Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube of length 30cm

Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required.

Figure shows a cylindrical tube of length $30 \mathrm{~cm}$ which is partitioned by a tight-fitting separator. The separator is 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 temperatures in the parts A and B are $400 \mathrm{~K}$ and $100 \mathrm{~K}$ respectively. The separator slides to a momentary equilibrium position shown in the figure. Find the final equilibrium position of the separator, reached after a long time.