14.3. Second Law of Thermodynamics http://www.ck12.org
Heat Engines
Any device that uses heat (thermal) energy to produce mechanical work is called aheat engine. One of the first heat
engines was the steam engine. Wood or coal was burned, and the thermal energy released by the fuel was transferred
to water and produced steam. The steam was then directed into a cylinder with a movable piston which turned a
crank of some sort that was attached to another mechanical device which turned a paddle wheel. Thus, work was
performed. But plenty of thermal energy was also transmitted to the environment (the engine room on a steamship
gets pretty hot!).
Using thermal energy to produce mechanical work led to the question ofefficiency: How much of the energy input
to a system can be used to produce a given amount of work? It is never the case that all of the thermal energy can be
converted to mechanical energy. Here is another way of stating the second law of thermodynamics: no heat engine
can be 100% efficient. There is a simple way to appreciate this fact. If you have ever felt the hood of an automobile
after it’s been running for a while (do this carefully) you’ll notice that the hood is very hot. The engine has grown
hot while performing work and heated the hood of the car. The heat engine in this case is the internal combustion
engine.
The internal combustion engine is not very efficient. About two-thirds of the energy of the gasoline used to power an
automobile is converted to heat. That is why automobiles have cooling systems composed of radiators, water pumps
and fans. As the water circulates through the system, heat is transferred from the hot engine to the cooler water. The
water is then cooled by the radiator fan (and the “wind” through the grills of the car).
Briefly, the internal combustion process is as follows.
- (Intake) Gasoline and air are mixed together in a cylinder that expands against a piston.
- (Compression) A crankshaft then moves the piston upward compressing the mixture.
- (Ignition) At the instant of maximum compression a spark plug “fires” (it releases an electric spark into the
mixture) igniting the gasoline-air mixture and rapidly increasing the temperature in the cylinder. - (Expansion—the power stroke) The hot mixtureQHexpands rapidly.
- (Exhaust) The exhaust gasesQLare ejected at a lower temperature as the piston and the process repeats.
During the internal combustion process, some of the thermal energy produced by burning gasoline is used to perform
work (to move the car!) but a good deal of the thermal energy is used to heat the engine as well as the exhaust gases
which do not perform work. The second law of thermodynamics tells us that only some of the chemical energy of
the gasoline is available to perform work.Figure14.11 explains how the typical heat engine works. The quantity
QHis the initial thermal energy transferred to the system andWis the work done by the system. (In the case of
the internal combustion process,QHis the heat produced when the spark ignites the gasoline-air mixture.) The
remaining thermal energyQLleaves the engine at a lower temperature.
The efficiency of a heat engineeis defined as
e=QWH×100 (Multiplication by 100 expresses the efficiency as a percentage.)
Illustrative Example 1
a. Use the conservation of energy to express the relationship between,QHthe high(H)temperature thermal energy,
the low(L)temperature thermal energy,QLand the work performedWby a heat engine.
Solution:
LetQHbe the initial energy of the system,QLthe energy of the spent gases, andWthe work output.
Conservation of energy statesEi=Ef→QH=QL+W
b. Use the result above to express the efficiencyein terms ofQHand QL.
Solution: