The Internal Energy as a State Function

When a chemical system gains or loses energy, we need a quantity that represents the total energy stored inside it — chemical, electrical, mechanical, and every other form combined. In thermodynamics we call this the internal energy, $U$, and this part shows that $U$ is a genuine state function by examining every way it can change:

• Work — changing $U$ by doing work alone, through an adiabatic (heat-blocking) wall.
• Heat — changing $U$ by transferring heat alone, through a thermally conducting wall. …