Isentropic process

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In thermodynamics, an isentropic process (a combination of the Greek word "iso" -same- and entropy) is one during which the entropy of the working fluid remains constant. By the second law of thermodynamics we may write

[\delta Q \le TdS]

where [\delta Q] is the amount of energy the system gains by heating, [T] is the temperature of the system, and [dS] is the change in entropy. The equal sign will hold for a reversible process. It is seen that, for a reversible process, there will be no transfer of heat energy in an isentropic process, and therefore it is equivalent to an adiabatic process. For an irreversible transformation however, the entropy will be increasing, and a certain amount of cooling of the system may be necessary to maintain a constant entropy. In this case the transformation will not be adiabatic.

For reversible processes then, an isentropic transformation is carried out by thermally insulating the system from its surroundings. Temperature is the thermodynamic variable conjugate to entropy, and so the conjugate process would be an isothermal process in which the system is thermally connected to a constant-temperature heat bath.

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