A monatomic gas at a temperature of 27 ° C has an internal energy of 37.4 kJ.

A monatomic gas at a temperature of 27 ° C has an internal energy of 37.4 kJ. What is the mass of the gas if it is argon?

Initial data: T (absolute temperature of argon) = 300 K (27 ºС); U (internal energy of argon) = 37.4 kJ (37.4 * 103 J).

Reference values: i (number of degrees of freedom of argon molecules) = 3; R (universal gas constant) = 8.31 J / (mol * K); M (molar mass of argon) ≈ 0.04 kg / mol.

The mass of argon is determined from the formula: U = i * m * R * T / 2M, whence m = 2M * U / (i * R * T).

Calculation: m = 2 * 0.04 * 37.4 * 10 ^ 3 / (3 * 8.31 * 300) = 0.4 kg (400 g).

Answer: The mass of argon is 400 grams.