Heat Engines
A heat engine is defined as any engine that uses heat to
perform work. As such, the physics underlying the
operation of a heat engine is a direct consequence of the
first law of thermodynamics. Heat engines take heat from
a higher temperature heat source and transform it into
work and a release of heat in the lower temperature
surroundings, Heat engines can also convert internal
energy (heat) into mechanical energy.
A classical description of a heat engine is provided by the
Carnot cycle, named after its inventor Nicolas-L(onard-
Sadi Carnot, who first designed it in 1824. The Carnot
heat engine is only used as a standard of heat engine
performance. It operates as a reversible process and
consists of a gas confined by a piston moving back and
forth in a cylinder. The process has four steps. First, the
gas is heated and it expands, moving the piston up. This
is called isothermal expansion to the higher temperature.
The second step is adiabatic expansion of the gas to
lower its temperature, followed by the third step,
isothermal contraction, cooling the piston so that it will
move back down. Finally, adiabatic contraction of the gas
with warming to the higher temperature maintains a
cycle of heating and cooling to displace the piston up and
down. It is the motion of the piston that allows useful
work to be done and the efficiency of a heat engine
describes how efficient the engine is at turning heat into
work. Two temperatures are then required to run a heat
engine; at one temperature the system is heated, at the
other temperature it is cooled.
The refrigerator and the air conditioner are examples of
heat engines that run in reverse because they take heat
from a lower temperature source through work
performed by a compressor, and transfer it to higher
temperature surroundings.
To be efficient, a heat engine must operate using a
reversible process, that is, a process after which the
thermodynamic system and its surroundings are returned
to the state they were in before the process started.
Theoretically, the most efficient heat engine is the Carnot
cycle, although the Carnot cycle is not used for practical
applications because of engineering difficulties that
cannot be overcome.
An example of a thermodynamic cycle used to design
practical heat engines is the Otto cycle (isentropic
compression, reversible constant volume heating,
isentropic expansion, reversible constant volume cooling)
of which the gas engine is the most well-known
application. Other examples of thermodynamic cycles
used in heat engine design include the Diesel cycle
(isentropic compression, reversible constant pressure
heating, isentropic expansion, reversible constant volume
cooling), the Brayton cycle (isentropic compression,
isobaric heat supply, isentropic expansion, isobaric heat
output) used for closed-cycle gas turbines in many
industrial applications, the
heating, isothermal expansion, isochoric cooling,
isothermal compression), and the Clausius-Rankine cycle
(isentropic expansion, isobaric heat rejection, isentropic
compression, isobaric heat supply), which defines the
operating principle of steam engines and turbines. Aside
from their different operating principles and applications,
these cycles also differ in their relative efficiency.
By dealing with thermodynamic quantities such as heat
and work, the heat engine is also used to formulate the
second law of thermodynamics in various ways. For
example, the second law states that heat flows naturally
from regions of higher temperature to regions of lower
temperature and not the other way. Another form of the
second law derived from the heat engine states it is
impossible to build a heat engine that can use all the heat
from a higher temperature surrounding it and turn it
entirely into work. Accordingly, it is impossible to make a
heat engine with a 100% efficiency.
In engineering and thermodynamics, a heat engine
performs the conversion of heat energy to mechanical
work by exploiting the temperature gradient between a
hot "source" and a cold "sink". Heat is transferred to the
sink from the source, and in this process some of the
heat is converted into work by exploiting the properties of
a working substance (usually a gas or liquid).
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Examples of everyday heat engines include: the steam
engine, the diesel engine, and the gasoline (petrol)
engine in an automobile. A common toy that is also a
heat engine is a drinking bird. All of these familiar heat
engines are powered by the expansion of heated gases.
The general surroundings are the heat sink, providing
relatively cool gases which, when heated, expand rapidly
to drive the mechanical motion of the engine.
In these cycles and engines, the working fluids are gases
and liquids. The engine converts the working fluid from a
gas to a liquid.
- Rankine cycle (classical steam engine)
- Regenerative cycle (more efficient than Rankine cycle)
- Drinking bird cycle
- Frost heaving - water changing from ice to liquid and
- back again can lift rock up to 60m.
In these cycles and engines the working fluid are always like gas:
- Carnot cycle (Carnot heat engine)
- Brayton cycle or Joule cycle (Gas turbine)
- Ericsson Cycle
- Stirling cycle (Stirling engine)
- Internal combustion engine (ICE):
- Otto cycle (eg. Gasoline/Petrol engine, high-speed diesel engine)
- Diesel cycle (eg. low-speed diesel engine)
- Atkinson Cycle
- Lenoir cycle (eg pulse jet engine)
- Miller cycle
- Otto cycle (eg. Gasoline/Petrol engine, high-speed diesel engine)
- Thermoelectric (Peltier-Seebeck effect)
- thermionic emission
- Thermotunnel cooling
A refrigerator is a heat pump: a heat engine in reverse. Work is used to create a heat differential.
- Carnot refrigeration
- Vuilleumier refrigeration
- Absorption refrigeration
The efficiency of a heat engine relates how much useful
power is output for a given amount of heat energy input.
From the laws of thermodynamics:
where
dW = − PdV is the work extracted from the engine. (It
is negative since work is done by the engine.)
dQh = ThdSh is the heat energy taken from the high
temperature system .(It is negative since heat is
extracted from the source, hence ( − dQh) is positive.)
dQc = TcdSc is the heat energy delivered to the cold
temperature system. (It is positive since heat is added to the sink.)
In other words, a heat engine absorbs heat energy from
the high temperature heat source, converting part of it to
useful work and delivering the rest to the cold temperature heat sink.
In general, the efficiency of a given heat transfer process
(whether it be a refrigerator, a heat pump or an engine)
is defined informally by the ratio of "what you get" to "what you put in."
In the case of an engine, one desires to extract work and puts in a heat transfer.
The theoretical maximum efficiency of any heat engine
depends only on the temperatures it operates between .
This efficiency is usually derived using an ideal imaginary
heat engine such as the Carnot heat engine, although
other engines using different cycles can also attain
maximum efficiency. Mathematically, this is due to the
fact that in reversible processes, the change in entropy of
the cold reservoir is the negative of that of the hot
reservoir (i.e., dSc = − dSh), keeping the overall change of entropy zero. Thus:
where Th is the absolute temperature of the hot source
and Tc that of the cold sink, usually measured in kelvins.
Note that dSc is positive while dSh is negative; in any
reversible work-extracting process, entropy is overall not
increased, but rather is moved from a hot (high-entropy)
system to a cold (low-entropy one), decreasing the
entropy of the heat source and increasing that of the heat sink.
The reasoning behind this being the maximal efficiency
goes as follows. It is first assumed that if a more efficient
heat engine than a Carnot engine is possible, then it
could be driven in reverse as a heat pump. Mathematical
analysis can be used to show that this assumed combination would result in a net decrease in entropy.
Since, by the second law of thermodynamics, this is
forbidden, the Carnot efficiency is a theoretical upper bound on the efficiency of any process.
Empirically, no engine has ever been shown to run at a greater efficiency than a Carnot cycle heat engine.
Other criteria of heat engine performance
One problem with the ideal Carnot efficiency as a criterion
of heat engine performance is the fact that by its nature,
any maximally-efficient Carnot cycle must operate at an
infinitesimal temperature gradient. This is due to the fact
that any transfer of heat between two bodies at differing
temperatures is irreversible, and therefore the Carnot
efficiency expression only applies in the infinitesimal
limit. The major problem with that is that the object of
most heat engines is to output some sort of power, and
infinitesimal power is usually not what is being sought.
A much more accurate measure of heat engine efficiency
is given by the endoreversible process, which is identical
to the Carnot cycle except in that the two processes of
heat transfer are not treated as reversible. As derived in Callen (1985), the efficiency for such a process is given by:
The accuracy of this model can be seen in the following table (Callen):
|
Efficiencies of Power Plants | |||||
|
Power Plant |
Tc (°C) |
Th (°C) |
η (Carnot) |
η (Endoreversible) |
η (Observed) |
|
25 |
565 |
0.64 |
0.40 |
0.36 | |
|
25 |
300 |
0.48 |
0.28 |
0.30 | |
|
80 |
250 |
0.32 |
0.175 |
0.16 | |
As shown, the endoreversible efficiency much more closely models the observed data.
|
Cycle/Process |
Compression |
Heat Addition |
Expansion |
Heat Rejection |
|
Carnot |
adiabatic |
isothermal |
adiabatic |
isothermal |
|
Otto (Petrol) |
adiabatic |
isometric |
adiabatic |
isometric |
|
Diesel |
adiabatic |
isobaric |
adiabatic |
isometric |
|
Brayton (Jet) |
adiabatic |
isobaric |
adiabatic |
isobaric |
|
|
isothermal |
isometric |
isothermal |
isometric |
|
Ericsson |
isothermal |
isobaric |
isothermal |
isobaric |
Each process is one of the following:
- isothermal (at constant temperature, maintained with heat added or removed from a heat source or sink)
- isobaric (at constant pressure)
- isometric/isochoric (at constant volume)
- adiabatic (no heat is added or removed from the working fluid)
- Kroemer, Herbert; Kittle, Charles (1980). Thermal
- Physics, 2nd ed., W. H. Freeman Company. ISBN 0716710889.
- Callen, Herbert B. (1985). Thermodynamics and an
- Introduction to Thermostatistics, 2nd ed., John Wiley & Sons, Inc.. ISBN 0471862568.
