the first law of thermodynamics

The first law of thermodynamics is the law of conservation of energy dressed for the world of heat. It says you cannot create energy out of nothing and you cannot destroy it — you can only move it around or change its form. If a system's internal energy goes up, that energy had to come from somewhere: either heat flowed in, or work was done on it, or both. There is no free lunch and no leaks left unaccounted for.

More precisely, the change in a system's internal energy equals the heat added to it minus the work it does on its surroundings: ΔU = Q - W. Here ΔU is the change in internal energy, Q is heat added TO the system (positive when heat flows in), and W is work done BY the system (positive when the system pushes on its surroundings, for example a gas expanding against a piston). Rearranged, Q = ΔU + W: heat you pour in either raises the internal energy or gets spent doing work, or is split between the two.

This bookkeeping rules all of thermodynamics, from engines to refrigerators to your own metabolism. One honest warning about signs: physics textbooks usually write ΔU = Q - W with W as work done BY the system, while chemistry books often write ΔU = Q + W with W as work done ON the system. The physics is identical — only the label on W flips — but you must know which convention you are using or every calculation will come out wrong.