An adiabatic process is any process occurring without input or output of heat within a system (i.e. during the process the system is thermodynamically isolated- there is no heat transfer with the surroundings). This is the opposite of a diabatic process, where there is heat transfer. A key concept in thermodynamics, many rapid chemical and physical processes are described or approximated in this way. Such processes are usually followed or preceded by events that do involve heat transfer (i.e. are non-adiabatic). Examples include electron-transfer.
Adiabatic processes can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time, so that there is no opportunity for significant heat exchange. Although the terms adiabatic and isocaloric can often be interchanged, adiabatic processes may be considered a subset of isocaloric processes; the remaining complement subset of isocaloric processes being processes where net heat transfer does not diverge regionally such as in an idealized case with mediums of infinite thermal conductivity or non-existent thermal capacity.
In an adiabatic irreversible process, dQ = 0 is not equal to TdS (TdS > 0) where Q is thermal energy, T is temperature, and S is entropy. dQ = TdS = 0 holds for reversible processes only. For example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically (or thermally) insulated; an insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process that is reversible is also called an isentropic process. Conversely, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.
One opposite extreme—allowing heat transfer with the surroundings, causing the temperature to remain constant—is known as an isothermal process. Since temperature is thermodynamically conjugate to entropy, the isothermal process is conjugate to the adiabatic process for reversible transformations.
A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside. At the opposite extreme, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside.
The term "adiabatic" literally means impassable, coming from the Greek roots ἀ- ("not"), διὰ- ("through"), and βαῖνειν ("to pass"); this etymology corresponds here to an absence of heat transfer.
Read more about Adiabatic Process: Adiabatic Heating and Cooling, Ideal Gas (reversible Process), Graphing Adiabats
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