How much will the internal energy of three moles of an ideal diatomic gas increase when it is isochorically heated from 190 to 210C.

Data: ν (amount of substance of an ideal diatomic gas) = 3 mol; T1 (initial gas temperature) = 190 ºС; T2 (final gas temperature) = 210 ºС; isochoric process.

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

The increase in the internal energy of 3 mol of gas during isochoric heating is determined by the formula: U = 0.5 * i * ν * R * ΔT = 0.5 * i * ν * R * (T2 – T1).

Calculation: U = 0.5 * 5 * 3 * 8.31 * (210 – 190) = 1246.5 J.