Two different adiabatic paths for the same gas intersect two… | JEE Main 2024 (8 Apr, Shift 1)

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P-V Diagrams & Cyclic Processes

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

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Answer: (c)

Adiabatic: $TV^{\gamma-1} =$ const. a and b lie on the hotter isotherm $T_1$ ; d and c on the colder one $T_2$ .
Path a to d: $T_1V_a^{\gamma-1} = T_2V_d^{\gamma-1} \Rightarrow \left(\frac{V_a}{V_d}\right)^{\gamma-1} = \frac{T_2}{T_1}$ .
Path b to c: $T_1V_b^{\gamma-1} = T_2V_c^{\gamma-1} \Rightarrow \left(\frac{V_b}{V_c}\right)^{\gamma-1} = \frac{T_2}{T_1}$ .
So the answer is (c) $\frac{V_a}{V_d} = \frac{V_b}{V_c}$ .

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P-V Diagrams & Cyclic Processes question from JEE Main 2024 (8 Apr, Shift 1)

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