powers are INTERCHANGED in option D: PᵞT⁽¹⁻ᵞ⁾ = constant. This is NOT generally an adiabatic relation. Final answer: (D).