Two gases A and B having same initial state (P, V, n, T). Now gas A is compressed to V 8 by isothermal process and other gas B is compressed to V 8 by adiabatic process. The ratio of final pressure of gas A and B is (Both gases are monoatomic, =5 / 3 )

Step-by-step solution

For isothermal process (gas A) aligned & P₁ V₁=P₂ V₂ & P₀ (8 V₀ )=P₂ (V₀ ) & P₂=8 P₀ aligned For adiabatic process (gas B) aligned & P^ = constant & P₂ P₁ =(8)^ & P₂=(8)^ P₀ aligned Hence, ( P ₂ )_ B ( P ₁ )_ A = (8)^ P ₀ 8 P ₀ =(8)^ -1 aligned & (P₂ )_B (P₁ )_A =8^ 2 / 3 & = [3] 64 =4 & (P₁ )_A (P₂ )_B = 1 4 aligned ( given , =5 / 3)