As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition (P₁) and a freely movable but thermally insulated piston (P₂) . The partition P₁ with thermal conductivity K , cross sectional area A and width x divides the container into two sections, S₁ and S₂ , each containing one mole of a monoatomic gas. The piston P₂ moves freely such that the gas in S₂ is always at th

Step-by-step solution

Let T₁ and T₂ be the temperatures of the gases in sections S₁ and S₂ respectively. Assume T₁ > T₂ , so heat flows from S₁ to S₂ . The rate of heat transfer through the partition P₁ is given by Fourier's law of heat conduction: dQ dt = KA x (T₁ - T₂) For section S₁ , the volume is constant (since P₁ is immovable). Thus, the process is isochoric. The heat lost by S₁ is: dQ = -n₁ C_V dT₁ Since the gas is monoatomic and n₁ = 1 mole, C_V = 3 2 R . dT₁ = - 2 dQ 3R For section S₂ , the pressure is constant (since P₂ is fr