Chapter 18 Heat Engines, Entropy and the Second Law of Thermodynamics.
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Transcript of Chapter 18 Heat Engines, Entropy and the Second Law of Thermodynamics.
Chapter 18
Heat Engines,
Entropy
and the
Second Law of Thermodynamics
First Law of Thermodynamics – Review Review: The First Law is a statement of
Conservation of Energy The Law places no restrictions on the
types of energy conversions that can occur In reality, only certain types of energy conversions
are observed to take place Some events (processes) in one direction are
more probable than those in the opposite direction
William Thomson, Lord Kelvin 1824 – 1907 Physicist and
mathematician Proposed the use of
absolute temperature scale Now named for him
Work in thermodynamics led to idea that energy cannot spontaneously pass from colder to hotter objects
Heat Engine A heat engine is a device that takes in
energy by heat, and, operating in a cycle, expels a fraction of that energy by means of work
A heat engine carries some working substance through a cyclical process
Heat Engine, cont. The working substance
absorbs energy by heat from a high temperature energy reservoir (Qh)
Work is done by the engine (Weng)
Energy is expelled by heat to a lower temperature reservoir (Qc)
Heat Engine, cont. Since it is a cyclical process,
ΔEint = 0 Its initial and final internal energies
are the same Therefore, Qnet = Weng The work done by the engine
equals the net energy absorbed by the engine
The work is equal to the area enclosed by the curve of the PV diagram
If the working substance is a gas
Thermal Efficiency of a Heat Engine Thermal efficiency is defined as the
ratio of the net work done by the engine during one cycle to the energy input at the higher temperature
We can think of the efficiency as the ratio of what you gain to what you give
1eng h c c
h h h
W Q Q Q
Q Q Q
e
More About Efficiency In practice, all heat engines expel only
a fraction of the input energy by mechanical work
Therefore, their efficiency is always less than 100% To have e = 100%, QC must be 0
Second Law: Kelvin-Planck Form
It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work Means that Qc cannot equal 0
Some Qc must be expelled to the environment
Means that e cannot equal 100%
Perfect Heat Engine No energy is
expelled to the cold reservoir
It takes in some amount of energy and does an equal amount of work
e = 100% It is an impossible
engine
Reversible and Irreversible Processes
A reversible process is one for which the system can be returned to its initial state along the same path And one for which every point along some path is
an equilibrium state An irreversible process does not meet these
requirements Most natural processes are known to be
irreversible Reversible process are an idealization, but some
real processes are good approximations
Reversible and Irreversible Processes, cont A real process that is a
good approximation of a reversible one will occur very slowly
The system is always very nearly in an equilibrium state
Adding and removing the grains of sand is an example of a real process that can occur slowly enough to be reversible
Reversible and Irreversible Processes, Summary The reversible process is an idealization All real processes on Earth are
irreversible
Sadi Carnot 1796 – 1832 First to show the
quantitative relationship between work and heat
Book reviewed importance of the steam engine
Carnot Engine A theoretical engine developed by
Sadi Carnot A heat engine operating in an ideal,
reversible cycle (now called a Carnot Cycle) between two reservoirs is the most efficient engine possible This sets an upper limit on the efficiencies
of all other engines
Work by a Carnot Cycle The net work done by a working
substance taken through the Carnot cycle is the greatest amount of work possible for a given amount of energy supplied to the substance at the upper temperature
Carnot Cycle
Overview of the processes in a Carnot Cycle
Carnot Cycle, A to B A to B is an isothermal
expansion The gas is placed in
contact with the high temperature reservoir, Th
The gas absorbs heat |Qh|
The gas does work WAB in raising the piston
Carnot Cycle, B to C B to C is an adiabatic
expansion The base of the cylinder
is replaced by a thermally nonconducting wall
No heat enters or leaves the system
The temperature falls from Th to Tc
The gas does work WBC
Carnot Cycle, C to D The gas is placed in
contact with the cold temperature reservoir
C to D is an isothermal compression
The gas expels energy QC
Work WCD is done on the gas
Carnot Cycle, D to A D to A is an adiabatic
compression The gas is again placed
against a thermally nonconducting wall
So no heat is exchanged with the surroundings
The temperature of the gas increases from TC to Th
The work done on the gas is WDA
Carnot Cycle, PV Diagram The work done by
the engine is shown by the area enclosed by the curve, Weng
The net work is equal to |Qh| – |Qc|
Eint = 0 for the entire cycle
Efficiency of a Carnot Engine Carnot showed that the efficiency of the
engine depends on the temperatures of the reservoirs
Temperatures must be in Kelvins All Carnot engines operating between the
same two temperatures will have the same efficiency
1C C CCarnot
h h h
Q T Tand e
Q T T
Notes About Carnot Efficiency Efficiency is 0 if Th = Tc
Efficiency is 100% only if Tc = 0 K Such reservoirs are not available Efficiency is always less than 100%
The efficiency increases as Tc is lowered and as Th is raised
In most practical cases, Tc is near room temperature, 300 K So generally Th is raised to increase efficiency
Real Engine vs. Carnot Engine All real engines are less efficient than
the Carnot engine because they all operate irreversibly so as to complete a cycle in a brief time interval
In addition, real engines are subject to practical difficulties that decrease efficiency Friction is an example
Heat Pumps and Refrigerators Heat engines can run in reverse
This is not a natural direction of energy transfer Must put some energy into a device to do this Devices that do this are called heat pumps or
refrigerators Examples
A refrigerator is a common type of heat pump An air conditioner is another example of a heat
pump
Heat Pump Process Energy is extracted
from the cold reservoir, QC
Energy is transferred to the hot reservoir, Qh
Work must be done on the engine, W
Coefficient of Performance The effectiveness of a heat pump is
described by a number called the coefficient of performance (COP)
In heating mode, the COP is the ratio of the heat transferred in to the work required
hheat pump
Qenergy transferred to hot resCOP
work done on pump W
COP, Heating Mode COP is similar to efficiency Qh is typically higher than W
Values of COP are generally greater than 1 It is possible for them to be less than 1
We would like the COP to be as high as possible
COP, Carnot in Heating Mode A Carnot cycle heat engine operating in
reverse constitutes an ideal heat pump It will have the highest possible COP for
the temperatures between which it operates
,h
Carnot heat pumph c
TCOP
T T
COP, Cooling Mode In cooling mode, you “gain” energy
from a cold temperature reservoir
A good refrigerator should have a high COP Typical values are 5 or 6
crefrigerator
QCOP
W
COP, Carnot in Cooling Mode The highest possible COP is again the Carnot
engine running in reverse
As the difference in temperature approaches zero, the theoretical COP approaches infinity In practice, COP’s are limited to values below 10
,c c
Carnot refrigeratorh c h c
Q TCOP
Q Q T T
Second Law – Clausius Form Energy does not flow spontaneously by
heat from a cold object to a hot object The Second Law can be stated in multiple
ways, all can be shown to be equivalent The form you should use depends on the
application
Perfect Heat Pump Takes energy from
the cold reservoir Expels an equal
amount of energy to the hot reservoir
No work is done This is an
impossible heat pump
The Second Law of Thermodynamics, Summary Establishes which processes do and which do
not occur Some processes can occur in either direction
according to the First Law They are observed to occur only in one
direction Real processes proceed in a preferred
direction This directionality is governed by the Second
Law
Entropy Entropy, S, is a state variable related to
the Second Law of Thermodynamics The importance of entropy grew with the
development of statistical mechanics A main result is isolated systems tend
toward disorder and entropy is a natural measure of this disorder
Microstates vs. Macrostates A microstate is a particular
configuration of the individual constituents of the system
A macrostate is a description of the conditions from a macroscopic point of view It makes use of macroscopic variables
such as pressure, density, and temperature for gases
Microstates vs. Macrostates, cont For a given macrostate, a number of
microstates are possible The number of microstates associated
with a given macrostate is not the same for all macrostates
When all possible macrostates are examined, it is found that the most probable macrostate is that with the largest number of possible microstates
Microstates vs. Macrostates, Probabilities High-probability macrostates are disordered
macrostates Low-probability macrostates are ordered
macrostates All physical processes tend toward more
probable macrostates for the system and its surroundings The more probable macrostate is always one of
higher disorder
Entropy Entropy is a measure of disorder of a state Entropy can be defined using macroscopic
concepts of heat and temperature
Entropy can also be defined in terms of the number of microstates, W, in a macrostate whose entropy is S
S = kB ln W
reversibledQdS
T
Entropy and the Second Law The entropy of the Universe increases
in all real processes This is another statement of the Second
Law of Thermodynamics The change in entropy in an arbitrary
reversible process isf f
r
i i
dQS dS
T
S For A Reversible Cycle S = 0 for any reversible cycle In general,
This integral symbol indicates the integral is over a closed path
0T
dQr
Entropy Changes in Irreversible Processes To calculate the change in entropy in a
real system, remember that entropy depends only on the state of the system
Do not use Q, the actual energy transfer in the process Distinguish this from Qr, the amount of
energy that would have been transferred by heat along a reversible path
Qr is the correct value to use for S
In general, the total entropy and therefore the total disorder always increase in an irreversible process
The total entropy of an isolated system undergoes a change that cannot decrease This is another statement of the Second
Law of Thermodynamics
Entropy Changes in Irreversible Processes, cont
Entropy Changes in Irreversible Processes, final If the process is irreversible, then the
total entropy of an isolated system always increases In a reversible process, the total entropy of
an isolated system remains constant The change in entropy of the Universe
must be greater than zero for an irreversible process and equal to zero for a reversible process
Heat Death of the Universe Ultimately, the entropy of the Universe should
reach a maximum value At this value, the Universe will be in a state of
uniform temperature and density All physical, chemical, and biological
processes will cease The state of perfect disorder implies that no
energy is available for doing work This state is called the heat death of the Universe
S in Free Expansion Consider an adiabatic free expansion The process is neither reversible or
quasi-static W = 0 and Q = 0 Need to find Qr, choose an isothermal
process1f f
rri i
dQS dQ
T T
S in Free Expansion, cont For an isothermal process, this becomes
Since Vf > Vi, S is positive This indicates that both the entropy and the
disorder of the gas increase as a result of the irreversible adiabatic expansion
ln f
i
VS nR
V
Atmosphere as a Heat Engine The Earth’s atmosphere can be
modeled as a heat engine The energy from the Sun undergoes
various processes Reflected Absorbed by the air or the surface
Energy Balance in the Atmosphere
Work Done on the Atmosphere One process is missing from the
previous energy balance The various processes result in a small
amount of work done on the atmosphere This work appears as the kinetic energy of
the prevailing winds in the atmosphere
Schematic, Atmosphere as a Heat Engine The amount of
incoming solar energy converted to kinetic energy of the winds is about 0.5%
It is temporarily kinetic energy, eventually radiated into space As radiation
Efficiency of the Atmospheric Heat Engine The warm reservoir is the surface The cold reservoir is empty space The efficiency can be calculated:
0.5%0.8%
64%eng
h
We
Q