Sections
An eruptive prominence is not the same as a coronal mass ejection: it is probably much less powerful. The blob can still make it to Earth. This is an extreme ultraviolet image from the SOHO probe and so the color is false.
Sol Invictus: The unconquered Sun.
The energy source for almost all of the biosphere.
The Sun's diameter is about 100 = 10**2 times the Earth's diameter.
The Sun's mass is about 3*10**5 times the Earth's mass.
Credit: NASA.
A heat engine is a machine that operates in a cycle.
Examples are steam engines, steam turbines (which are a kind of steam engine, but not so called usually), and internal combustion engines (ICEs)
A part of the machine is the working fluid (e.g., water in steam engine).
Caption: The aeolipile of Hero of Alexandria (c. 10--70 CE).
The high-pressure steam from the heated vessel flows out the pipes on the rotating sphere.
The reaction force of the steam on the outflow pipes drives the rotation which could be used for useful work of some kind.
The sphere rotates and in that sense there is a cycle. But the working fluid does not run in a cycle. But one could imagine recapturing it and feeding it back into the heated vessel to complete a cycle.
Really, there is a cycle. One feeds in water that's part of the whole water cycle and it returns to the water cycle as steam.
Credit: Knight's American Mechanical Dictionary, 1876. Uploaded by User: Quadell.
Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Aeolipile_illustration.JPG.
Public domain.
Caption: "Work input on a working fluid by means of a cylinder-piston arrangement."
Credit: User Dmic0001 in 2008.
Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Piston_cylinder.jpg.
Public domain.
The equation relating these quantities is dead simple:
This is because the time averaged thermal energy of the working fluid is a constant: i.e.,
where Q=C_H-Q_C is the net heat into the system and W is the work done by the system.
We are just obeying the law of the conservation of energy or the first law of thermodynamics.
This is the ideal heat engine. In real heat engines periodic behavior can only be approximate.
For this to happen, of course, the thermal energy of the HOT BATH must be replenished to keep the HOT BATH on average unchanging.
And the excess thermal energy of the COLD BATH must be disposed of to keep the COLD BATH on average unchanging..
And the work W
must go someplace: e.g., spinning car wheels or turning the
Here is a schematic heat engine.
A schematic diagram of a heat engine.
Legend
Nuclear reactors use water as a cold bath, but the water is cooled in cooling towers to something like the ambient medium.
Download site: Wikipedia: Image:Carnot heat engine 2.svg.
Note the replenishment of thermal energy to the HOT BATH and disposal of thermal energy from COLD BATH keeps the heat engine unchanging thermodynamically (i.e., which includes keeping the entropy constant) averaged over multiple cycles.
Entropy of the of the heat engine and the environment must increase or at least stay constant.
Answer 3 is right.
The mathematical demonstration is beyond this course---and currently beyond me---but it can be shown that heat engines do as answer 3 says.
Actual heat engines usually reject far more than the mimimum possible heat to the COLD BATH.
They have less than the ideal maximum engine efficiency.
The efficiency of heat engine is defined by the equation:
Since Q_H > = Q_C > 0 always, we must have:
In other words, the most bang for the buck.
In fact, many actual heat engine are often run in zero-efficiency mode from time to time.
Efficiencyizers are eager to store up the energy that is otherwise going into waste heat.
In order for the overall entropy of the whole heat engine system NOT to decrease, it turns out that
Those temperatures are Kelvin temperatures.
The F_eff_max = 1 - T_C/T_H is a bit of an idealization in that seldom in real heat engines are there fixed HOT BATH and COLD BATH temperatures.
But average temperatures can be used to find a characteristic F_eff_max = 1 - T_C/T_H.
Most heat engines work at far less than F_eff_max = 1 - T_C/T_H.
Typically, internal combustion engines of cars have an efficency of about 20 % although the hybrid cars (e.g., the Prius) may optimally reach 37 %.
Caption: "2004-2007 Toyota Prius photographed in USA."
The Prius: nothing special to look at, but it gets about 45 miles per gallon which makes it the most fuel-efficient car currently sold in the US.
Of course, in 1991, the standard GM Geo Metro got 60 miles per gallon at least according to the specifications.
Credit: IFCAR
Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:2nd-Toyota-Prius.jpg.
Public domain.
This is often just left as understood in discussions.
T_C = 300 K which is warmish air by human standards. The COLD BATH is the ambient medium ultimately. 2000 K which is a characteristic value adiabatic value for liquid fuels (combustion temperatures). But that sounds way too high for engines. Iron melts at 1811 K under standard pressure of about 0.1 MPa (I'd guess). Faute de mieux say 600 K. Thus F_eff_max = 1 - T_C/T_H = very roughly 1 - 300/6000 = 0.50 = 50 %. Maybe this calculation is badly wrong.
There's no absolute right or wrong, but I'd take 4 myself.
Practicality and safety limit us.
Fuels only burn so hot and engines can only take so much heat before they melt.
One can't usually do much about the COLD BATH. It's the ambient medium. Trying to get a colder COLD BATH would require refrigeration and that would cost energy.
The AMBIENT MEDIUM is what nature has given us.
How is work actually extracted from a heat engine?
Well steam turbines are most easy to understand in bare outline.
A diagram of a electric generator and a turbine for hydropower.
Actual images of electric generators and turbines in power plants are often complex.
So many prongs and ridges and covers that it is hard to see what is happening.
This image, of course, cannot stand for the whole range of possibilities, but it is generally instructive.
In hydropower plants just pouring, fast water turns the rotor.
In thermal power stations high-pressure steam turns the rotor.
Credit: United States Army Corps of Engineers As the creator is a US Government Agency the image in the public domain.
Download site: Wikipedia: Image:Water turbine.jpg.
The simplest turbine is just a rotor blade like a windmill.
But more complex turbines with stators to direct the steam flow on the rotar are more efficient depending on the case.
The hot steam loses some energy turning the turbine, but it cannot lose it all.
So the steam is collected and cooled in a condenser and it returns to liquid state.
Cooling the steam is usually done contact with cool water in cooling towers or in more primitive days from rivers and the like.
It's not environmentally sound to dump the hot cooling water back in the natural environment (i.e., rivers and the like).
So power stations with steam turbines usually have cooling towers as one of their most conspicuous and recognizable features.
Of course, my outline here does not cover all the variations and may not even be the best practices, but it will do for now.
Here is a diagram of thermal power station which illustrates my outline.
A diagram of thermal power station
Legend by image creator 1. Cooling tower 10. Steam governor valve 19. Superheater 2. Cooling water pump 11. High pressure turbine 20. Forced draught fan 3. Three-phase 12. Deaerator 21. Reheater transmission line 4. Unit transformer 13. Feed heater 22. Air intake 5. Three-phase electrical 14. Coal conveyor 23. Economiser generator 6. Low pressure turbine 15. Coal hopper 24. Air preheater 7. Boiler feed pump 16. Pulverised fuel mill 25. Precipitator 8. Condenser 17. Boiler drum 26. Induced draught fan 9. Intermediate pressure 18. Ash hopper 27. Chimney stack turbine
A detailed description can be found at the download source Wikipedia: Image:PowerStation2.svg.
Credit: Wikipedia contributor Magicflame. According to Wikipedia permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version.
Download site: Wikipedia: Image:PowerStation2.svg.
But the traditional reciprocating steam engine is what is often first thought of as a steam engine.
It uses pistons and cylinders like an internal combustion engine.
But the combustion (as with the steam turbine) is external.
The cylinder and the turbine are really the only widespread practical heat engine designs I believe.
It is arguably distinct from an engine with a
Wankel engines have had niche market uses, but havn't made much of an inroad into the car market though cars with Wankel engines have been made most notably by Mazda.
Then there is the toy drinking bird.
The cylinder appeared with the first practical steam engines circa 1700 or a bit earlier.
Modern turbines were invented in the 19th century if you don't count windmills. The modern steam turbine was invented in 1884, although precursor devices back to ancient times---i.e., the aeolipile of Hero of Alexandria (c. 10--70 CE).
At some point the steam turbine outperformed the traditional reciprocating steam engine and these are now little used.
An animated diagram of a triple expansion engine
Looks like at Heath Robinson machine.
Credit: Wikipedia contributor Emoscopes. According to Wikipedia permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version.
Download site: Wikipedia: Image:Triple expansion engine animation.gif.
This may be almost their only use.
Now for refrigerators or heat pumps.
The words are synonyms as I and many use them and I prefer refrigerator, but Wikipedia likes to use refrigerator for a food storage device only---which is a thing I call a FRIG.
An air conditioner is another kind of refrigerator.
A refrigerator is in many essentials much like a heat engine run in reverse.
But now the WORKING FLUID absorbs heat Q_C from a COLD BATH and by means of some macroscopic work W and rejects some heat Q_H to a HOT BATH.
The interpretation is a bit different.
The work W now goes into the WORKING FLUID and is transformed into heat that is rejected to the HOT BATH.
So running a refrigerator takes work (i.e., an ordered energy input).
The gain is that the COLD BATH can be made colder by taking thermal energy out of it or maintained at a cold temperature if heat flows from elsewhere are trying to heat it up.
A schematic diagram of a heat engine.
With the arrows reversed, it is the schematic diagram of a refrigerator.
Legend
A schematic diagram of a refrigerator.
Legend (by image creator: see below)
Credit: Wikipedia contributor Ilmari Karonen. The creator has put the image in the public domain.
Credit: Wikipedia contributor Ilmari Karonen. The creator has put the image in the public domain.
Download site: Wikipedia: Image:Heatpump.svg.
The pressure is low and this causes evaporative cooling in the EVAPORATOR.
The cooling makes the EVAPORATOR lower in temperature than the surroundings which are, in fact, the COLD BATH (which could be the INSIDE of your FRIG or your air-conditioned house).
Because the EVAPORATOR is colder than the COLD BATH heat spontaneously flows from the COLD BATH to the EVAPORATOR. This cools the COLD BATH. It can take considerable heat flow FROM the COLD BATH to make up the latent heat of vaporization.
The EVAPORATOR is often a coil with fins to facilitate heat inflows from the COLD BATH. Fans may be used to blow the air in the COLD BATH by the fins to accelerate the heat flow.
The EVAPORATOR and COLD BATH are shielded by insulation in the inner region of the refrigerator from the outer region of the refrigerator.
There a COMPRESSOR (e.g., a piston and cylinder) compresses the EVAPORATED WORKING FLUID.
The compression actually heats the EVAPORATED WORKING FLUID, but the higher pressure nonetheless leads to condensation when the working fluid is forced through another one-way valve in the CONDENSER.
The COMPRESSOR is also providing---I think---the pressure force to the keep the working fluid flowing throughout the refrigerator.
The CONDENSER is heating the HOT BATH though this may not be noticed.
The heat flow occurs spontaneously because the working fluid is hotter than the HOT BATH initially.
The heat it loses came both from the COLD BATH and the work done it in the COMPRESSOR.
Because it is high density, the working fluid condenses even at the temperature of the HOT BATH or higher.
The working fluid may reach about the temperature of the HOT BATH before leaving the CONDENSER.
It can't get lower.
The CONDENSER is often a coil with fins to facilitate heat outflows to the HOT BATH. Fans may be used to blow the air in the HOT BATH by the fins to accelerate the heat flow.
The EXPANSION VALVE has the effect of changing disordered pressure-causing thermal energy into partially ordered kinetic energy of a faster flowing LIQUID WORKING FLUID.
This lowers the pressure significantly.
For the
The low pressure LIQUID WORKING FLUID is now back in the
EVAPORATOR and is unstable toward evaporation
because of its low pressure.
The LIQUID WORKING FLUID will now begin the cycle again.
I don't know of any
refrigerators
that work in with continuous constant flow, but they may exist.
But in many designs the COMPRESSOR has a piston
that has be pushed in and pulled out in cycle.
So the
working fluid
flow has to be stopped and started.
This may be the cause of some
FRIG and air conditioner noises.
However, fans may cause much of the noise.
Also so much cooling can be achieved in a few cycles that continuous cycling
is often not needed, and so FRIGS and air conditioners are often in a
rest mode.
To be practical for a moment, what is the
working fluid
in a practical FRIG or
air conditioner?
It has to be
substance
that can be condensed and evaporated over a large range of
temperatures.
This enables the
FRIG or
air conditioner
to operate under many conditions.
The substance
shouldn't be toxic nor chemically active: we don't want leaks
to poison us nor reactions to clog to foul up the inner workings.
For many years,
chlorofluorcarbons (CFCs) were used:
Freon is
a DuPont trade name for
CFCs.
But leakage of
CFCs
from frigs,
air conditioners,
and other sources
turned out to be destructive of the
ozone layer.
The
ozone layer (at
an altitude of approximately 15--35 km) protects
the biosphere
from dangerous solar ultraviolet light.
Caption: "Levels of ozone at various altitudes, and related blocking of several types
of ultraviolet radiation."
A DU is a Dobson unit
is a bizarre unit used in ozone science.
A DU/km is a ozone number density: i.e., ozone molecules per unit volume.
The volume unit, however, is very strange---and people think
astronomers use wacko units.
Credit: NASA. Posted in 2005
Linked source: Wikipedia
image
http://en.wikipedia.org/wiki/Image:Ozone_altitude_UV_graph.jpg.
Public domain at least in USA.
Hydrofluorocarbons
are NOT as good as
CFCs
in other respects.
The permformance of
refrigerators
is usually measured using the
coefficient of performance (COP) which is just 1/F_eff = Q_H/W with
the meanings of the quantities changed,
mutatis mutandis.
The smaller G_eff, the better.
As a neologism, let us call G_eff the reverse efficiency.
The impossible would be to have W=0 and Q_H=Q_C.
This would be a spontaneous flow of
heat
from COLD to HOT
Spontaneous, because it happens without work done---and this
never happens.
Actually, the minimum possible G_eff satisfies
where T_C and T_H are on the
Kelvin temperature scale.
So you see a
heat engine
efficiency is bounded above by
Carnot engine
or
Carnot cycle
was discovered by
Sadi Carnot at least in some form if not quite what we know today.
The actual history is beyond my scope.
Nicolas Leonard Sadi Carnot (1796--1832): a pioneer of
thermodynamics.
Sadi Carnot in the dress uniform of a student of the Ecole Polytechnique.
Carnot is noted for his discovery of the
Carnot engine or
Carnot cycle.
The Carnot engine has the most
efficient cycle possible for a heat engine or refrigerator.
Credit: Unknown artist to the web.
Wikipedia judges its copyright status as uncertain.
But it must have been painted no later than the 1820s and
surely the artist's copyright is now long expired if it ever
exited.
Download site
Wikipedia: Image:Sadi Carnot.jpeg
Caption: "Lazare Carnot" with braids and
epaulets.
Lazare Carnot (1753--1823), one of the French Revolution leaders.
Carnot was called the ``Organizer of Victory''.
Credit: Unknown artist. Uploaded by User: Nk in 2005.
Linked source: Wikipedia
image
http://en.wikipedia.org/wiki/Image:Lazare_carnot.jpg.
Public domain.
Caption: "Sadi Carnot's pison-and-cylinder diagram from 1824".
A and B may
Carnot's
HOT BATH and COLD.
Credit: Sadi Carnot
(1796--1832). Uploaded by User:
Sadi Carnot who is not
Sadi Carnot.
Linked source: Wikipedia
image
http://en.wikipedia.org/wiki/Image:Carnot-engine-1824.png.
Public domain at least in USA.
Run forward, it is a
heat engine.
Run in reverse, it is a
refrigerator.
The Q_H, Q_C, and W quantities are the same if the
Carnot engine
is run forward
as heat engine
or in reverse
as
refrigerator.
A schematic diagram of a
heat engine.
Legend
Download site:
Wikipedia: Image:Carnot heat engine 2.svg.
Caption: "El libro mas antiguo que se conserva en la Biblioteca Publica
del Estado - Biblioteca Provincial de Huelva.
Una edicion de la Logica de Aristoteles impresa en Lyon en 1570".
Credit: Biblioteca Huelva and
Aristotle (384--322 BCE).
Linked source: Wikipedia
image
http://en.wikipedia.org/wiki/Image:Aristoteles_Logica_1570_Biblioteca_Huelva.jpg .
Use under
GNU
Free Documentation License
One operates as a heat engine
and the other as a
refrigerator.
``Give me a break. I'm working on it.''
Since
the Q_H, Q_C, and W quantities are the same for both
Carnot engines,
the overall effect of the two
Carnot engines
viewed a one system
is NOTHING.
No net heat is removed from the HOT BATH and no
net heat is reject to the COLD BATH and no net work is done and the
entropy does NOT change.
Now imagine one had a heat engine
more efficient than the Carnot heat engine.
It rejects the same heat to the COLD BATH, but takes more heat from the
HOT BATH and thus does more work than the
Carnot heat engine.
We replace
Carnot heat engine
with the more efficient
heat engine
and use its work to drive the
Carnot refrigerator engine.
Now what is the overall system doing?
Net heat is extracted from the HOT BATH and net work is done, but
no net heat is rejected to the COLD BATH.
In effect, an amount of
thermal energy
has been
transformed entirely into
thermodynamic work
with
no heat rejected to a COLD BATH by
a heat engine
operating in a cycle.
This violates
2nd law of thermodynamics
by causing entropy to increase---as one
can show by a calculation we will NOT do.
Now
Sadi Carnot
came before the word
thermodynamics was coined and
knew nothing about
the formal 2nd law of thermodynamics
or entropy as a well defined
thermodynamic variable.
But he did know that no one had seen in
nature or
technology any cycle which
turned thermal energy
entirely into
thermodynamic work
with no heat rejected to a COLD BATH.
So Sadi Carnot
(at least the ideal Carnot if not the Carnot of history) concluded that
a reversible engine
(which we call a Carnot engine)
had to be the most
efficient
possible heat engine.
A similar argument shows that the
Carnot engine has to be
the most efficient refrigerator.
We distinguish the HYPOTHETICAL FRIG quantities by subscript ``hyp''.
You could scale this
HYPOTHETICAL FRIG to use the work W of
the Carnot heat engine:
i.e., set W_hyp=W.
Since it has a lower reverse efficiency:
From an overall perspective, there is a spontaneous flow of
heat from
HOT to COLD.
A similar argument shows that if you have a
heat engine
more efficient than a
Carnot engine,
then
you can turn
heat entirely
into work without rejecting any net
heat
to a COLD BATH.
Carnot
did not know of the
second
law of thermodynamics: it was formulated after his day.
But he did know that no one had every seen
a spontaneous flow of
heat from
HOT to COLD
nor a
heat engine
without rejection to a COLD BATH.
The ideal
Carnot
(if not the Carnot of history)
argued that
Carnot heat engine
must be the most efficient
heat engine
and
the most efficient
refrigerator
possible.
In the above, arguments our hypothetical
heat engine
and
refrigerator
that are more efficient than
the Carnot engine
DO violate the
second
law of thermodynamics and cannot exist.
The main trick is to only let heat flows occur when
the
working fluid
is in thermal contact with
the HOT BATH and the COLD BATH
and only let those flows occur
between vanishingly small temperature differences.
Caption: "Pressure-volume (p-V)
diagram for the Carnot cycle."
Credit: User Keta in 2006.
Linked source: Wikipedia
image
http://en.wikipedia.org/wiki/Image:Carnot_cycle_p-V_diagram.svg.
Use under
GNU
Free Documentation License
You could imagine the working fluid
as contained in a cylinder with a piston---just like in
Sadi Carnot's image
http://en.wikipedia.org/wiki/Image:Carnot-engine-1824.png
The piston pushes out when the
working fluid
does work and pushes in when work is done on the
working fluid.
The
Carnot engine
is running in a cycle and hence the curve forms a closed loop.
As the working fluid
expands (1--3), it does thermodynamic work (PdV;
as it contracts (3--1)
PdV work is done on it.
The less steep segments are
isotherms where
working fluid absorbs (when expanding)
or rejects (when contracting) heat
at ZERO
temperature gradient
(or difference).
This is the magic trick of the
Carnot engine
to make heat flow
at ZERO
temperature gradient.
If you could actually do this, then there would be no change in
entropy
and, thus the process would be REVERSABLE---you could make the
heat flow either way.
Well it can't actually be done quite.
But, in principle, one could approach
ZERO
temperature gradient
flow of heat
as closely as you like.
Just let temperature gradient
be very small and let the heat flow
very slowly.
Such ideal slow processes are called
quasistatic processes:
the system is always vanishingly
close to thermodynamic equilibrium
in a quasistatic process.
The steeper segments
PV diagram
are
adiabats
along which no heat flows occur
to or from the working fluid.
No entropy changes occur in
working fluid,
HOT BATH, and COLD BATH, along an
adiabat where
thermodynamic equilibrium
is maintained in all elements of the system.
To maintain exact
thermodynamic equilibrium
during changes the adiabats
are also quasistatic processes.
Since no entropy changes
occur during the quasistatic
adiabats, they
are REVERSIBLE and the
system can be run up or down them.
We conclude that all segments in the
PV diagram
are REVERSIBLE as an ideal limit.
So the whole cycle in the PV diagram
can be run either way since entropy of the
system doesn't change going either way.
Going 1, 2, 3, 4, 1, as shown in the
PV diagram,
yields net PdV work
since the expansion segments 1-2 and 2-3 have more area under them than the
contraction segments 3-4 and 4-1.
In this direction, the
Carnot engine is
a heat engine
moving thermal energy
from the
HOT BATH to the COLD BATH and doing
PdV work.
Going 1, 4, 3, 2, 1, as NOT shown in the
PV diagram
absorbs net PdV work
since the contraction segments 3-2 and 2-1 have more area under them than the
expansion segments 1-4 and 4-3.
In this direction, the
Carnot engine is
a refrigerator
moving thermal energy
from the
COLD BATH to the HOT BATH and absorbing
PdV work.
Thus, the Carnot engine
is the most efficient
heat engine
and
refrigerator.
You can't quite build an ideal
Carnot engine.
But you can get very close.
A nearly ideal
Carnot heat engine
must operate very slowly since all the segments must
be quasistatic.
In particular, the
heat transfers
must happen over
NEARLY ZERO
temperature gradients.
The lower the temperature gradients,
the slower
the heat transfer---we are just asserting this, but
it's true.
Carnot engines
do have special experimental uses.
But actually the only one I know of is to measure
temperature
in some special cases.
You can for example build a
Carnot engine
using a gas as a
working fluid.
They may be mostly small desktop affairs with tubes and cylinders and pistons---just
guessing.
The
Carnot engine
as it is reversible has
It can be shown---but we won't do it---that for the
Carnot engine
the ratio
This leads to our results
And, of course, people don't even try to get extremely close
usually since they don't want
the nearly ``powerless''
Carnot engine.
Nevertheless the ideal efficiency results set absolute limits on
what is obtainable and guide designers in
getting the best they can out
heat engines
and
refrigerators.
For actual
heat engines there
is often something to be gained by making T_C/T_H as small
as one can subject to other desiderata: i.e., safety and high power.
Thus,
CFCs are being/have been phased out
in favor of
hydrofluorocarbons
which are much less destructive of
the
ozone layer.
An other definition of the
coefficient of performance (COP) which Q_C/W
(e.g.,
Halliday et al. 2001, p. 494).
I just prefer to the use
G_eff = W / Q_H = ( Q_H - Q_C )/ Q_H = 1- Q_C/Q_H
where everything is the same as for F_eff, except the
interpretation.
G_eff = 1 - Q_C/Q_H >= G_eff_min = 1 - T_C/T_H ,
F_eff_max = 1 - T_C/T_H
and a
refrigerator
reverse efficiency is bounded below by
G_eff_min = 1 - T_C/T_H .
We are now at the point where we
can discuss the
Carnot engine.
He also had a famous father,
What
Carnot imagined (at least the ideal Carnot if not the
Carnot of history) was a reversible THERMODYNAMIC ENGINE.
This machine now is called the
Carnot engine.
Thus, one has
Credit: Wikipedia
contributor Eric Gaba (Sting) .
The creator has put the image in the public domain.
F_eff = G_eff = W/Q_H = 1- Q_C/Q_H
for the
Carnot engine.
Now for some logic.
Say you had two identical Carnot engines
both operating between the same HOT BATH and COLD BATH.
``Say a diagram would really help here.''
The work W from the heat engine
is used to drive the
refrigerator.
The refrigerator in
gory mathematical form---which we omit from any classroom presentation.
Now imagine that you had a HYPOTHETICAL FRIG with a lower
reverse efficiency, than the
Carnot heat engine.
This means the HYPOTHETICAL FRIG
has a better efficiency than the
Carnot heat engine
run in reverse as
refrigerator.
Q_H_hyp > Q_H
and
recall
W = Q_H - Q_C where W is output
and
where Q_H is absorbed from the HOT BATH and Q_C is rejected to the COLD BATH
and
W_hyp = W = Q_H_hyp - Q_C_hyp where W is work input
and
where Q_H_hyp is rejected to the HOT BATH and Q_C is absorbed from the COLD BATH.
Subtracting the former from the latter, we find
0 = ( Q_H_hyp - Q_H ) - ( Q_C_hyp - Q_C )
or
( Q_H_hyp - Q_H ) = ( Q_C_hyp - Q_C ) > 0
The upshot in words is that no net work is done and
yet a finite amount of heat
( Q_H_hyp - Q_H ) > 0
has been moved from the COLD BATH to the HOT BATH.
Question: Now I know what you are thinking,
can a Carnot engine exist.
You can almost build a
Carnot engine.
Answer 3 is right.
The PV diagram plots the
pressure
and
volume of the
working fluid
during a full cycle of the
the Carnot engine.
So the Carnot engine
is the reversible engine
Sadi Carnot
imagined.
In a perfect sense, there can be no
thermodynamic equilibrium
if a system is changing, but
but, in principle, one can
approach an quasistatic process
as closely as you like.
ZERO
temperature gradient
flow of heat
is the ideal limit of an actual physical process.
Question: If a nearly ideal
Carnot heat engine
can be built, why
are they not widely used?
The last point leads us to the ideal maximum efficiency and mimimum reverse
efficiency we have discussed above.
Answer 3.
F_eff = G_eff= 1 - Q_C/Q_H
and F_eff is the biggest that can be obtained for a
heat engine
and
G_eff is the lowest that can be obtained for a
refrigerator.
Q_C/Q_H = T_C/T_H ,
where the
temperatures
are Kelvin temperatures.
F_eff_max = 1 - T_C/T_H ,
and
G_eff_min = 1 - T_C/T_H .
These ideal results can never be quite obtained.