Inexact Differential - First Law of Thermodynamics

First Law of Thermodynamics

Inexact differentials are known especially for their presence in the first law of thermodynamics:

The symbol δ instead of the plain d, which originated from the work of German mathematician Carl Gottfried Neumann indicates that Q and W are path-dependent.

Internal energy U is a state function, meaning its change can be inferred just by comparing two different states of the system (not its transition path), which we can therefore indicate with U₁ and U₂. Since we can go from state U₁ to state U₂ either by providing heat Q = U₂ − U₁ or work W = U₂ − U₁, such a change of state does not identify uniquely the values of provided W and Q, but only the change in internal energy ΔU.