Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio Vₐ/Vd and the ratio Vᵦ/Vc is:

Question

G1 Physics · Accepted Answer

Image For an adiabatic process: TVᵞ⁻¹ = constant For path a → d: TₐVₐᵞ⁻¹ = TdVdᵞ⁻¹ Therefore: (Vₐ/Vd)ᵞ⁻¹ = Td/Tₐ For path b → c: TᵦVᵦᵞ⁻¹ = TcVcᵞ⁻¹ Therefore: (Vᵦ/Vc)ᵞ⁻¹ = Tc/Tᵦ Since points a and b lie on the same isotherm: Tₐ = Tᵦ and points c and d lie on the same isotherm: Tc = Td Hence: (Vₐ/Vd)ᵞ⁻¹ = (Vᵦ/Vc)ᵞ⁻¹ Therefore: Vₐ/Vd = Vᵦ/Vc