You have two identical containers, one containing gas Aand the other gas B. The masses of these molecules are and . Both gases are under the same pressure and are at . (a) Which molecules (Aor B) have greater translational kinetic energy per molecule and rms speeds? (b) Now you want to raise the temperature of only one of these containers so that both gases will have the same rms speed. For which gas should you raise the temperature? (c) At what temperature will you accomplish your goal? (d) Once you have accomplished your goal, which molecules (Aor B) now have greater average translational kinetic energy per molecule?

The translational kinetic energy depends on motion through space, and for a rigid body of constant mass is equal to the product of half the mass times the square of the speed.

Formula for translational kinetic energy is

Gases consist of atoms or molecules that move at different speeds in random directions. The root mean square velocity (RMS velocity) is a way to find a single velocity value for the particles. The average velocity of gas particles is found using the root mean square velocity formula:

Translational kinetic energy is the function oftemperatureonly

Mass of gas A and B are

Temperatureof both gas

Both gases are at same pressure

As we have

Therefore,

Boltzman constant is given as

The rms speed for A type molecule

The rms speed for B type molecule

Therefore , A type have greater molecular speed

Hence , rms speed of molecule A is greater than rms speed of molecule B

By increasing thetemperaturerms speed of gas increases Thus to equate the speed of both gases we increase thetemperatureof gas B because gas B have less rms speed

Therefore, we have to increase the temperature of container B as B type gas has less rms speed .

Solve fortemperatureat which RMS speed of both gases are same

Therefore , At temperature RMS speed of both gases are the same.

Thus we get

Therefore ,

Translational Kinetic Energy depends ontemperatureonly

Thus .

Therefore at stage Translational Kinetic Energy of gas B is greater than Gas A .