The first law of thermodynamics is the principle of conservation of energy applied to thermodynamic systems. It states that energy cannot be created or destroyed, although it can be transferred between a system and its surroundings or converted from one form into another. For a closed system, a common sign convention expresses the law as delta U equals Q minus W, where delta U is the change in internal energy, Q is heat supplied to the system and W is work done by the system on its surroundings.
Other sign conventions define work differently, so the exact algebraic form depends on the convention being used. The fundamental physical content is unchanged: the change in a system's total energy equals energy entering minus energy leaving. Internal energy includes microscopic kinetic and potential contributions associated with the particles of the system. The first law therefore provides the basic energy accounting framework for heating, cooling, compression, expansion, engines, refrigerators, chemical reactions and phase changes.
Internal energy is a state function, meaning that its value depends on the thermodynamic state rather than on the particular process used to reach that state. Heat and work, by contrast, are modes of energy transfer rather than properties stored in a system. A system does not contain a quantity of heat in the same sense that it contains internal energy.
Heat is energy transferred because of a temperature difference, while work is energy transferred through organised interactions such as mechanical displacement, electrical processes or other generalised forces. This distinction is essential because two processes can produce the same change in internal energy while involving very different combinations of heat and work. For example, a gas can be heated while expanding, receiving energy as heat while transferring some energy to its surroundings as work. Another process can increase the same gas's internal energy primarily through mechanical compression. The first law accounts for both processes through the same conservation principle.
The historical development of the first law involved the gradual replacement of the caloric theory of heat with the concept of energy conservation. Early theories treated heat as a material substance called caloric, but experiments demonstrated that mechanical work could generate apparently unlimited amounts of heat. Benjamin Thompson, also known as Count Rumford, observed heat generation during cannon boring, while James Prescott Joule performed quantitative experiments connecting mechanical work with thermal energy.
These developments supported the mechanical equivalent of heat and contributed to the formulation of the first law. Julius Robert Mayer, Hermann von Helmholtz and others also contributed to the broader conservation of energy principle. The law was not invented as a single isolated statement by one person; it emerged from nineteenth century developments linking mechanics, heat, chemistry and electricity into a general conservation principle.
The first law applies to several types of thermodynamic systems. A closed system can exchange energy with its surroundings but does not exchange matter across its boundary. An open system, or control volume, can exchange both energy and matter, requiring energy accounting that includes enthalpy, kinetic energy, potential energy and mass flow. An isolated system exchanges neither matter nor energy with its surroundings.
For a steady flow device such as a turbine, compressor or heat exchanger, the first law can be written as an energy balance involving heat transfer, shaft work, mass flow enthalpy and changes in kinetic and potential energy. These equations allow engineers to calculate quantities such as turbine output, compressor power, boiler heat input and cooling requirements. The same conservation principle applies regardless of whether the system is microscopic, domestic, industrial or astronomical.
The first law explains how common thermal devices operate. In a heat engine, energy enters primarily as heat from a high temperature source, some becomes work and the remainder leaves as rejected heat. In a refrigerator, electrical or mechanical work enters the system and permits heat to be transferred from a colder region to a warmer environment.
In a combustion engine, chemical energy stored in fuel is converted through combustion and expansion into mechanical work, with some energy leaving as exhaust and heat. In a battery, chemical energy is converted into electrical energy, with losses and internal processes represented in the energy balance. In an electric heater, electrical work is converted primarily into internal energy and subsequently thermal radiation or heat transfer to the surroundings. The first law permits quantitative accounting for all these transformations.
The first law also governs phase changes and chemical processes. When ice melts at constant pressure and temperature, energy supplied as heat increases the system's enthalpy without necessarily increasing its temperature during the phase transition. During boiling, energy is required to change liquid into vapour because molecular interactions and volume related effects change. Chemical reactions can release or absorb energy, and thermochemical measurements use the first law to establish relationships between reaction enthalpies and other energy quantities.
Calorimetry measures heat transfer under controlled conditions to determine properties such as specific heat capacity, latent heat and reaction enthalpy. The law does not by itself determine whether a process will occur spontaneously or how much useful work can be extracted. Those questions require the second law and concepts such as entropy and exergy.
The first law has important limitations because energy conservation alone does not determine direction or efficiency. It permits many hypothetical transformations that do not occur spontaneously. For example, the first law does not by itself prohibit heat from moving from a colder object to a hotter object, provided the overall energy balance remains satisfied. The second law supplies that missing restriction by introducing entropy and establishing limits on energy conversion.
Similarly, the first law does not tell an engineer what fraction of an energy input is theoretically available as useful work. Two systems can contain the same total energy while having very different abilities to perform useful work depending on temperature, pressure and environmental conditions. Exergy analysis supplements the first law by identifying the maximum useful work obtainable relative to a specified environment and the losses caused by irreversibility.
The first law is therefore a universal bookkeeping principle rather than a complete theory of thermodynamic behaviour. It establishes that every change in a system's energy must be accounted for through transfers and transformations. The law is deeply connected with conservation principles throughout physics, including conservation of mechanical energy, electric charge and relativistic mass energy equivalence, although thermodynamic energy accounting has its own specialised definitions.
Modern thermodynamics applies the first law to engines, refrigeration, power generation, chemical processing, biological metabolism, atmospheric systems and astrophysical processes. Its practical value comes from allowing measurable quantities such as temperature, pressure, heat, work, mass flow and composition to be related quantitatively. Without the first law, energy balances in physical and engineering systems would have no consistent foundation.
