The first law of thermodynamics is the expression of conservation of energy in thermodynamics. It states that energy transferred into or out of a system must be accounted for by changes in its stored energy. For a closed system whose bulk motion and elevation remain unchanged, the change in internal energy equals the heat supplied to the system minus the work it performs. The law establishes an energy balance, rather than specifying which processes can occur spontaneously. (openstax.org)
Formulation and sign conventions
A thermodynamic system is a selected quantity of matter or region of space separated conceptually from its surroundings. For a closed system, no matter crosses its boundary. When changes in bulk kinetic and potential energy are negligible, the first law is written
[ \Delta U=Q-W, ]
where (U) is internal energy, (Q) is net heat transferred into the system, and (W) is net work done by the system on its surroundings. Thus, heating gives positive (Q), while expansion against an external load ordinarily gives positive (W). (openstax.org)
Another convention, widely used in chemistry, assigns positive work to energy transferred into the system:
[ \Delta U=q+w. ]
The two expressions describe the same physical balance; their work variables have opposite signs. Heat, work, and internal energy are measured in joules in the International System of Units. A stated sign convention is essential when interpreting equations or numerical results. (openstax.org)
More generally, a closed system satisfies
[ \Delta E=\Delta U+\Delta K+\Delta E_{\mathrm p}=Q-W, ]
where (K) and (E_{\mathrm p}) are the system’s bulk kinetic energy and potential energy. Internal energy excludes these contributions associated with motion or position of the system as a whole. (ocw.mit.edu)
Stored energy and energy transfer
Internal energy includes microscopic energy associated with particle motion and interactions. It is a state function: its change between two specified equilibrium states does not depend on the path connecting them. Heat and work, by contrast, describe transfers during a process, not quantities stored inside a body. Different paths can involve different amounts of heat and work while producing the same (\Delta U). (openstax.org)
The differential form makes this distinction explicit:
[ dU=\delta Q-\delta W. ]
Here (dU) is an exact differential, whereas (\delta Q) and (\delta W) denote path-dependent transfers. Heating is energy transfer caused by a temperature difference. Work transfers energy through mechanisms such as displacement against a force or rotation of a shaft. Insulating a system therefore prevents heat transfer, but does not necessarily prevent energy transfer by work. (openstax.org)
For quasistatic, mechanically reversible expansion or compression with only pressure–volume work,
[ \delta W=p,dV, \qquad dU=\delta Q-p,dV, ]
where (p) is pressure and (V) is volume. Using the system pressure in this expression requires the relevant quasistatic conditions; it is not a general prescription for arbitrary irreversible processes. (openstax.org)
Important processes
Several common process constraints simplify the energy balance:
- Constant volume: If pressure–volume work is the only possible work, (W=0), so (Q=\Delta U).
- Adiabatic: In an adiabatic process, (Q=0), giving (\Delta U=-W). The system can change temperature despite receiving no heat.
- Isothermal ideal gas: For a fixed amount of an ideal gas, internal energy depends only on temperature. Constant temperature therefore gives (\Delta U=0) and (Q=W); this conclusion does not apply universally to all substances.
- Complete cycle: Returning to the initial thermodynamic state gives (\Delta U=0), so net heat input equals net work output. (openstax.org)
At constant pressure, with only pressure–volume work and negligible bulk energy changes, heat supplied equals the change in enthalpy, defined by (H=U+pV). This relationship underlies much of calorimetry and the measurement of energy changes in chemical reactions. Enthalpy’s state-function character also supports Hess’s law, which allows reaction enthalpies to be combined independently of the reaction pathway. (openstax.org)
Open systems and flowing matter
An open system exchanges matter as well as heat and work. Its energy balance must include the energy carried by entering and leaving material. For steady flow through one inlet and one outlet,
[ \dot Q-\dot W_{\mathrm s}
\dot m\left[ h_2-h_1+\frac{c_2^2-c_1^2}{2}+g(z_2-z_1) \right]. ]
Here (\dot m) is mass flow rate, (h) is specific enthalpy, (c) is speed, (z) is elevation, and (\dot W_{\mathrm s}) is work output excluding flow work. Enthalpy incorporates internal energy and the pressure-related work needed to move matter across the boundary. (live.ocw.mit.edu)
This formulation describes devices including turbines, compressors, and nozzles. In an adiabatic turbine with negligible speed and elevation changes, a decrease in the fluid’s enthalpy corresponds to shaft-work output. In an adiabatic nozzle without shaft work, an enthalpy decrease can instead produce an increase in flow speed. (live.ocw.mit.edu)
Experimental basis and limits
Nineteenth-century experiments established quantitative relationships between mechanical work and thermal effects. James Prescott Joule reported electrical experiments in 1843 and paddle-wheel experiments in 1845 and 1847, comparing mechanical energy expenditure with the warming of liquids through friction. These measurements helped establish the equivalence of mechanical and thermal energy transfers. (me.psu.edu)
The first law rules out sustained net energy production without a corresponding energy input or depletion of stored energy. It does not, however, determine the direction of heat flow or the maximum efficiency of a heat engine. Those restrictions belong to the second law of thermodynamics: a cyclic engine cannot convert heat extracted from a single reservoir entirely into work with no other effect, even though such a proposed conversion could satisfy an energy balance. (ocw.mit.edu)