Thermal physics

Internal energy and its change

Internal energy is a system's microscopic energy; it changes through heat transfer or work done on the system.

A gas can warm because heat flows into it or because it is compressed. Either process can change its microscopic energy, although the transfer mechanisms differ.

Heat and work transfer energy

Heat $Q$ and work $W$ are not energy stored as properties of a system's state; they describe energy crossing the system boundary during a process. Internal energy $U$ is a state function, so $\\Delta U$ depends only on the initial and final states.

Quick check

Internal energy is the microscopic energy within a system: it includes thermal motion and interactions among particles, but not the motion of the whole object as a body. Stirring water can therefore raise its internal energy without heat crossing the container wall, while placing a warm object beside a cool one changes internal energy through heat transfer. For a monatomic ideal gas, internal energy depends only on temperature and U=rac32nRT; this is a model result, not a formula for every substance. Because internal energy is a state function, its change depends only on initial and final states, not on the path between them. Heat and work, by contrast, describe ways energy crosses the system boundary during a process; they are not energy stored inside an object. In calculations, define the system carefully and distinguish heat entering it from work done on it by the surroundings.

If a gas receives 200 J of heat and the surroundings do 50 J of work on it, then under the convention $\Delta U=Q+W_{on}$ its internal energy rises by 250 J. Another path between the same initial and final states may involve different heat and work, but the internal-energy change is unchanged.