# What is the mean square velocity of gas molecules, the density of which at a pressure of 49 kPa is 0.04 kg / m3?

August 28, 2021 | education

| Task data: P (gas pressure) = 49 kPa (49 * 10 ^ 3 Pa); ρ (gas density at a given pressure) = 0.04 kg / m3.

We express the mean square velocity of the molecules of the gas under consideration from the formula: P = ρ * Vav ^ 2/3, whence Vav2 = 3P / ρ and Vav = √ (3P / ρ).

Calculation: Vav = √ (3 * 49 * 10 ^ 3 / 0.04) = 1917 m / s.

Answer: Gas molecules have a root mean square velocity of 1917 m / s.

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