## 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 jN · m · c2 ≈  0.004 kg · c2 ≈  3.59 · 1014 J
sd
• the heat content contributes mmminmmmUjjN · 1.5 · k · T jNA · 1.5 · k · 108 K  =  1.5 · R · T  ≈  12.5 · 108 J
mmm
• the thermodynamic work yields mmmmm P · V nN · k · T j ≈  NA · k · 108 K  =  R · T  ≈  8.3 · 108 J
nnn

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 jE / c2 jif thermal energy is added to the system. However, the rest energy due to heat and pressure is negligible.