The cylinder contains 4 kg of gas with a temperature of 270K (Kelvin). What mass of gas must be removed

The cylinder contains 4 kg of gas with a temperature of 270K (Kelvin). What mass of gas must be removed from the cylinder so that when it is heated to 300K, the pressure remains the same?

In accordance with the Mendeleev-Clapeyron law, the parameters of the gas in the initial state are related by the relation

p * V = m1 / M * R * T1.

After Δm = m1 – m2 of the gas mass and the gas were heated from the cylinder, its parameters of steel are related by the ratio:

p * V = m2 / M * R * T2;

p * V = (m1 – Δm) / M * R * T2.

Divide the second equation by the first:

(p * V) / (p * V) = [(m1 – Δm) / M * R * T2] / [m1 / M * R * T1];

1 = (m1 – Δm) / m1 * T2 / T1;

Δm / m1 = 1 – T1 / T2;

Δm = m1 * (1 – T1 / T2);

Δm = 4 * (1 – 270/300) = 0.4 kg.