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The left and right compartments of a thermally isolated container of length L are separated by a thermally conducting, movable piston of area A . The left and right compartments are filled with 3 2 and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length 2 L 5 . In thermodynamic equilibrium, the piston is at a distance L 2 from the

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Extension in spring aligned & x=0.5 ~L -0.4 ~L & =0.1 ~L aligned FBD of piston aligned & kx + P ₂ ~A = P ₁ ~A & P ₂ ~A = P ₁ ~A - kx aligned P₂=P₁- k L A(10) ....(i) aligned & P ₁ ~V = n ₁ RT & P ₂ ~V = n ₂ RT & P ₁ P ₂ = n ₁ n ₂ = 3 2 aligned P ₁= 3 2 P ₂ ....(ii) aligned & P₂= 3 2 P₂- k L 10 A & P₂ 2 = k L 10 A & P₂= k L 5 A = k L A & = 1 5 =0.2 aligned

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