## 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 · c*j =^{2}*N*·*m*·*c*≈ 0.004 kg ·^{2}*c*≈ 3.59 · 10^{2}^{14}J

sd - the heat content contributes mmminmmm
*U*jj=*N*· 1.5 ·*k · T*j =*N*· 1.5 ·_{A}*k*· 10^{8}K = 1.5 ·*R · T*≈ 12.5 · 10^{8}J

mmm - the thermodynamic work yields mmmmm
*P · V*n=*N*·*k · T*j ≈*N*·_{A}*k*· 10^{8}K =*R · T*≈ 8.3 · 10^{8}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 j∆*E* / *c*^{2} jif thermal energy is added to the system. However, the rest energy due to heat and pressure is negligible.