## Increase in Entropy Principle

### 1. Non-flow Processes

We previously found from considerations of the
**Clausius
Inequality** that the following cyclic
integral is always less than or equal to zero, where the equality
occurred for a reversible cycle.

This lead to the definition of the property Entropy
(S). Consider now an irreversible cycle in which process (1)
-> (2)
follows an irreversible path, and process (2) ->
(1) a reversible path, as shown:

Thus the entropy change of an adiabatic process is
always greater than or equal to zero, where the equality applies to
reversible processes. However not all processes are adiabatic.
Nevertheless we can always enclose a system in a surrounding
environment which is adiabatic, thus considering the total entropy
change of both the system and surroundings we obtain:

Thus the Increase in Entropy Principle states that
for any process the total change in entropy of a system together with
its enclosing adiabatic surroundings is always greater than or equal
to zero. This total change of entropy is denoted the Entropy
Generated during the process (S_{gen} [kJ/K]
or s_{gen} [kJ/kg.K]).

### 2. Flow Processes (Steady Flow)

We now consider the entropy generated during a steady
flow process through a single-input/single-output Control Volume (CV)
enclosed in an adiabatic surroundings as shown:

Notice that for a steady flow system there can be no
change of any of its property values with time, thus the rate of
increase of entropy can only be associated with the surroundings.
Notice also that at station (2) we are also dumping entropy from the
control volume into the surroundings, and at station (1) we are
sucking entropy out of the surroundings, leading to:

Surprisingly the form of the specific entropy
generated function s_{gen} for a control
volume is identical to that for a system.

For multiple-input, multiple-output control volumes
under steady flow conditions, the entropy generated function is
extended to:

where
the summations ()
are taken over all the exit ports (e) and inlet ports (i).

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Engineering Thermodynamics by Israel
Urieli is licensed under a Creative
Commons Attribution-Noncommercial-Share Alike 3.0 United States
License