http://www.ck12.org Chapter 14. Thermodynamics
FIGURE 14.11
The functioning of a typical heat engine.SinceQH=QL+W→W=QH−QLsubstitution intoe=QWH×100 gives
e=W
QH
× 100 =
QH−QL
QH
× 100 =
(
1 −
QL
QH
)
× 100 →e=(
1 −
QL
QH
)
× 100.
Check your understanding
At high temperature (Ignition) an engine transfers 8. 52 × 104 Jinto the system and at low temperature (Exhaust)
transfers 5. 96 × 104 Jout of the system.
What is the efficiency of the engine?
Answer:e=
(
1 −QQHL
)
× 100 →
(
1 −^5.^96 ×^10
(^4) J
8. 52 × 104 J
)
× 100 = 30 .0%
The Carnot Engine
Maximizing the efficiency of a heat engine was an important topic during the early 19thcentury. The Frenchman
Sadi Carnot (1796-1832), analyzed the characteristics of an ideal heat engine. Such an engine assumes that each
process the engine preforms is reversible. TheCarnot engine, as it is called today, belongs to the same idealized
category as the frictionless inclined plane. (Such an engine is a mathematical abstraction conceived by assuming
physical processes that are impossible. Carnot was able to establish the upper limit of a heat engine’s efficiency by
using his idealized model.
He assumed his reversible engine could perform with maximum efficiency if an ideal engine made use of isothermal
and adiabatic processes only. All processes were assumed to occur infinitely slowly, having the engine move from
one approximate equilibrium state to the next, thus ensuring that the processes could be reversed. Such an engine of
course could never exist. The idea of constructing infinitely slow processes is impossible. The Carnot engine, as we
will see, is just a useful conceptual idea for establishing the upper limit of a heat engine’s efficiency for a given pair
of high and low temperatures.
Carnot was able to show that at maximum efficiency the highQHand lowQLenergy transfers were proportional to
the highTHand lowTLtemperatures under which the engine operated.
We can therefore writee=
(
1 −TTLH
)
×100% whereTis in kelvins.This was a very important result because it showed, all things being equal, that those substances that could produce
the highest temperature when burning would produce greater efficiency.