Editing Adiabatic process (section)

=== Various applications of the adiabatic assumption ===

For a closed system, one may write the [[first law of thermodynamics]] as {{math|1=Δ''U'' = ''Q'' − ''W''}}, where {{math|Δ''U''}} denotes the change of the system's internal energy, {{math|''Q''}} the quantity of energy added to it as heat, and {{math|''W''}} the work done by the system on its surroundings.

*If the system has such rigid walls that work cannot be transferred in or out ({{math|1=''W'' = 0}}), and the walls are not adiabatic and energy is added in the form of heat ({{math|''Q'' > 0}}), and there is no phase change, then the temperature of the system will rise.
*If the system has such rigid walls that pressure–volume work cannot be done, but the walls are adiabatic ({{math|1=''Q'' = 0}}), and energy is added as [[Isochoric process|isochoric]] (constant volume) work in the form of friction or the stirring of a [[viscous]] fluid within the system ({{math|''W'' < 0}}), and there is no phase change, then the temperature of the system will rise.
*If the system walls are adiabatic ({{math|1=''Q'' = 0}}) but not rigid ({{math|''W'' ≠ 0}}), and, in a fictive idealized process, energy is added to the system in the form of frictionless, non-viscous pressure–volume work ({{math|''W'' < 0}}), and there is no phase change, then the temperature of the system will rise. Such a process is called an [[isentropic process]] and is said to be "reversible". Ideally, if the process were reversed the energy could be recovered entirely as work done by the system. If the system contains a compressible gas and is reduced in volume, the uncertainty of the position of the gas is reduced, and seemingly would reduce the entropy of the system, but the temperature of the system will rise as the process is isentropic ({{math|1=Δ''S'' = 0}}). Should the work be added in such a way that friction or viscous forces are operating within the system, then the process is not isentropic, and if there is no phase change, then the temperature of the system will rise, the process is said to be "irreversible", and the work added to the system is not entirely recoverable in the form of work.
*If the walls of a system are not adiabatic, and energy is transferred in as heat, entropy is transferred into the system with the heat. Such a process is neither adiabatic nor isentropic, having {{math|''Q'' > 0}}, and {{math|Δ''S'' > 0}} according to the [[second law of thermodynamics]].

Naturally occurring adiabatic processes are irreversible (entropy is produced).

The transfer of energy as work into an adiabatically isolated system can be imagined as being of two idealized extreme kinds. In one such kind, no entropy is produced within the system (no friction, viscous dissipation, etc.), and the work is only pressure-volume work (denoted by {{math|''P'' d''V''}}). In nature, this ideal kind occurs only approximately because it demands an infinitely slow process and no sources of dissipation.

The other extreme kind of work is [[isochoric process|isochoric]] work ({{math|1=d''V'' = 0}}), for which energy is added as work solely through friction or viscous dissipation within the system. A stirrer that transfers energy to a viscous fluid of an adiabatically isolated system with rigid walls, without phase change, will cause a rise in temperature of the fluid, but that work is not recoverable. Isochoric work is irreversible.<ref>{{cite book|last=Münster |first=A. |date=1970 |title=Classical Thermodynamics |translator-first=E. S. |translator-last=Halberstadt |publisher=Wiley–Interscience |location=London |isbn=0-471-62430-6 |page=45}}</ref> The second law of thermodynamics observes that a natural process, of transfer of energy as work, always consists at least of isochoric work and often both of these extreme kinds of work. Every natural process, adiabatic or not, is irreversible, with {{math|Δ''S'' > 0}}, as friction or viscosity are always present to some extent.