A cylindrical tube of length 30 cm is partitioned by a tight-fitting separator. The separator is very thin, very weakly conducting and can freely slide along the tube. Ideal gases are filled in the two parts of the vessel. In the beginning, the temperature in the parts A and B are 400 K and 100 K respectively. The separator slides to a momentary equilibrium position at which the length of the tube at part A is 20 cm. Find the final equilibrium position of the separator, reached after a long time.

Explanation

Apply `(p_1V_1)/(T_1) = (p_2V_2)/(T_2)` for part A under the given two conditions and again for part B. Remember that at both the equilibrium positions, both sides will have the same pressure.
10 cm along part A