A fixed diathermic separator partitions a vessel as shown in the figure. Different ideal gases are contained in the two parts. The rms speed of the molecules in the left part is equal to the mean speed of the molecules in the right part. Evaluate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.

Step-by-step solution

Since the vessel is partitioned by a diathermic separator, heat can flow between the two parts until thermal equilibrium is reached. Therefore, the temperatures of the gases in both parts are equal. Let T_L = T_R = T . The root mean square (rms) speed of gas molecules is given by v_ rms = 3kT m , where k is the Boltzmann constant, T is the temperature, and m is the mass of a single molecule. The mean (average) speed of gas molecules is given by v_ mean = 8kT m . According to the problem, the rms speed of the molecu