First Law of Thermodynamics

The inner energy of a system can be changed by either inserting mechanical work $$\mathrm{d}W = p\,\mathrm{d}V$$ or heat energy $\mathrm{d}Q$. This can be written as $$\boxed{\mathrm{d}U = p\,\mathrm{d}V+\mathrm{d}Q}$$