A cylindrical tube of volume V having adiabatic walls contains an ideal gas. The internal energy of this ideal gas is given by 1.5 nRT . A fixed diathermic wall divides the tube into two equal parts. Initially, the pressure and temperature are p₁, T₁ on the left side and p₂, T₂ on the right side. The system is allowed sufficient time for the temperatures on both sides to become equal. Determine the final equilibrium

Step-by-step solution

Let the total volume of the cylindrical tube be V . Since the diathermic wall divides the tube into two equal parts, the volume of each part is V 2 . The number of moles of gas in the left and right parts initially are: n₁ = p₁ (V/2) R T₁ n₂ = p₂ (V/2) R T₂ Since the outer walls are adiabatic and the inner wall is fixed, there is no heat exchange with the surroundings ( Q = 0 ) and no work is done by the system ( W = 0 ). Thus, the total internal energy of the system remains conserved. Initial internal energy of th