Heat is the transfer of energy between systems as a result of a temperature difference. In thermodynamics, it describes energy crossing a system boundary, not a substance or a quantity contained within an object. Heat is distinct from internal energy, which characterizes a system’s microscopic energy, and from work, another means of transferring energy. Spontaneous net heat transfer proceeds from higher to lower temperature. The transferred quantity is commonly denoted by (Q) and measured in joules. (openstax.org)
Heat, temperature, and equilibrium
Temperature describes the thermal condition of a body; heat describes an interaction between bodies or between a system and its surroundings. A high temperature therefore does not specify an amount of heat. The energy required to produce a particular temperature change depends on the material, its amount, and the conditions under which it is heated. Two objects at the same temperature can have very different internal energies. (openstax.org)
When bodies at different temperatures can exchange energy thermally, their temperatures tend toward equality. At thermal equilibrium, there is no net heat transfer between them. The zeroth law of thermodynamics establishes the consistency of thermal equilibrium: if two systems are separately in thermal equilibrium with a third, they are in thermal equilibrium with each other. This provides the basis for temperature measurement. (openstax.org)
Energy accounting and process dependence
The first law of thermodynamics expresses conservation of energy. For a closed system with negligible changes in bulk kinetic and potential energy,
[ \Delta U=Q-W, ]
where (\Delta U) is the change in internal energy, (Q) is heat entering the system, and (W) is work performed by it. Under this convention, heat leaving the system and work done on it have negative signs. Other conventions are possible, so signs must be defined explicitly. (openstax.org)
Internal energy is a state function: its change depends only on the initial and final states. Heat and work depend on the process connecting those states. Consequently, there is no general “heat content” whose change equals (Q). In differential notation, this distinction is often expressed as
[ dU=\delta Q-\delta W, ]
with (\delta) marking process-dependent transfers. (openstax.org)
An adiabatic process involves no heat exchange, but its temperature can still change through work. Compressing a thermally insulated gas illustrates why heating and temperature increase are not equivalent concepts. (ocw.mit.edu)
Mechanisms of transfer
Three principal mechanisms are conduction, convection, and thermal radiation. They can operate simultaneously. Conduction transfers energy through microscopic interactions without requiring bulk material motion. Convection involves the movement of a fluid, either through buoyancy-driven circulation or externally imposed flow. Thermal radiation transfers energy through electromagnetic radiation and can operate across a vacuum. Bodies at equal temperature can exchange radiation while having zero net radiative heat transfer. (openstax.org)
For steady conduction through a uniform slab,
[ \dot Q=kA\frac{T_{\mathrm h}-T_{\mathrm c}}{L}, ]
where (A) is area, (L) is thickness, and (k) is thermal conductivity. Larger temperature differences and areas increase the transfer rate; greater thickness reduces it. The rate (\dot Q), unlike the transferred energy (Q), is measured in watts. (openstax.org)
More generally, Fourier’s law relates conductive heat flux to the negative temperature gradient. Combining this relation with local energy conservation yields the heat equation, which describes temperature evolution in a conducting medium under specified material assumptions and boundary conditions. (ocw.mit.edu)
Heat capacity and measurement
For heating or cooling without a phase change, a common approximation is
[ Q=mc\Delta T, ]
where (m) is mass and (c) is specific heat capacity. The corresponding heat capacity of the object is (C=mc). This expression assumes that (c) remains approximately constant over the temperature interval and that the relevant heating conditions are specified. Gas heat capacities differ notably between constant-volume and constant-pressure processes because expansion can require work. (openstax.org)
Calorimetry determines heat exchange from measurable changes, usually temperatures or phase changes. In an ideally thermally isolated assembly, heat released by warmer components balances heat absorbed by cooler components. Actual measurements must also account for the calorimeter’s own heat capacity and energy exchanged with the surroundings. (openstax.org)
During a phase transition, energy transfer need not change temperature. For a pure substance melting or boiling at fixed pressure under equilibrium conditions,
[ Q=mL, ]
where (L) is the specific latent heat of the transition. Energy absorbed during melting or vaporization is released during the reverse transition. Temperature remains at the transition value while the two phases coexist; the amount of each phase changes instead. (openstax.org)
Entropy and thermal machines
The second law of thermodynamics constrains heat transfer and its conversion into work. For a reversible transfer,
[ dS=\frac{\delta Q_{\mathrm{rev}}}{T}, ]
where (S) is entropy and (T) is absolute temperature. Heat transfer across a finite temperature difference is irreversible and produces entropy in the combined system and surroundings. Entropy can change without heat exchange when irreversible processes occur within an adiabatic system. (ocw.mit.edu)
A cyclic heat engine receives heat from a hot reservoir, produces work, and rejects some heat to a colder reservoir. A reversible engine operating between temperatures (T_{\mathrm h}) and (T_{\mathrm c}) has the maximum efficiency
[ \eta_{\max}=1-\frac{T_{\mathrm c}}{T_{\mathrm h}}. ]
The Carnot cycle realizes this ideal limit, with temperatures expressed in kelvins. (openstax.org)
Refrigerators and heat pumps use work to transfer heat from a colder region to a warmer one. Their coefficient of performance compares useful heat transfer with work input and can exceed one because the device moves energy rather than converting work alone into heat. (openstax.org)