Question

Two samples of the same ideal gas have the same pressure and density. Sample B has twice the volume of sample A.
What is the rms speed of the molecules in sample B?

Answer 1

Given pressure and volume is same, then ratio of rms speed will be 1.

As rms velocity is given by $V_{rms}=\sqrt{\frac{3kT}{M}}=\sqrt{\frac{3P}{\rho}}$ , so by the formula, both sample will have same rms velocity.