Considering oxygen at a temperature of 627 degrees as an ideal gas with an internal energy

Considering oxygen at a temperature of 627 degrees as an ideal gas with an internal energy of 83.2 kJ, determine its mass.

Task data: T (oxygen temperature) = 627 ºС (absolute temperature T = 900 K); U (internal energy) = 83.2 kJ (83.2 * 10 ^ 3 J).

Constants: M (molar mass) = 0.032 kg / mol; R (universal gas constant) = 8.31 J / (mol * K); i (number of degrees of freedom of oxygen) = 5.

We express the mass of oxygen taken from the formula: U = i * m * R * T / 2M, whence m = U * 2M / (i * R * T).

Calculation: m = 83.2 * 10 ^ 3 * 2 * 0.032 / (5 * 8.31 * 900) = 0.142 kg.

Answer: The mass of taken oxygen is 0.142 kg.