Answer to Question #160228 in Molecular Physics | Thermodynamics for Gill Allain

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?
(a) twice that in sample A
(b) equal to that in sample A
(c) half that in sample A
(d) impossible to determine

Answer 1

The rms speed of the molecules can be written as follows:

$$v_{rms}=\sqrt{\dfrac{3RT}{M}}=\sqrt{\dfrac{3P}{\rho}},$$

here, $R$ is the universal gas constant, $T$ is the temperature of the gas, $M$ is the molar mass of the gas, $P$ is the pressure of the gas, $\rho$ is the density of the gas.

As we can see from the formula, the rms speed of the molecules is independent of the volume. Therefore, the rms speed of the molecules of sample A and B will be the same. Hence, the correct answer is (b).

Answer:

(b) equal to that in sample A.