First Law of Thermodynamics

The first law of thermodynamics is thermodynamics' version of the law of conservation of energy: the total energy of an isolated system remains constant, no matter how many times it changes from one form to another internally.

When a system moves from an initial state 1 (internal energy $U_1$) to a final state 2 (internal energy $U_2$), the change in internal energy is simply $\Delta U=U_2-U_1$. This change is brought about by some combination of heat being absorbed or evolved, and/or work being done by or on the system. Because the total energy of the system must stay conserved, the mathematical statement of the first law follows directly:

where $q$ is the heat supplied TO the system, and $w$ is the work done ON the system (matching the sign conventions fixed in Section ~7.2.6).

The textbook lists several equivalent ways of phrasing the very same law, each emphasising a slightly different angle on it:

1. Whenever energy of one particular type disappears, an equivalent amount of another type must appear in its place.
2. The total energy of a system together with its surroundings remains constant (is conserved).
3. "Energy can neither be created nor destroyed, but may be converted from one form to another." …