An ideal gas with a mass of m = 6.0 kg is in a cylinder with a capacity of V = 5.0 m3.

An ideal gas with a mass of m = 6.0 kg is in a cylinder with a capacity of V = 5.0 m3. If the mean square velocity of gas molecules kv = 700 cm, then its pressure p on the walls of the cylinder is

Let’s write the Mendeleev-Clapeyron equation:

p * v = m / M * R * T, where p – pressure, v – volume, m – mass, M – mole mass, R – universal gas constant, T – temperature.

Let us express the product R * T from it:

R * T = p * v * M / m.

To find the root mean square speed, we use the formula:

v = √3 * R * T / M.

Substituting the product R * T into it, we get:

v = √3 * p * v / m.

We express the pressure p:

p = v ^ 2 * m / 3 * v.

We substitute the known values:

p = 700 ^ 2 * 6/3 * 5 = 294 * 10 ^ 4/15 = 1.96 * 10 ^ 5 Pa.