The thermodynamic cycle consists of a series of operations (e.g. expansion/compression of a volume - see Figure 1) carried out on a gas or steam (which is often called a working substance, WS), after which it returns to its original state.
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For example, imagine that initially there is an expansion of volume from
V1 to
V2, corresponding to a work output of
W1. Figure 2 shows such a process with a pressure (
P) - volume (
V) plot, where the work output (
W1) equals the area under curve
A 9 (shaded blue).
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Next the gas is compressed back to its original volume, i.e.
V2 back to
V1, which requires a work input of
W2 (the shaded area under the curve in Figure 3).
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When we combine the two processes on a single
plot, we get a closed loop (see Figure 4A). This closed loop corresponds to a thermodynamic cycle.
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As the net work output
is given by:
it will thus equal the area of the cycle (the blue shaded area in Figure 4B).
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Such thermodynamic cycles can also be represented on temperature (
) - entropy (
) diagrams. For example, imagine that initially there is a certain amount of heat supplied (
) to the
WS, leading to an increase in entropy. If we are to illustrate such a process on a
plot (see Figure 5A), then the heat energy supplied
will equal the area under curve
(the blue shaded area in Figure 5B).
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Next, consider that there is a certain amount of heat rejected in the
WS and in losses (
), reverting the system back to its initial state. By plotting this process on a
diagram (see Figure 6A), the heat rejected
will equal the area under curve
(the blue shaded area in Figure 6B).
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If we are to illustrate both processes on a single
plot, then we will get again a closed loop, corresponding to the thermodynamic cycle (see Figure 7A)
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By denoting the energy of the
WS at the start of the cycle with
, and the energy of the
WS at the end of the cycle with
, and by applying the law of conservation of energy, we can write that:
where
is the work output (for a more detailed discussion on the law of conservation of energy see
First Law of Thermodynamics ).
However, as
(the system is reverted back to its initial state), equation (
3) becomes:
from which:
Therefore, when plotting the thermodynamic cycle on a
diagram (as in Figure 7A), the work output will again equal the area of the cycle (the blue shaded area in Figure 7B).
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It is important to note that, although the work done can be calculated from the area of the thermodynamic cycle for both a
and a
plot, the results obtained are expressed in different units. For example, if calculating in imperial units, the area of the cycle on the
diagram gives the work done in
, while the area of the cycle on the
diagram gives the work done in
.
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