A 100-liter cylinder contains gas at a pressure of 8MPA. Weighing after completely evacuating the gas showed

A 100-liter cylinder contains gas at a pressure of 8MPA. Weighing after completely evacuating the gas showed that the cylinder became 1.2 kg lighter. What was the mean square velocity of the gas molecules?

To calculate the required value of the root mean square velocity of the gas molecules in the cylinder, we use the formula: P = 1/3 * ρ * Vav ^ 2 = 1/3 * (m / Vb) * Vav2, whence we express: Vav = √ (3P * Vb / m).

Variables: P – pressure (P = 8 MPa = 8 * 10 ^ 6 Pa); Vb – the volume of the cylinder (Vb = 100 l = 0.1 m3); m is the mass of the gas (m = 1.2 kg).

Let’s calculate: Vav = √ (3P * Vb / m) = √ (3 * 8 * 10 ^ 6 * 0.1 / 1.2) = 1414.2 m / s.

Answer: While in the cylinder, the gas molecules had a root mean square velocity of 1414.2 m / s.