Determine the temperature of nitrogen having a mass of 2 g, occupying a volume of 830 cm3

Determine the temperature of nitrogen having a mass of 2 g, occupying a volume of 830 cm3 at a pressure of 0.2 MPa.

Data: m (mass of taken nitrogen) = 2 g (2 * 10 ^ -3 kg); V (nitrogen volume) = 830 cm3 (830 * 10 ^ -6 m3); P (pressure) = 0.2 MPa (0.2 * 106 Pa).

Constants: M (molar mass of nitrogen, nitrogen is a diatomic gas) = 0.028 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

The desired temperature of the taken nitrogen is determined by the Mendeleev-Clapeyron law: P * V = (m / M) * R * T, whence T = P * V * M / (m * R).

Calculation: T = 0.2 * 10 ^ 6 * 830 * 10 ^ -6 * 0.028 / (2 * 10 ^ -3 * 8.31) = 279.7 K.