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Two different adiabatic paths for the same gas intersect two isothermal curves as shown in the P-V diagram. The relation between the ratio (Vₐ)/(V_d) and the ratio (V_b)/(V_c) is

Asked in JEE Main 8th April 1st Shift 2024 · Comparing Two Processes

Figure: Comparing Two Processes
Answer: (2) (Vₐ)/(V_d)=(V_b)/(V_c)

Step-by-step solution

Let the two isotherms be at T₁ and T₂, and the two adiabats carry

a→ d and b→ c.

On each adiabat TV^γ-1= constant, so

T₁Vₐ^γ-1=T₂V_d^γ-1 and T₁V_b^γ-1=T₂V_c^γ-1.

Dividing, ((Vₐ)/(V_b))^γ-1=((V_d)/(V_c))^γ-1,

so (Vₐ)/(V_d)=(V_b)/(V_c).

Why the other options are wrong

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