SECOND LAW OF THERMODYNAMICS
Equation 1-23 shows that the maximum possible efficiency exists when TH is at its largest
possible value or when TC is at its smallest value. Since all practical systems and processes are
really irreversible, the above efficiency represents an upper limit of efficiency for any given
system operating between the same two temperatures.
The systems maximum possible
efficiency would be that of a Carnot efficiency, but because Carnot efficiencies represent
reversible processes, the actual system will not reach this efficiency value. Thus, the Carnot
efficiency serves as an unattainable upper limit for any real systems efficiency. The following
example demonstrates the above principles.
Example 1: Carnot Efficiency
An inventor claims to have an engine that receives 100 Btu of heat and produces 25 Btu
of useful work when operating between a source at 140°F and a receiver at 0°F. Is the
claim a valid claim?
= 140oF + 460 = 600°R
= 0oF + 460 = 460°R
= (600-460)/600 x 100 = 23.3%
Claimed efficiency = 25/100 = 25%
Therefore, the claim is invalid.
The most important aspect of the second law for our practical purposes is the determination of
maximum possible efficiencies obtained from a power system. Actual efficiencies will always
be less than this maximum. The losses (friction, for example) in the system and the fact that
systems are not truly reversible preclude us from obtaining the maximum possible efficiency.
An illustration of the difference that may exist between the ideal and actual efficiency is
presented in Figure 22 and the following example.
Example 2: Actual vs. Ideal Efficiency
The actual efficiency of a steam cycle is 18.0%. The facility operates from a steam
source at 340°F and rejects heat to atmosphere at 60°F. Compare the Carnot efficiency
to the actual efficiency.