Calculate the internal energy of an ideal gas in an amount of 3 mol at a temperature of 127C

To calculate the required internal energy of the taken ideal gas, we use the formula: U = 0.5 * i * (m / M) * R * T = 0.5 * i * ν * R * T.

Variables and constants: i – the number of degrees of freedom of molecules (i = 3, monoatomic gas); ν is the amount of substance (ν = 3 mol); R – universal gas constant (R = 8.31 J / (mol * K)); T – abs. temperature (Т = 127 ºС = 400 К).

Calculation: U = 0.5 * i * ν * R * T = 0.5 * 3 * 3 * 8.31 * 400 = 14 958 J ≈ 15 kJ.

Answer: The sought internal energy is 15 kJ.