I would like to understand the first law of thermodynamics, but I have some problems with the basic concept. How to define exactly the internal energy?
As I see it, given a system of particles, which the principle of work is in force for. Can it be considered 'per definitionem' the isolated thermodynamical system? If yes, the diatermic system can be defined as a system where the priciple of work isn't met. Therefore, if we define the internal energy as the sum of kinetic and potential energies of the particles, there is a term missing from the equation of the sum-work in diatermic case, called heat, which the first law postulates. How can heat be mathematically characterized?