SECOND LAW OF THERMODYNAMICS
This calculation indicates that the Carnot cycle, operating with ideal components under real world
constraints, should convert almost 3/4 of the input heat into work. But, as will be shown, this
ideal efficiency is well beyond the present capabilities of any real systems.
To understand why an efficiency of 73% is not possible we must analyze the Carnot cycle, then
compare the cycle using real and ideal components. We will do this by looking at the T-s
diagrams of Carnot cycles using both real and ideal components.
The energy added to a working fluid during the Carnot isothermal expansion is given by qs. Not
all of this energy is available for use by the heat engine since a portion of it (qr) must be rejected
to the environment. This is given by:
qr = To Ds in units of Btu/lbm,
where To is the average heat sink temperature of 520°R. The available energy (A.E.) for the
Carnot cycle may be given as:
A.E. = qs - qr.
Substituting equation 1-37 for qr gives:
A.E. = qs - To Ds in units of Btu/lbm.
and is equal to the area of the shaded
Figure 28 Carnot Cycle
region labeled available energy in
Figure 28 between the temperatures
1962° and 520°R. From Figure 28 it
can been seen that any cycle operating
at a temperature of less than 1962°R
will be less efficient. Note that by
developing materials capable of
1962°R, we could greatly add to the
energy available for use by the plant
From equation 1-37, one can see why
the change in entropy can be defined
as a measure of the energy unavailable
to do work. If the temperature of the
heat sink is known, then the change in
entropy does correspond to a measure
of the heat rejected by the engine.