Editing Isentropic process (section)

== Background ==

The [[second law of thermodynamics]] states<ref name="MortimerBook">Mortimer, R. G. ''Physical Chemistry'', 3rd ed., p. 120, Academic Press, 2008.</ref><ref name="FermiBook">Fermi, E. ''Thermodynamics'', footnote on p. 48, Dover Publications,1956 (still in print).</ref> that
:<math>T_\text{surr}dS \ge \delta Q,</math>

where <math>\delta Q</math> is the amount of energy the system gains by heating, <math>T_\text{surr}</math> is the [[temperature]] of the surroundings, and <math>dS</math> is the change in entropy. The equal sign refers to a [[Reversible process (thermodynamics)|reversible process]], which is an imagined idealized theoretical limit, never actually occurring in physical reality, with essentially equal temperatures of system and surroundings.<ref>[[Edward A. Guggenheim|Guggenheim, E. A.]] (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0444869514}}, p. 12: "As a limiting case between natural and unnatural processes[,] we have reversible processes, which consist of the passage in either direction through a continuous series of equilibrium states. Reversible processes do not actually occur..."</ref><ref>Kestin, J. (1966). ''A Course in Thermodynamics'', Blaisdell Publishing Company, Waltham MA, p. 127: "However, by a stretch of imagination, it was accepted that a process, compression or expansion, as desired, could be performed 'infinitely slowly'[,] or as is sometimes said, ''quasistatically''."  P. 130: "It is clear that ''all natural processes are irreversible'' and that reversible processes constitute convenient idealizations only."</ref> For an isentropic process, if also reversible, there is no transfer of energy as heat because the process is [[adiabatic process|adiabatic]]; ''δQ'' = 0. In contrast, if the process is irreversible, entropy is produced within the system; consequently, in order to maintain constant entropy within the system, energy must be simultaneously removed from the system as heat.

For reversible processes, an isentropic transformation is carried out by thermally "insulating" the system from its surroundings. Temperature is the thermodynamic [[conjugate variables (thermodynamics)|conjugate variable]] to entropy, thus the conjugate process would be an [[isothermal process]], in which the system is thermally "connected" to a constant-temperature heat bath.