Figure 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 figure. The temperature of left part of cylinder is 100 K and that on right part is 400 K. Initially the separator is in equilibrium. As heat is conducted from right to left part, separator displaces to the right. The displacement of separator (in cm) when two gases on the parts of cylinder are in thermal equilibrium is __________.

It is given that initially the separator is in equilibrium thus pressure on both sides of gas are equal say, it is Pi. If A be the area of cross-section of cylinder, number of moles of gas in left and right part n1 and n2 can be given asn1=Pi(10A)R(100) and n2=Pi(20A)R(400)Finally if separator is displaced to right by a distance x, we haven1=Pf(10+x)ARTf and n2=Pf(20−x)ARTflf Pf and Tf be the final pressure and temperature on both sides after a long time.Now if we equate the ratio of moles n1/n2 in initial and final state we set         n1n2=10A10020A400=(10+x)A(20−x)A or  2(20−x)=10+x or  x=10cmThus in final state when gases in both parts are in thermal equilibrium, the piston is displaced to 10 cm right from its initial position.