35 The Proportion of Heat Energy to Total Energy
What is the contribution of heat energy to the total energy of a volume of gas ? Does the mass of a gas cloud noticeably increase when it is heated ?
We calculate this contribution for 1 mol of helium at a temperature of 100 million K. In the rest system of the gas cloud, we determine the proportions as follows:
- the mass at 0 K contributes mmmmmmm M · c2 j = N · m · c2 ≈ 0.004 kg · c2 ≈ 3.59 · 1014 J
- the heat content contributes mmminmmmUjj= N · 1.5 · k · T j = NA · 1.5 · k · 108 K = 1.5 · R · T ≈ 12.5 · 108 J
- the thermodynamic work yields mmmmm P · V n= N · k · T j ≈ NA · k · 108 K = R · T ≈ 8.3 · 108 J
At a temperature of 100 million K, heat and thermodynamic work account for less than a thousandth of one percent of the rest energy due to mass ! And this rest energy precisely consists of the sum of the above three terms as stated in 23 . Heat and pressure likewise contribute to the inertia of the ensemble. Mass increases by j∆E / c2 jif thermal energy is added to the system. However, the rest energy due to heat and pressure is negligible.