<p>Contrary to the first law of thermodynamics which is generally considered as easily understandable, the second law is often felt as raising conceptual difficulties. It can be noted that their usual presentation is not homogeneous, since the expressions referring to the first law are generally energy equations, while those referring to the second law are entropy equations. If we give to the second law the form of an energy equation, it seems that we are led to extend the significance of the first law. The reason is that, doing so, the change in internal energy corresponding to a given process appears to be different as we are in conditions of irreversibility or of reversibility. In thermodynamic language, this is a way to say that the equality <em>dU<sub>irr</sub> = dU<sub>rev</sub></em> classically interpreted as the formulation of the first law must be substituted by the inequality <em>dU<sub>irr</sub> > dU<sub>rev</sub></em>. Writing this last expression under the form<em> dU<sub>irr</sub> = dU<sub>rev</sub></em> <em>+ dU<sub>add</sub></em>, the question asked concerns the origin of the additional energy noted <em>dU<sub>add</sub></em>,. The suggested answer is that <em>dU<sub>add</sub></em> is a consequence of the Einstein mass-energy relation <em>E = mc<sup>2</sup></em>. This would mean that the laws of thermodynamics are closely linked to the concept of relativity and that the difference <em>dU<sub>irr</sub> - dU<sub>rev</sub></em> can also be formulated <em>dU<sub>irr</sub> = dU<sub>rev</sub></em> <em>- c<sup>2</sup>dm. </em>Such an interpretation was evidently impossible for the creators of the thermodynamic theory, since relativity was unknown at that time. The aim of the present paper is to detail the reasons which lead to this hypothesis, with the hope that it can be felt as a clarification and extension of the theory.</p>
Supplement to the Theory of Relativity