A monoatomic ideal gas with a mass of 20 g, when expanded without heat exchange, performed work of 249 J.

A monoatomic ideal gas with a mass of 20 g, when expanded without heat exchange, performed work of 249 J. How many degrees did the gas temperature change? The molar mass of the gas is 0.04 kg / mol.

Data: m (ideal gas mass) = 20 g (0.02 kg); A (work done by gas) = 249 J; M (molar mass) = 0.04 kg / mol.

Constants: R (universal gas constant) = 8.31 J / (mol * K); i (number of degrees of freedom of molecules) = 3.

1) Because gas expansion occurred without heat exchange (Q = 0), then A = ΔU (internal energy) = 249 J.

2) Determine the change in gas temperature: ΔU = i / 2 * (m / M) * R * ΔT, whence ΔT = 2 * ΔU * M / (i * m * R) = 2 * 249 * 0.04 / (3 * 0.02 * 8.31) = 39.95 K.