## Exergy Analysis of an Air Nozzle

In this example we consider the nozzle of an
aircraft jet engine.

One may wonder at the purpose of determining
the maximum available work potential of a nozzle, whose entire
purpose is to maximise the kinetic energy at the exit state (2).
Indeed, a perfect nozzle is isentropic, and has no work potential,
since any work done would decrease the kinetic energy. In a practical
nozzle there could be an increase in entropy from state (1) to
state (2) as well as possible heat loss to the surroundings which
will decrease the kinetic energy output and thus the exergy analysis
is mainly in order to evaluate this **lost kinetic energy potential**,
or the **irreversibility**. We recall that kinetic energy is
entirely equivalent to exergy.

Recall the **previous
section** in which we determined the **irreversibility**
(irrev) as follows:

Thus referring to the figure above the irreversibility
is given by:

However, since there is no actual work done
in the nozzle, we have from the energy equation:

Thus by substituting q we obtain the irreversibility
as:

Once again, in order to get an intuitive understanding
of this analysis we consider the following equivalent nozzle in
which we wish to capture the heat loss over the entire nozzle
by means of summing the work output of an infinite number of elemental
reversible heat engines.

The reason for the many elemental reversible
heat engines is that the temperature T of the nozzle varies continuously
between the inlet state (1) and the outlet state (2), thus:

However, since there is no actual work done
in the nozzle, we have from the energy equation:

Thus by substitution we obtain the final available
work potential form:

Since there is no actual work done, the irreversibility
can be determined as follows:

Note that this equation is identical to that
for the irreversibility given above.

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Engineering Thermodynamics by Israel Urieli is licensed under a
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