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[a] While processes in isolated systems are never reversible, [3] cyclical processes can be reversible or irreversible. [4] Reversible processes are hypothetical or idealized but central to the second law of thermodynamics. [3] Melting or freezing of ice in water is an example of a realistic process that is nearly reversible.
An irreversible process increases the total entropy of the system and its surroundings. The second law of thermodynamics can be used to determine whether a hypothetical process is reversible or not. Intuitively, a process is reversible if there is no dissipation. For example, Joule expansion is irreversible because initially the system is not ...
For any irreversible process, since entropy is a state function, we can always connect the initial and terminal states with an imaginary reversible process and integrating on that path to calculate the difference in entropy. Now reverse the reversible process and combine it with the said irreversible process.
Entropy was found to vary in the thermodynamic cycle but eventually returned to the same value at the end of every cycle. Thus it was found to be a function of state, specifically a thermodynamic state of the system. While Clausius based his definition on a reversible process, there are also irreversible processes that change entropy.
It is in this sense that entropy is a measure of the energy in a system that cannot be used to do work. An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production. The entropy generation during a reversible process is zero. Thus entropy production is a ...
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.
According to the second law, in a reversible heat transfer, an element of heat transferred, , is the product of the temperature (), both of the system and of the sources or destination of the heat, with the increment of the system's conjugate variable, its entropy (): [1]
Entropy is produced in irreversible processes. The importance of avoiding irreversible processes (hence reducing the entropy production) was recognized as early as 1824 by Carnot. [ 1 ] In 1865 Rudolf Clausius expanded his previous work from 1854 [ 2 ] on the concept of "unkompensierte Verwandlungen" (uncompensated transformations), which, in ...