The first law of thermodynamics simply states that energy is conserved. But it is useful to look at those two non-state variables work and heat. Both are changes in energy of a system, so we can write the first law as $$\Delta U=Q+W$$ where $U$ is the internal energy of the system, $Q$ is the energy added to the system by heating, and $W$ is the work done by the system (or the energy removed from the system by working). It is more convenient mathematically, however, to have a framework for talking about infinitesimal changes in the total energy… $$dU=đQ+đW$$ If I stretch a rubber band and snap it shut repeatedly, what will happen to its temperature? If students look puzzled, suggest they assume that as long as you do this reasonably quickly, the air doesn't get heated up much (nor the fingers). [SWBQ]