First law of thermodynamics

Thermodynamics. The first law of thermodynamics is the principle of the conservation of energy stating that there is a state function, the internal energy U, of which the difference between two states of a system is equal to the sum of the work and the quantity of heat provided to the system between these two states (whatever the process leading from one state to the other). This principle establishes the equivalence of work and heat.

A mathematical consequence: dU = dW + dQ is a total derivative.