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.
Read more about this topic: Inexact Differential
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