I was looking at the fundamental equation ##dU = Tds - Pdv + \sum_i \ \mu_i \ dN_i## and I was thinking of how many different ways one has for deriving it. I know I have to look through a book on Thermodynamics. I actually have done that some time ago and I will do that again. But the following seems to me not to violate any principle of physics. So I just like to know whether it is valid. So one way of thinking about the fundamental equation above seems like Suppose we increase the energy of a system by a tiny amount. This corresponds (in average) to an increase of the kinetic energy of a typical molecule of the system. As the system expands after we added the tiny amount of energy to it, that increment on the kinetic energy of the particle is lost by the work the particle has done. The last term in the equation could the regarded as due chemical interactions of molecule-to-molecule, and the plus sign indicates that the potential energy associated with the interaction becomes less negative as molecules moves a little bit apart from each other.