The First Law of Thermodynamics

We have already studied this! The first law of thermodynamics is nothing more than a re-statement of the work energy theorem, which was

Recall that the total work W was always W = ΔK. Identify heat Q as Q ≡ W_NC and internal energy (such as energy stored in a gas, which is just potential energy) is E_int ≡ U and we have

or

which is the first law of thermodynamics. The meaning of this law is that the internal energy of a system can be changed by adding heat or doing work. Often the first law is written for tiny changes as