To do chemical thermodynamics, you have to accept only three laws. Everything else can be argued from them, once you or a scientific colleague supplies some of the details describing your system and its chemical interactions.
The first law of thermodynamics is a essentially a law of conservation of energy and can be expressed in a concise mathematical form:
In words, this equation says that the change in energy of the system (ΔU) has to equal the sum of the heat transferred into the system (q) and the work done on the system (w). The symbol Δ means change and here it represents the difference in energy (U) between the initial state (where you began your experiment) and final state (where you ended your experiment) of the system. Heat and work have units of energy, but they are changes in energy. All of these quantities, ΔU, q, w, can be positive, negative or zero, as long as the equation adds up. When q is positive, heat is added to the system and the energy of the system increases by this amount. When q is negative, heat is removed from the system and the energy of the system decreases by this amount. To find out the total increase or decrease of internal energy, however, we have to include the contribution from work.
We will discuss heat and work in just a little bit, but first you have to know that there are (unfortunately!) two different sign conventions for work. Chemists like to define work as positive if it increases the energy of the system. Engineers, however, care mostly about how much energy in the form of work they can get from their system (like a car engine, for example) and they define work as positive if the system does work - that is if the system loses energy. If I distinguish the engineers' work by w*, then
w = -w*
and the first law of thermodynamics becomes
Alas! The engineers and chemists are both convinced that their convention is the best one and they both use the same symbol w despite the fact that the two differ in sign. So as you navigate the various web pages or read different texts on the subject you are apt to see both
This does not mean that w = - w! It means that one source used one sign convention; one used the other.
Internal energy, U, is the energy contained in a system that is associated with random, thermal disorder. You might find ΔU represented by ΔE, instead, and you can use the symbols ΔU and ΔE interchangeably in thermodynamics.
