## 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
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