The diagram shows a horizontal cylindrical container of length 30 cm , which is partitioned by a tight-fitting separator. The separator is diathermic but conducts heat very slowly. Initially, the separator is in the state shown in the diagram. The temperature of the left part of the cylinder is 100 K and that on the right part is 400 K . Initially the separator is in equilibrium. As heat is conducted from the right t

Step-by-step solution

It is given that initially, the separator is in equilibrium; thus pressure on both sides of the gas is equal say, it is P i . If A be the area of cross-section of cylinder, number of moles of gas in the left and right part, n 1 and n 2 , can be given as n 1 = P i 1 0 A R 1 0 0 and n 2 = P i 2 0 A R 4 0 0 Finally, if the separator is displaced to right by a distance x, we have n 1 = P f ⁡ i 1 0 + x A RT f ⁡ and n 2 = P f ⁡ 2 0 - x A RT f ⁡ Here P f ⁡ and T f ⁡ are the final pressure and temperature on both sides aft