A 40 liter cylinder contains 2.6 kilograms of nitrogen. At what temperature there is a danger

A 40 liter cylinder contains 2.6 kilograms of nitrogen. At what temperature there is a danger of explosion, if the permissible pressure is 50 * 10 ^ 5.

We calculate the dangerous gas temperature using the Mendeleev-Clapeyron equation:

P * V = (m / M) * R * T, where P is the permissible pressure (P = 50 * 10 ^ 5 Pa), V is the volume of the cylinder (V = 40 l = 40 dm3 = 40 * 10 ^ -3 m3 ), m is the mass of nitrogen in the cylinder (m = 2.6 kg), M is the molar mass of nitrogen (diatomic gas, M = 0.028 kg / mol), R is universal. gas constant (R = 8.31J / (mol * K)), T is the absolute temperature of the gas.

T = P * V * M / (m * R) = 50 * 10 ^ 5 * 40 * 10 ^ -3 * 0.028 / (2.6 * 8.31) ≈ 259 K.