At the same temperature and pressure and volume of two gases, which of the following quantities is constant.

(A) Total number of molecules
(B) Average kinetic energy
(C) Root mean square velocity
(D) Mean free path

Hint:First start with finding the formula for all the given options such as formula for the average kinetic energy, root mean square velocity and the mean free path. Then try to understand what are the variable and constant quantity in the formula and finally you will get the required answer.



Complete answer:

Let start with Option(A):
Total number of the molecules of gas does not depends on the volume, pressure and temperature of the gas. Therefore, number of molecules is not constant.

Now, for Option(B):
We know that formula for the average kinetic energy of a gas is as follows;
${K_{avg}} = \dfrac{3}{2}{K_B}T$
Here, it is only depended on temperature of the gas molecule.
Hence the average kinetic energy is constant in this case.

Now, for Option(C):
We know; ${V_{rms}} = \sqrt {\dfrac{{3{k_B}t}}{m}} $
Here, it depends also on the m. Therefore, it is not constant.

Now, for Option(D):
We know; $\lambda = \dfrac{{{K_B}T}}{{\sqrt 2 \pi {d^2}P}}$
Here it also depended on the value of d. Therefore, it is not constant.

Hence the correct answer is Option(B).



Note: Formula for the average kinetic energy, root mean square velocity and the mean free path is needed in order to solve the particular question. Also note that here in the option average kinetic energy is mentioned if it is kinetic energy only then the value will not be constant hence the answer will get changed.