Work, Heat and the First Law of Thermodynamics

Work and heat are the two ways energy can be exchanged between a system and its surroundings, and both are path functions — their values depend on exactly how a process is carried out, not merely on the initial and final states.

Work in thermodynamics most commonly refers to pressure-volume (mechanical, or "$PV$") work, done when a system's volume changes against an external pressure. For an irreversible process against a constant external pressure $P_{ext}$, the work is

Here the negative sign follows the IUPAC sign convention, under which $w$ is defined as work done on the system. When a gas expands ($\Delta V > 0$), it does work on the surroundings, so $w$ is negative (energy leaves the system); when a gas is compressed ($\Delta V < 0$), work is done on the gas by the surroundings, so $w$ is positive (energy enters the system). This diagram is captured on a pressure-volume graph, where the (shaded) area under a constant-pressure line between the initial and final volumes gives the magnitude of the work exchanged.

Heat, denoted $q$, is energy transferred between system and surroundings purely because of a temperature difference between them, without any accompanying change in the system's volume against a pressure. Under the same IUPAC convention, $q$ is positive when heat is absorbed by the system (flows in) and negative when heat is released by the system (flows out).

The First Law of Thermodynamics states that although heat and work are both path-dependent, their algebraic sum for any given process is always the same and equal to the change in a state function called internal energy, $U$:

$\Delta U = q + w$ …