The two vessels contain two different gases. The gas pressures are the same, and the ratios

The two vessels contain two different gases. The gas pressures are the same, and the ratios of the root mean square velocities are v1 / v2 = 4. What is the density ratio of these gases?

These problems: V1 / V2 – the ratio of the mean square velocities of the indicated gases (V1 / V2 = 4).

To find the value of the ratio of the densities of these gases, we will use the formula: P = 1/3 * ρ * V ^ 2, whence we express: V = √ (3P / ρ).

The resulting ratio is: V1 / V2 = √ (3P / ρ1) / √ (3P / ρ2) = √ (ρ2 / ρ1) = 4 and ρ2 / ρ1 = 4 ^ 2 = 16.

Answer: The ratio of the densities of these gases is 16 (ρ2 / ρ1 = 16).