Thermal Reservoirs and Heat Engines
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A conceptual schematic of a heat engine. Two channels of heat transfer,
with thermal reservoirs of two different temperatures TH and TL, are shown,
along with one channel of work transfer..
(URL for notes:
http://www.colorado.edu/ASEN/asen3113)
• The thermal reservoirs are assumed to be large enough that their
temperatures don’t change as heat flows in or out of them.
• The arrows indicate the direction of energy transfer (heat flow or work)
in the forward time direction.
• According to the first law of thermodynamics we have Q = W + q.
• The efficiency h of this engine is defined as the ratio of work energy
output to the heat energy input, so we have h = W/Q = 1 – q/Q
All heat engines:
1. Receive heat from a high-temperature source (solar
energy, blast furnace, ocean, land surface, etc.)
2. Convert part of this heat to work
3. Reject the remaining waste heat to a low-temperature
sink (the atmosphere, rivers, etc.)
4. Operate on a cycle
5. Have a working fluid
Qin
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pump
turbine
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Qout
Wnet = Wout - Win = Qin - Qout
Heat Engine Components
Wout
• The Rankine cycle is a thermodynamic cycle.
• Like other thermodynamic cycles, the maximum
efficiency of the Rankine cycle is given by
calculating the maximum efficiency of the Carnot
cycle.
• It is named after William John Macquorn Rankine, a
Scottish scientist.
• Rankine cycles describe the operation of steam heat
engines commonly found in power generation plants.
• In such power plants, power is generated by
alternately vaporizing and condensing a working fluid (in
many cases water, although refrigerants such as
ammonia may also be used).
• The working fluid in a Rankine cycle follows a closed
loop and is re-used constantly.
• Water vapor seen billowing from power plants is
evaporating cooling water, not working fluid. (NB: steam
is invisible until it comes in contact with cool, saturated
air, at which point it condenses and forms the white
billowy clouds seen leaving cooling towers).
Understanding Thermal Reservoirs
Bodies that don’t change their temperature even though
heat is being added or subtracted.
1. Blast furnce; hot enough that heat removed does not
change the temperature of the furnace.
2. Large lake or ocean; large enough that temperature
changes only very slowly in spite of heat entering or
leaving at the surface.
3. Land beneath the surface; temperature remains
constant even though heat energy is transferred from
the surface.
The Underground Motels and Church in Coober Pedy, Australia
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outside 90-120 °F,
inside constant 70 °F
RUN GEOEXCHANGE MOVIE
Thermal Efficiency
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Basic Heat Engine
LTER= Low Temperature Energy Reservoir
HTER= High Temperature Energy Reservoir
The thermal efficiency of a cycle (or more precisely a forward heat
engine) is defined as the ratio of net work output, W, to the heat
supplied at high temperature, Q1, i.e.
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or net work/total heat in
1.
Calculate the maximum theoretical thermal efficiency of a coal-fired
power station that heats steam to 510°C and cools it in a condenser at
30°C.
Answer: Maximum efficiency = (THOT – TCOLD)/THOT
= [(510+273) – (30+273)] / (510+273)
= 480 / 783 = 0.61 or 61%
2. The temperature of the gases in a car engine during combustion is 1800°C.
The exhaust is expelled at 80°C. Calculate the maximum theoretical thermal
efficiency of the engine.
Answer: Maximum theoretical efficiency = (THOT – TCOLD)/THOT
= [(1800+273) – (80+273)] / (1800+273)
= 1720/2073 = 0.83 or 83%
Of course, in both case, the actual efficiency will be
smaller. Students should consider why.
Second Law of Thermodynamics: Kelvin-Planck Statement
It is impossible for any device that operates on a cycle to
receive heat from a single reservoir and produce a net amount
of work.
Thus, a heat engine must exchange heat with a low temperature
sink as well as a high temperature source to keep operating.
or
No heat engine can have a thermal efficiency of 100%, or
for a power plant to operate, the working fluid must
exchange heat with the environment as well as the furnce
(must have waste heat).
If all the energy transfer processes in a given heat engine are reversible, we
can just as well reverse all the arrows, and run the heat engine “backwards in
time”. (A kitchen refrigerator is a common example of a heat engine running
in reverse.)
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A Real Refrigerator
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Second Law of Thermodynamics
The second law of thermodynamics is a general principle which places
constraints upon the direction of heat transfer and the attainable
efficiencies of heat engines. In so doing, it goes beyond the limitations
imposed by the first law of thermodynamics. It's implications may be
visualized in terms of the waterfall analogy.
The maximum efficiency which can be achieved is the Carnot efficiency.
Waterfall Analogy
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Heat Engine Cycle and the Laws of Thermo
The Otto Cycle A schematic version of the four-stroke engine cycle
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The Diesel Engine
The diesel internal combustion engine differs from the gasoline
powered Otto Cycle by using a higher compression of the fuel to
ignite the fuel rather than using a spark plug ("compression
ignition" rather than "spark ignition").
Processing crude oil - refining
Name
Carbon chain
length
Boiling range
oC
Petroleum
gases
1-4
<5
Naphtha
5-9
20-180
Gasoline
5-10
20-200
Kerosine
10-16
180-260
Gas oil
(diesel oil)
14-20
260-340
Lubricating
oil
20-50
370-600
Fuel oil
20-70
330 upwards
Residue
>70
Non-distillable
Some properties of crude oil fractions.
How bubble caps work
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In the diesel engine, air is
compressed adiabatically with a
compression ratio typically
between 15 and 20. This
compression raises the
temperature to the ignition
temperature of the fuel mixture
which is formed by injecting fuel
once the air is compressed.
Diesel Engine Theoretical Efficiency
Since the compression and power strokes of this idealized cycle are adiabatic,
the efficiency can be calculated from the constant pressure and constant volume
processes. The input and output energies and the efficiency can be calculated
from the temperatures and specific heats:
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It is convenient to express this efficiency in terms of the compression
ratio rC = V1/V2 and the expansion ratio rE = V1/V3. The efficiency can be
written
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and this can be rearranged to the form
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Theoretical Diesel Efficiency (what does we assume?)
Nuclear power plant; thermal rods in water
Simulation of temperatures inside a nuclear reactor. From Argonne
A nuclear power station. The nuclear reactors are inside the
two cylindrical containment buildings in the foreground—
behind are the
cooling
Steam
fromtowers
cooling(venting
towers water vapor).
U.S. commercial pressurized water reactor (PWR) nuclear power plants
Nuclear power generator
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The picture above shows the release of steam from geothermal
plants in Santa Rosa -- geothermal plants tap the heat within the
Earth to produce energy in the form of electricity.The heat trapped
within the Earth, which was generated during its formation billions of
years ago and through the decay of radioactive elements with rocks,
is trying to escape
Earth as a heat engine
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Convection, also occurs within the Earth as hot, less dense
portions of the mantle rise and displace cooler, denser rocks,
which then sink into the mantle -- in summary the
cooler, dense rocks sink in the mantle, whereas the warmer
rocks within the mantle rise by a process called mantle
convection (shown by red arrows in the diagram above).
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Andes Mountains in South America,
which in this particular locale are
composed of sediments that
formed on the seafloor -- miles
below the sea surface -- millions of
years ago. Now these sediments
rest on the top of the
mountains, miles above the sea
surface -- how can this be? How
can something as heavy as the
surface of the Earth rise to such a
high elevation?
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Mountains of molten rock, or
lava, on the big island of
Hawaii. Once again, how can
molten (liquid) rock at
temperatures more than
1000oC find its way to the
surface of the Earth and why
should this happen in
Hawaii?
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Here is a map of the major plates that make up
the surface of the Earth.These plates are
formed by a strong, rigid surface layer of rocks
between 80 and 300 kilometers-thick.
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• Harry Hess was the first to
come up with an explanation for
the mid-ocean ridges -- he
suggested that the seafloor was
created by volcanism within the
rift valley along the axis of the
ridge.
• With time the seafloor and
underlying crust will spread
away from the ridge in opposite
directions on either side -thereby creating a mobile
seafloor -- like a conveyor belt - very interesting idea, which he
called seafloor spreading.
• How do we know that the
seafloor is spreading at the
mid-Atlantic ridge?
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• Reversals in the
polarityof magnetic
materials in the seafloor
that formed at geologic
periods when the Earth’s
magnetic field was
reversed.
• What does that mean for
us on Earth if the magnetic
field reverses?
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• The time-scale of the magnetic field reversals is shown at the
top.
• Regions with orange or yellow patterns denote time of
"normal polarity" or a magnetic direction with the same
direction as today's field.
• The white regions represent times when the field was in the
opposite (or reversed) direction from what it is today.
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Polar Reversals
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Here you see a map of the mid-ocean ridge system. The
ridge in the Pacific is called the East Pacific Rise, in the
Atlantic is is called the Mid-Atlantic Ridge, and in the
Indian Ocean it is either the Southwest Indian Ridge,
Central Indian Ridge or Southeast Indian Ridge.
Formation of Hurricane
A Giant Heat Engine
Waves in the trade winds in the
Atlantic Ocean—areas of
converging winds that move along
the same track as the prevailing
wind—create instabilities in the
atmosphere that may lead to the
formation of hurricanes.
Hurricanes form when the energy released
by the condensation of moisture in rising air
causes a chain reaction. The air heats up,
rising further, which leads to more
condensation. The air flowing out of the top
of this “chimney” drops towards the ground,
forming powerful winds
Hurricane or tropical cyclone/typhoon
Schematic representation of flow
around a low-pressure
area
instorms
the
Why do these
two
Northern hemisphere.
The pressure
rotate in opposite
gradient force
is represented by
directions?
blue arrows, the Coriolis
acceleration (always perpendicular
to the velocity) by red arrows
Hurricane
Katrina on
August 28 at
1:00 pm EDT
Image of Cyclone Catarina on March 26, 2004, the
first South Atlantic hurricane ever recorded
Sadie Carnot
• French engineer 1796 - 1832 (Paris)
• Father was involved in the French revolution and was exciled
• Sadie Carnot joined the military and became interested in steam
engines.
• He worked with his brother on steam engines and did
experiments similar to those of Joule 20 years before Joule.
• He died of Cholera at the age of 36.
Carnot Cycle
• The most efficient heat engine cycle is the Carnot cycle, consisting of two
isothermal processes and two adiabatic processes. The Carnot cycle
can be thought of as the most efficient heat engine cycle allowed by physical
laws.
• When the second law of thermodynamics states that not all the supplied
heat in a heat engine can be used to do work, the Carnot efficiency sets the
limiting value on the fraction of the heat which can be so used.
• In order to approach the Carnot efficiency, the processes involved in the
heat engine cycle must be reversible and involve no change in entropy.
• This means that the Carnot cycle is an idealization, since no real engine
processes are reversible and all real physical processes involve some
increase in entropy.
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Engine Cycles
• For a constant mass of gas, the operation of a heat engine is a repeating
cycle and its PV
diagram will be a closed figure.
• The idea of an engine cycle is illustrated below for one of the simplest kinds
of cycles.
• If the cycle is operated clockwise on the diagram, the engine uses heat to do
net work.
• If operated counterclockwise, it uses work to transport heat and is therefore
acting as a refrigerator or a heat pump.
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The Clausius Theorem and Inequality
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• The equality above represents the Clausius Theorem and applies only
to the the ideal or Carnnot cycle.
• Since the integral represents the net change in entropy in one
complete cycle, it attributes a zero entropy change to the most efficient
engine cycle.
• The Clausius Inequality applies to any real engine cycle and implies
a negative change in entropy on the cycle.
• That is, the entropy given to the environment during the cycle is
larger than the entropy transferred to the engine by heat from the hot
reservoir.
So, what is entropy?? (we will do it in more detail later)
• The second law of thermodynamics (the entropy law or law
of entropy) was formulated in the middle of the last century
by Clausius and Thomson following Carnot's earlier
observation that, like the fall or flow of a stream that turns a
mill wheel, it is the "fall" or flow of heat from higher to lower
temperatures that motivates a steam engine.
• The key insight was that the world is inherently active,
and that whenever an energy distribution is out of
equilibrium a potential or thermodynamic "force" (the
gradient of a potential) exists that the world acts to
dissipate or minimize.
• All real-world change or dynamics is seen to follow, or
be motivated, by this law.
• So whereas the first law expresses that which remains
the same, or is time-symmetric, in all real-world
processes the second law expresses that which changes
and motivates the change, the fundamental timeasymmetry, in all real-world process.
• Clausius coined the term "entropy" to refer to the
dissipated potential and the second law, in its most
general form, states that the world acts spontaneously
to minimize potentials (or equivalently maximize
entropy), and with this, active end-directedness or timeasymmetry was, for the first time, given a universal
physical basis.
• The balance equation of the second law, expressed as
S > 0, says that in all natural processes the entropy of
the world always increases, and thus whereas with the
first law there is no time, and the past, present, and
future are indistinguishable, the second law, with its oneway flow, introduces the basis for telling the difference.
• The active nature of the second law is intuitively easy to
grasp and empirically demonstrate. If a glass of hot liquid, for
example, as shown in the Fig., is placed in a colder room a
potential exists and a flow of heat is spontaneously produced
from the cup to the room until it is minimized (or the entropy
is maximized) at which point the temperatures are the same
and all flows stop.
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A glass of liquid at temperature
TI is placed in a room at
temperature TII such that . The
disequilibrium produces a field
potential that results in a flow of
energy in the form of heat from
the glass to the room so as to
drain the potential until it is
minimized (the entropy is
maximized) at which time
thermodynamic equilibrium is
reached and all flows stop.
refers to the conservation of
energy in that the flow from
the glass equals the flow of
heat into the room.
• The active macroscopic nature of the second law posed a
direct challenge to the "dead" mechanical world view which
Boltzmann tried to meet in the latter part of the 19th century
by reducing the second law to a law of probability following
from the random collisions of mechanical particles.
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Ludwig Eduard
Boltzmann
(Vienna, Austrian Empire,
February 20, 1844
Duino near Trieste,
September 5, 1906)
• His father, Ludwig Georg Boltzmann was a tax
official. His grandfather, who had moved to Vienna
from Berlin, was a clock manufacturer, and
Boltzmann’s mother, Katharina Pauernfeind, was
originally from Salzburg.
• He received his primary education from a private
tutor at the home of his parents. Boltzmann attended
high school in Linz, Upper Austria. At age 15,
Boltzmann lost his father.
• Boltzmann studied physics at the University of
Vienna, starting in 1863. Among his teachers were
Josef Loschmidt, Joseph Stefan, Andreas von
Ettingshausen and Jozef Petzval.
• Boltzmann received his PhD degree in 1866 working
under the supervision of Stefan; his dissertation was on
kinetic theory of gases. In 1867 he became a
Privatdozent (lecturer). After obtaining his doctorate
degree, Boltzmann worked two more years as Stefan’s
assistant. It was Stefan who introduced Boltzmann to
Maxwell's work.
• In 1869, at age 25, he was appointed full Professor of
Mathematical Physics at the University of Graz.
• In 1869 he spent several months in Heidelberg working
with Robert Bunsen and Leo Königsberger and then in 1871
he was with Gustav Kirchhoff and Hermann von Helmholtz in
Berlin.
• In 1873 Boltzmann joined the University of Vienna as
Professor of Mathematics and where he stayed till 1876.
• In 1872, long before women were admitted to Austrian
universities, he met Henriette von Aigentler, an aspiring
teacher of mathematics and physics in Graz.
• She was refused permission to unofficially audit lectures,
and Boltzmann advised her to appeal; she did, successfully.
• On July 17, 1876 Ludwig Boltzmann married Henriette von
Aigentler; they had three daughters and two sons.
Boltzmann went back to Graz to take up the chair of
Experimental Physics.
• He was shortly the president of the U. of Graz, but later moved to
Munich, then back to Vienna. He then moved to Berlin and eventually
back to Graz.
• Following the lead of Maxwell who had modeled gas
molecules as colliding billiard balls, Boltzmann argued that
the second law was simply a consequence of the fact that
since with each collision nonequilibrium distributions would
become increasingly disordered leading to a final state of
macroscopic uniformity and microscopic disorder.
• Because there are so many more possible disordered
states than ordered ones, he concluded, a system will
almost always be found either in the state of maximum
disorder or moving towards it.
• Entropy always increases.
Clausius Statement of the Second Law
It is impossible to construct a device that operates in a cycle
and produces no effect other than the transfer of heat from a
lower-temperature body to a higher-temperature body.
Both versions of the Second Law are negative statements
which cannot be proven. They are, however, based on
empirical evidence and no experiment has yet been
found to contradict this law.
Perpetual Motion Machines
• A machine that violates either the first or second laws of
thermodynamics is called a Perpetual Motion Machine.
• What does that mean to you? Do you think you could
build one? Are there some people that do?
Turns out there are two types:
a. PMM1 - violates the first
b. PMM2 - violates the second law
Qin
boiler
Compress to
boiler
pressure
pump
W net,out
turbine
condenser
Qout
PMM1
Gen
• Claims to run on heat supplied by the resistance units run
off of the generator.
• Remainder of electrical energy is available for power.
• Idea is to start it externally and it would run indefinitely.
Problem**
• Initially the resistance heat would balance the heat externally
used to start it.
• After it is disconnected system stops with no energy. It can’t
create energy out of nothing.
• Violates the first law.
Qin
boiler
Compress to
boiler
pressure
pump
W net,out
turbine
Qout
PMM2
• This inventor wants to use all his waste heat so sends it
back to the pump and skips the condenser.
• BUT now he has only one thermal reservoir.
• Violates the second law (we can’t have a heat engine
with 100% efficiency)
• Surprising number of quacks:
1. J.W. Kelly collected millions between 1874-98 for the
“hydrodynamic-pulsating-vacu-engine” which could push a
railroad train 3,000 miles on 1 liter of WATER. (After he
died investors found a hidden motor.)
2. More recently investors wanted to invest 2.5 million in an
“energy augmentor” but their lawyer wanted an expert
opinion at which the inventor fled.
3. I remember when I was younger (a long time ago) someone
trying to sell a device you put on your carburetor to increase
your gas mileage by a factor of 10. It cost $20.
• Do any of you have a good story to tell? There are lots of
them around.
• Here an understanding of thermodynamics will help you
avoid any of these false claims.
Reversible processes:
• One that can be run in reverse without leaving any effect
on the surroundings...both are returned to their original
state.
• Intuition tells you that this doesn’t happen (and it
doesn’t).
• Example is put a hot cup of fluid in a cold room, it cools
and will actually take more to heat it up again than it gave
off to the room.
• Reversible processes DO NOT occur in nature
• What is one of the biggest sources of irreversibility in
nature?
• Is there some way to avoid it completely?
• We are back to our perpetual motion machines.
Heat Pump
• A heat pump is a device which applies external work to extract an amount of
heat QC from a cold reservoir and delivers heat QH to a hot reservoir.
• A heat pump is subject to the same limitations from the second law of
thermodynamics as any other heat engine and therefore a maximum
efficiency can be calculated from the Carnot cycle.
• Heat Pumps are usually characterized by a coefficient of performance which
is the number of units of energy delivered to the hot reservoir per unit work
input.
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Air Conditioners and Heat Pumps
• Air conditioners and heat pumps are heat engines like the
refrigerator.
• They make good use of the high quality and flexibility of electric
energy in that they can use one unit of electric energy to transfer
more than one unit of energy from a cold area to a hot area.
• For example, an electric resistance heater using one kilowatt-hour of
electric energy can transfer only 1 kWh of energy to heat your house at
100% efficiency.
• But 1 kWh of energy used in an electric heat pump could "pump" 3
kWh of energy from the cooler outside environment into your house for
heating.
• The ratio of the energy transferred to the electric energy used in the
process is called its coefficient of performance (CP).
• A typical CP for a commercial heat pump is between 3 and 4 units
transferred per unit of electric energy supplied.
Coefficient of Performance
The coefficient of performance (CP) for a heat pump is the ratio of the energy
transferred for heating to the input electric energy used in the process. In
reference to the standard heat engine illustration, the coefficient is defined by
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There is a theoretical maximum CP, that of the Carnot cycle:
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• For a refrigerator, however, the useful quantity is the heat extracted, QC , not
the heat exhausted.
• Therefore, the coefficient of performance of a refrigerator is expressed asFor
consumer refrigerators in the U.S., the coefficient of performance for
refrigerators is typically recast into a number called the Energy Efficiency
Ratio.
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Energy efficiency rating
EER = 3.412 COPr rating used for refrigerators and AC
* usually between 8 and 12 but heat pumps can go to 17
• Why do we care about processes that turn heat into
mechanical work?
• A device that performs such a process is called a
heat engine.
• According to the first law of thermodynamics, energy is
always conserved, so we obviously cannot “produce”
energy with a heat engine.
• We put energy into the process in the form of heat,
and extract a (generally lesser) amount of energy
from the process in the form of mechanical work.
• The reason for doing this is that energy in the form of
mechanical work is often more useful than the same
amount of energy in the form of heat.
• In a sense, mechanical work is coherent energy,
whereas heat energy is incoherent.
William Thomson, 1st Baron Kelvin,
(26 June 1824–17 December 1907) was an
Irish-Scottish mathematical physicist,
engineer, and outstanding leader in the
physical sciences of the 19th century.
• He did important work in the
mathematical analysis of electricity and
thermodynamics, and did much to unify the
emerging discipline of physics in its
modern form.
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• He also enjoyed a second career as a telegraph
engineer and inventor, a career that propelled him into
the public eye and ensured his wealth, fame and honour.
Second Law Broken
• One of the most fundamental rules of physics, the second law of
thermodynamics, has for the first time been shown not to hold
for microscopic systems.
• The demonstration, by chemical physicists in Australia, could
place a fundamental limit on miniaturisation, because it suggests
that the micro-scale devices envisaged by nanotechnologists will
not behave like simple scaled-down versions of their larger
counterparts - they could sometimes run backwards.
• The second law states that a closed system will remain the
same or become more disordered over time, i.e. its entropy will
always increase. It is the reason a cup of tea loses heat to its
surroundings, rather than being heated by the air around it.
• "In a typical room, for example, the air molecules are most
likely to be distributed evenly, which is the overall result of
their individual random motion", says theoretical physicist
Andrew Davies of Glasgow University. ”
• But because of this randomness there is always a probability
that suddenly all the air will bunch up in one corner."
Thankfully this probability is so small it never happens on
human timescales.
CARNOT Principles
• The efficiency of an irreversible heat engine is always less
than the efficiency of of a reversible process operating
between the same two heat reservoirs.
• Efficiencies of all reversible heat engines operating between
the same two reservoirs are the same.
First statement:
High Temp Reservoir at Th
Qh
Qh
Wrev
irreversible
reversible
Wirrev
Ql
Low Temp Reservoir at Tl
Ql,rev
• If we assume that the irreversible process is more
efficient (contradicts Carnot’s first principle) it will thus
deliver more work.
• Thus we have a system that produces net work
Wirrev - Wrev
with no net heat exchange.
• This is a clear violation of the Kelvin-Planck statement
of the 2nd law.
Rankine Steam Plant Cycle
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• There are four processes in the Rankine cycle, each
changing the state of the working fluid.
• These states are identified by number in the diagram
above.
•Process 4-1: First, the working fluid is pumped (ideally
isentropically..no change in entropy..) from low to high
pressure by a pump.
• Pumping requires a power input (for example
mechanical or electrical
•Process 1-2: The high pressure liquid enters a boiler
where it is heated at constant pressure by an external
heat source to become a superheated vapor.
• Common heat sources for power plant systems are
coal, natural gas, or nuclear power.
• Which do you think is the most economical?
• What are the consequences of each?
• Process 2-3: The superheated vapor expands through a
turbine to generate power output. Ideally, this expansion is
isentropic.
• This decreases the temperature and pressure of the
vapor.
• Process 3-4: The vapor then enters a condenser where it
is cooled to become a saturated liquid.
• This liquid then re-enters the pump and the cycle
repeats.
Real Rankine cycle (non-ideal)
• In a real Rankine cycle, the compression by the pump
and the expansion in the turbine are not isentropic.
• In other words, these processes are non-reversible and
entropy is increased during the two processes (indicated
in the figure as ∆S).
• This somewhat increases the power required by the
pump and decreases the power generated by the turbine.
It also makes calculations more involved and difficult.
Rankine cycle with reheat
• In this variation, two turbines work in series.
• The first accepts vapor from the boiler at high
pressure. After the vapor has passed through the first
turbine, it re-enters the boiler and is reheated before
passing through a second, lower pressure turbine.
• Among other advantages, this prevents the vapor
from condensing during its expansion which can
seriously damage the turbine blades.
Regenerative Rankine cycle
• The regenerative Rankine cycle is so named because
after emerging from the condenser (possibly as a subcooled liquid) the working fluid is heated by steam tapped
from the hot portion of the cycle.
• This increases the average temperature of heat addition
which in turn increases the thermodynamic efficiency of the
cycle.