## 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
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