first law of thermodynamics
The first law of thermodynamics is the universe's strict accounting rule: energy is never created or destroyed, only moved around or changed in form. Think of a bank account that nobody can secretly print money into or quietly drain. Every euro that arrives came from somewhere; every euro that leaves went somewhere. The total is always conserved. Energy behaves exactly like that.
Applied to a system, the law says the change in its internal energy equals the heat flowing in plus the work done on it: ΔU = q + w. If you heat a gas and also compress it, both deposits raise its internal energy. If it expands and pushes outward while also losing heat, both withdrawals lower it. The internal energy is the running balance, and heat and work are the only two ways the account changes.
This is why no machine can run forever on nothing — a so-called perpetual-motion machine that creates energy from scratch is forbidden. The first law does not say which way changes will go (that is the second law's job); it only insists that whatever happens, the energy books must balance to the last drop.
Rub your cold hands together briskly. Your muscles do work on them, and that work doesn't vanish — it shows up as a rise in the hands' internal energy, felt as warmth.
Work in, internal energy up — the first law keeps the energy books balanced.
The first law is the law of energy conservation written for thermal systems, with heat included as a form of energy transfer. It says nothing about direction or efficiency — a process can satisfy ΔU = q + w perfectly and still be impossible. Telling allowed from impossible is the work of the second law of thermodynamics.