First law of thermodynamics

The first law of thermodynamics is the statement of energy conservation for a thermodynamic system . It postulates the existence of a state function—internal energy —whose change accounts for energy transferred via heat and work during a thermodynamic process .

Definition (closed system form). For a closed system undergoing any process between equilibrium states,

where $Q$ is the net energy transferred as heat and $W$ is the net energy transferred as work . In differential form this is written

The precise sign of $W$ depends on the chosen work sign convention ; likewise, how pressure–volume contributions are recorded is fixed by the pressure–volume work convention .

Physical interpretation. The system’s microscopic energy content can change only by exchanging energy with the surroundings . The first law does not say how that energy exchange must occur; it only asserts that all exchanges add up consistently into a conserved accounting.

Heat and work are path-dependent. While $U$ is a state function (so $\Delta U$ depends only on the endpoints), $Q$ and $W$ are path functions : their values depend on the details of the process. This is why one writes $\delta Q$ and $\delta W$ rather than exact differentials.

Useful consequences and special cases.

• Cyclic processes. For a cyclic process , $\Delta U=0$, hence the net heat and work balance: $\oint \delta Q + \oint \delta W = 0.$
• Mechanical work example. In a quasistatic compression/expansion, work is often dominated by pressure–volume exchange involving pressure and volume ; the sign and exact form follow the adopted conventions referenced above.
• Particle exchange. For an open system where particles cross the system boundary , energy can also be transported with matter. In equilibrium thermodynamics this contribution is commonly organized using the chemical potential and a chemical work convention ; a common bookkeeping form is $dU = \delta Q + \delta W + \mu\, dN,$ with the understanding that what is counted as “work-like” versus “heat-like” depends on the chosen convention and description.

Together with the second law , the first law anchors the structure of equilibrium thermodynamics by linking measurable transfers ($Q,W$) to changes in a state property ($U$).