- #1

Saptarshi Sarkar

- 99

- 13

- Homework Statement
- A vessel at temperature T contains equal number of molecules of two gases whose masses are m and 4m respectively. What is the RMS velocity of molecules in the mixture?

- Relevant Equations
- ##v_{rms} = \frac {\sqrt {3k_bT}} m##

I know that for a single monoatomic gas with RMS velocity ##v_{rms}## , $$\frac 1 2mv_{rms}^2 = \frac 3 2k_bT$$ where ##m## is mass of a single molecule, ##k_b## is Boltzmann constant and ##T## is temperature of the gas.

For a mixture of gas, I know that the average kinetic energy after mixing the gases will be equal to the sum of average kinetic energy of the two constituent gases before mixing.

##\frac 1 2mv_{rms_1}^2 + \frac 1 24mv_{rms_2}^2 = \frac 1 25mv_{rms}^2##

But, I have no idea how to use this to find the RMS velocity of the mix.

For a mixture of gas, I know that the average kinetic energy after mixing the gases will be equal to the sum of average kinetic energy of the two constituent gases before mixing.

##\frac 1 2mv_{rms_1}^2 + \frac 1 24mv_{rms_2}^2 = \frac 1 25mv_{rms}^2##

But, I have no idea how to use this to find the RMS velocity of the mix.