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?
Best Answer
The first law tells you that you can change the internal energy of a system $\Delta U$ by either having work done by the system $W$ or adding heat to the system $Q$
$$\Delta U = Q-W$$
The system does not contain any heat.
Heat and work are not state functions of a system.
So you cannot say that this system has so much heat in it at one time and more heat in it at another time.
However you will see $\delta Q$ in textbooks which means a small amount of heat added not a change in the amount of heat in the system.
Another common form which I cannot reproduce here is a little $d$ with a line through it.
The internal energy of a system is the sum of the kinetic energies and the potential energies.
If a system does no work and you add heat to it, the internal energy of the system increases.
If your system is an ideal gas then this increase in internal energy is an increase in the kinetic energy of the atoms of the gas.
For most systems heat entering a system will affect both the kinetic energy and the potential energy of the system.
Temperature can be defined for a system in equilibrium and so you can define a difference in temperature.