This section is mainly concerned with an attempt to
develop an intuitive understanding of the exergy equations developed
in the previous section, by considering reversible equivalent
circuits of some common adiabatic components. We repeat equations
(3), (4) and (5) developed in **Chapter
7a** on the exergy analysis of a control
volume.

Note that the reversible work w_{rev} will
either be the maximum available output work for work producing
devices, or the minimum possible input work (negative value) for work
absorbing devices.

We now consider the Energy and Entropy Generation equations for adiabatic components (q = 0):

Applying all the above analysis to evaluating the
Second Law Efficiencies (η_{II}) of adiabatic work absorbing
and work producing components we obtain:

We now apply the above Second Law analysis to an
adiabatic refrigeration compressor. We wish to determine the minimum
work w_{C rev} required
to drive the compressor between the inlet state (1) and the exit
state (2). Note that the isentropic compression that we evaluated in
**Chapter
6** will not provide the answer, since
state (2s) is not the same as the actual state (2).

The above equations are in fact correct however we
have difficulty in understanding their significance. In examining the
adiabatic compressor above we cannot understand why the environment
(dead space) temperature T_{0} features so prominently in the
equations, when in fact there seems to be no obvious interaction
between the adiabatic compressor and the environment. Note that as
far as the adiabatic compressor is concerned we will assume that the
surroundings temperature T_{0} is equal to the exit
temperature.

In an attempt to find some intuitive meaning to these equations we consider a reversible system having the same inlet and exit states as our actual compressor. This comprises a three component system consisting of an inlet heat exchanger, a reversible heat engine and an isentropic compressor as shown below:

A typical *h-s* diagram for this system is shown
below, in which we have used typical inlet conditions of 140kPa,
-10°C and exit conditions of 700kPa, 60°C. The reversible heat
engine will provide extra work to drive the compressor, absorbing its
heat from the environment temperature T_{0} while rejecting
heat to the heat exchanger. The exit state (2) from the heat
exchanger has been chosen such that the compression process (2) - (3)
will be isentropic.

We now derive the exergy equations for the three
component system above, and consider first the heat engine. Since the
temperature T of the heat exchanger varies from the inlet temperature
T_{1} to the outlet temperature T_{2}, we use the
differential energy equation form for the reversible heat engine.

Since T_{0} is constant, this equation can be
integrated from the inlet state (1) to the outlet state (2), leading
to:

This familiar final form was to be expected. The net minimum work required to drive the compressor is thus:determined as follows:

Notice that this result is identical to that shown above for the actual adiabatic compressor, since we added the heat exchanger, thus state (3) is in fact equivalent to the original state (2).

**Problem 7.4 -** Recall
**Solved
Problem 6.5** in which we evaluated the
Adiabatic Efficiency (η_{C})
of a refrigeration compressor, and determined it to be 92%. Redo this
problem and determine the Second Law Efficiency (η_{II})
of this compressor. [92%]

We now apply the above Second Law Analysis to an
adiabatic steam turbine. We wish to determine the maximum available
turbine work output w_{T rev} between the inlet state (1) and
the exit state (2). We will then be able to determine the second law
eficiency by comparing the actual work output to the reversible
(maximum available) work output as follows:

Once again, in an attempt to find some intuitive
meaning to these equations we consider a reversible system having the
same inlet and exit states as the actual turbine, comprising an
isentropic turbine, a heat pump pumping heat from the surroundings to
the heat exchanger in the exit stream. Note that as far as the
adiabatic turbine is concerned we will assume that the surroundings
temperature T_{0} is equal to the exit temperature.

The *h-s* diagram for this system is shown
below, in which we have chosen as an example a steam turbine having
inlet conditions 6MPa, 600°C, and outlet conditions 50kPa, 100°C.

Notice from the h-s diagram that the heat exchanger temperature varies from the saturation temperature at 50 kPa (81°C) to 100°C at state (3). In order to accommodate that change we develop the differential form of the heat pump as follows:

Since T_{0} is constant, this differential
equation can be integrated from state (2) to state (3).

We can then subtract the work provided to the heat pump from the output work of the turbine leading to the final form of the maximum available work, as follows:

Notice that this result is identical to that shown in the box above for the actual adiabatic turbine, since state (3) is in fact equivalent to the original state (2).

**Problem 7.5 -** Recall
**Solved
Problem 6.1** in which we evaluated the
Adiabatic Efficiencies (η_{T})
of both the High Pressure and the Low Pressure steam turbines of the
supercritical steam power plantand found them to be 77% and 90%
respectively. Redo this problem and determine the respective Second
Law Efficiencies (η_{II})
of both turbines. [77%,
90%]

______________________________________________________________________________________

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