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2 Macroscopic Thermodynamics
2.5 Thermodynamic Engines
Very early on during the initial development of thermodynamics as a discipline,
engineers took an interest in its potential application in the design of more efficient
versions of the then recently-invented ‘heat engines’. An important contribution
to what is now the Second Law of Thermodynamics was made by Carnot [10],
who was interested in the efficiency of various types of heat engines, which quite
generally work in a cyclic manner by drawing energy from a higher-temperature
thermal reservoir, exporting a portion of it in the form of work, and discharging
the remainder into a lower-temperature thermal reservoir. This process is typically
shown schematically as in Fig. 2.1. Maximal efficiency of such a conversion of
thermal energy into work will occur when the cyclic process is carried out reversibly.
However, as reversible processes are idealizations, the attainable efficiency of any
conversion of thermal energy (more colloquially, ‘heat’) into work will be less than
the maximal, reversible, value.
If we assume that the thermodynamic system plus surroundings forms a closed
thermodynamic system, then the Second Law of Thermodynamics tells us that
((S) total ≥ 0 in general, with the equality holding when all processes are
reversible. Let us write ((S) total as
((S) total = ((S) sys + ((S) surr .
(2.5.1)
Taking the thermodynamic system through a closed cycle of reversible processes
results in ((S) sys = 0, while ((S) surr is given in terms of the heat Q import imported
Fig. 2.1 Cartoon illustrating
a typical ‘heat engine’ cycle
T = T high
T = T low
system
hot
thermal reservoir
cool
thermal reservoir
W
Q import
Q export
2 Macroscopic Thermodynamics
2.5 Thermodynamic Engines
Very early on during the initial development of thermodynamics as a discipline,
engineers took an interest in its potential application in the design of more efficient
versions of the then recently-invented ‘heat engines’. An important contribution
to what is now the Second Law of Thermodynamics was made by Carnot [10],
who was interested in the efficiency of various types of heat engines, which quite
generally work in a cyclic manner by drawing energy from a higher-temperature
thermal reservoir, exporting a portion of it in the form of work, and discharging
the remainder into a lower-temperature thermal reservoir. This process is typically
shown schematically as in Fig. 2.1. Maximal efficiency of such a conversion of
thermal energy into work will occur when the cyclic process is carried out reversibly.
However, as reversible processes are idealizations, the attainable efficiency of any
conversion of thermal energy (more colloquially, ‘heat’) into work will be less than
the maximal, reversible, value.
If we assume that the thermodynamic system plus surroundings forms a closed
thermodynamic system, then the Second Law of Thermodynamics tells us that
((S) total ≥ 0 in general, with the equality holding when all processes are
reversible. Let us write ((S) total as
((S) total = ((S) sys + ((S) surr .
(2.5.1)
Taking the thermodynamic system through a closed cycle of reversible processes
results in ((S) sys = 0, while ((S) surr is given in terms of the heat Q import imported
Fig. 2.1 Cartoon illustrating
a typical ‘heat engine’ cycle
T = T high
T = T low
system
hot
thermal reservoir
cool
thermal reservoir
W
Q import
Q export