Chapter 20 Second Law of Thermodynamics

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Physics is fun!
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Chapter 20Second Law of Thermodynamics
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Introduction

• Second law of thermodynamics
• Entropy (S)
• Heat engines

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20-1 The Second Law of Thermodynamics --
Introduction

• The first law of thermodynamics states that
  energy is conserved.
• Scientists in the 19th century noticed that many
  processes that did not violate the law of
  conservation of energy, never-the-less did not
  occur naturally.
• They formulated the second law of thermodynamics.
• Statement of the second law of thermodynamics by
  R.J.E. Clausius (1822 1888)
• Heat flows naturally from a hot object to a cold
  object heat will not flow spontaneously from a
  cold object to a hot object.

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20-2 Heat Engines

• Circa 1700, the steam engine, the first practical
  device to get work from thermal energy was
  developed.
• The basic idea behind any engine is that
  mechanical energy can be obtained from thermal
  energy only when heat is allowed to flow from a
  high temperature to a low temperature.
• In that process, heat can be transformed to
  mechanical work.

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Heat Engines

• By conservation of energy
• QH W QL.
• The high and low temperatures TH and TL are
  called the operating temperatures of the engine.
• We will considering only engines that run in a
  repeating cycle, that is, the system returns
  repeatedly to its starting point, and thus can
  run continuously.
• Absolute value signs are used because we are
  worried only about the magnitudes.

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Steam Engine
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Internal Combustion Engine

• The material that is heated and cooled, steam in
  the case of a steam engine, is called the working
  substance.
• In the steam engine, the high temperature is
  obtained by burning one of the four fuels
  mentioned.
• In an internal combustion engine, the high
  temperature is achieved by burning the
  gasoline-air mixture in the cylinder itself
  (ignited by the spark plug).

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Efficiency

• The efficiency of any heat engine, e, can be
  defined as the ratio of the work it does, W, to
  the heat input at the high temperature, QH
• e
• Using conservation of energy this works out to
• e 1 -

W QH
QL QH
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Example 20-1

• Car efficiency.
• An automobile engine has an efficiency of 20
  percent and produces an average of 23,000 J of
  mechanical work per second during operation. How
  much heat is discharged from this engine per
  second?

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Efficiency

• The lower we can make QL the more efficient the
  engine will be.
• If QL could be reduced to zero we would have a
  100 percent efficient engine.
• Experience has shown however, that it impossible
  to reduce QL to zero.
• That such a perfect engine, running continuously
  in a cycle (a perpetual motion machine) is not
  possible is another way of expressing the second
  law of thermodynamics.
• No device is possible whose sole effect is to
  transform a given amount of heat completely into
  work.
• This is the Kelvin-Planck statement of the second
  law of thermodynamics

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20-3 Reversible and Irreversible Process the
Carnot Engine

• In the early nineteenth century, the French
  scientist N.L. Sadi Carnot (1796 1832) studied
  in detail the process of transforming heat into
  mechanical energy.
• Goal to increase inefficiency.
• In 1824 Carnot invented, on paper, the Carnot
  engine. This is the ideal engine.

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Reversible and Irreversible Processes

• The Carnot engine involves reversible processes.
• A reversible process is one carried out
  infinitely slowly, so that the process can be
  considered as a series of equilibrium states, and
  the whole process could be done in reverse with
  no change in magnitude of the work done or heat
  exchanged.
• Of course this cannot be done since it would take
  an infinite time.
• All real processes are irreversible they cannot
  be done infinitely slowly, there can be
  turbulence in the gas, friction will be present,
  and so on.

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Carnot's Engine

• The Carnot engine makes use of a reversible
  cycle.
• This cycle is called the Carnot cycle and the
  working substance is an ideal gas.

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Carnot Cycle
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Carnot Efficiency and the Second Law of
Thermodynamics

• eideal 1 -
  1 -
• Carnots Theorem
• All reversible engines operating between the
  same two constant temperatures TH and TL have the
  same efficiency. Any irreversible engine
  operating between the same two temperatures will
  have an efficiency less than this.

TL TH
QL QH
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Example 20-2

• Steam engine efficiency.
• A steam engine operates between 500oC and 270oC.
  What is the maximum possible efficiency of this
  engine?

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Example 20-3

• A phony claim?
• An engine manufacturer makes the following
  claims The heat input per second of the engine
  is 9.0 kJ at 475 K. The heat output per second
  is 4.0 kJ at 325 K. Do you believe these claims?

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20-4 Refrigerators, Air Conditioners, and Heat
Pumps

• The operating principle of refrigerators, air
  conditioners, and heat pumps is just the reverse
  of the heat engine.
• By doing work W, heat is taken from a
  low-temperature region, TL (inside the
  refrigerator), and a greater amount of heat is
  exhausted at a high temperature, TH (into the
  room).
• The work is usually done by a compressor motor
  that compresses a fluid.
• A perfect refrigeratorone where no work is
  required to take heat from the low-temperature
  region to the high-temperature regionis not
  possible.

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Clausius

• Restatement of Clausius statement of the second
  law of thermodynamics
• No device is possible whose sole effect is to
  transfer heat from one system at one temperature
  into a second system at a higher temperature.

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Coefficient of Performance (CP)

• The coefficient of performance for a
  refrigerator is defined as the heat QL removed
  from the low-temperature area (inside a
  refrigerator) divided by the work W done to
  remove the heat.
• CP

QL W
Refrigerator and air conditioner
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CP Ideal

• Energy is conserved, so we can write
• QH QL W
• Therefore W QH - QL
• and CP
• so CPideal

QL
QL W
QH - QL
TL
TH - TL
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Coefficient of Performance (CP)

• The coefficient of performance for a heat pump
  acting as a heater can heat a house in the winter
  by taking heat QL from the outside at low
  temperature and delivering heat QH to the
  warmer inside of the house, by doing work W.
  Thus for a heat pump
• CP heat pump
• Most heat pumps can run in reverse and perform as
  an air conditioner.

QH W
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Example 20-5

• Heat pump.
• A heat pump has a coefficient of performance of
  3.0 and is rated to do work at 1500 W. (a) How
  much heat can it ass to a room per second? (b)
  If the heat pump were turned around to act as an
  air conditioner in the summer, what would you
  expect its coefficient of performance to be
  assuming all else stays the same?

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20-5 Entropy

• When you open a bottle of perfume you can smell
  the aroma as the molecules leave the bottle and
  reach your nose.
• Why dont they spontaneously go back into the
  bottle?
• It would not violate the first law of
  thermodynamics.
• There answer it they can do just that, but they
  most probably will not.
• The explanation is entropy.

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Definitions

• Entropy is
• a measure of the disorder of a system.
• a measure of the energy in a system or process
  that is unavailable to do work. In a reversible
  thermodynamic process, entropy is expressed as
  the heat absorbed or emitted divided by the
  absolute temperature.
• dS dQ/T

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Entropy

• The general statement of the quantity, S, entropy
  was introduced by Clausius in the 1860s.
• DS Sb Sa dS
• DS is independent of the path between the two
  points a and b. This tells us that the
  difference in entropy between two equilibrium
  systems does not depend on how you get from one
  state tot the other. Thus, entropy is a state
  variable.

b
b
dQ T
reversible processes
a
a
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20-6 Entropy and the Second Law of Thermodynamics

• Entropy, S, can be used to define the state of a
  system, along with P, T, V, U, and n.
• We can calculate entropy only for reversible
  processes.
• To calculate entropy for an irreversible process
  find a reversible process that takes the system
  between the same two states and calculate the
  entropy.
• It will be the same as for the irreversible
  process because it depends only on the two states.

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Example 20-6

• Entropy change in melting.
• A 1.00-kg piece of ice melts very slowly to
  water at 0oC. Assume the ice is in contact with
  a heat reservoir whose temperature is only
  infinitesimally greater than 0oC. Determine the
  entropy change of (a) the ice cube, (b) the heat
  reservoir.

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Example 20-7

• Entropy change when mixing water.
• A sample of 50.0 kg of water at 20oC is mixed
  with 50.0 kg of water at 24oC. Estimate the
  change in entropy without using calculus.

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Example 20-8

• Entropy changes in a free expansion.
• Consider the adiabatic free expansion of n moles
  of an ideal gas from volume V1 to volume V2,
  where V2 gt V1, as was discussed in Section 19-7,
  Fig. 19-13. Calculate the change in entropy (a)
  of the gas (b) of the surrounding environment.
  (c) Evaluate DS for 1.00 mole, with V2 V1.

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Example 20-9

• Heat conduction.
• A red-hot 2.0-kg piece of iron at temperature T1
  880 K is thrown into a huge lake whose
  temperature T2 280 K. Assume the lake is so
  large that its temperature rise is insignificant.
  Determine the change in entropy (a) of the iron,
  (b) of the surrounding environment (the lake).

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Total Entropy

• For any reversible process
• DS DSsyst DSenv 0
• For irreversible processes
• DS DSsyst DSenv gt 0
• The second law the entropy of an isolated
  system never decreases. It either stays constant
  (reversible process) or increases (irreversible
  process).
• Although the entropy in one part of the universe
  may decrease in any process, the entropy of some
  other part of the universe always increases by a
  greater amount, so the total entropy always
  increases.

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20-7 Order to Disorder

• The entropy of a system can be considered a
  measure of the disorder of the system.
• Then the second law of thermodynamics can be
  stated as
• Natural processes tend to move toward a state of
  greater disorder.

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The Second Law

• The second law of thermodynamics can be stated
  in several equivalent ways
• Heat flows spontaneously from a hot object to a
  cold one, but not the reverse.
• There cannot be a 100 percent efficient heat
  enginethat is, one that can change a given
  amount of heat completely into work.
• Natural processes tend to move toward a state of
  greater disorder or greater entropy.

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20-8 Energy Availability Heat Death

• In any natural process, some energy becomes
  unavailable to do useful work.
• As time goes on, energy is degraded, in a sense
  it goes from more orderly forms (such as
  mechanical) eventually to the least orderly form,
  internal or thermal energy.
• The amount of energy that becomes unavailable to
  do work is proportional to the change in entropy
  during any process.
• A natural consequence of this is that over time,
  the universe will approach a state of maximum
  disorder.
• Heat Death!

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20-9 Statistical Interpretation of Entropy and
the Second Law

• By Ludwig Boltzmann (1844 1906)
• The microstate of a system would be specified
  when the position and velocity of every particle
  (or molecule) is the system is specified.
• The macrostate of a system is specified by giving
  the macrostate properties of the system by using
  state variables, P, T, S, etc.
• A great many microstates can correspond to the
  same macrostate.

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Macrostates and Microstates

• Take four coins and toss them, calling the
  number of heads and tales that show on each toss.

Macrostates Possible
Microstates Number of Microstates 4 heads
HHHH
1 3 heads,
1 tale HHHT, HHTH, HTHH, THHH
4 2 heads, 2 tales HHTT,
HTHT, THHT, HTTH, THTH, TTHH 6 1 head, 3
tales TTTH, TTHT, THTT, HTTT
4 4 tales
TTTT
1
16 possible microstates
5 possible macrostates
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Macrostates and Microstates

• Each microstate is equally probable.
• Thus, the number of microstates that give the
  same macrostate corresponds to the relative
  probability of that state occurring.
• The macrostate of two heads and two tales is the
  most problem one in this example.
• Out of a total of 16 possible microstates, six
  correspond to tossing two heads and two tales, so
  the probably of throwing two heads and two tales
  is 6 out of 16, or 38.

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Macrostates and Microstates

• There are a total of 1030 microstates and 100
  macrostates possible. For 99 heads and 1 tale
  there are 100 microstates possible since each
  coin could come up tales once. But any
  macrostate of 99 heads and 1 tale is equivalent.
• The probability of all heads is 1 in 1030. NOT a
  good bet!
• The probability of 50 heads and 50 tales is 1.0 x
  1029/ 1030 0.10 or 10.
• Therefore as the number of coins increases we see
  the probability or obtaining an orderly
  arrangement of say, 100 heads becomes extremely
  unlikely.

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Macrostates and Microstates

• That was for 100 coins. Can you imagine the
  numbers when you have 1030 air molecules in a
  room.
• The most probable arrangement is the air
  molecules is to take up the whole space and move
  randomly. This is described by the Maxwellian
  distribution.
• On the other hand a very orderly arrangement of
  all the air molecules concentrated in one corner
  of the room and all moving with the same velocity
  is extremely unlikely.
• This is why perfume molecules to not go back into
  the bottle. They are allowed to by the first law
  of thermodynamics, but the second law tells us
  that the probability that they will do so is
  essentially zero.

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Entropy
macroscopic
microscopic

• S k ln W

W is the number of microstates corresponding to
the macrostate whose entropy is S. That is, it
is proportional to the probably of occurrence of
that state. W is called the thermodynamic
probability.
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Problem Solving Thermodynamics

• Define the system you are dealing with be
  careful to distinguish the system under study
  from its surroundings.
• Be careful of the signs associated with work and
  heat. In the first law
• work, done by the system is positive work done
  on the system is negative.
• Heat added to the system is positive heat
  removed from the system is negative.
• With heat engines, we usually consider heat and
  work as positive and write the conservation
  equations with and signs taking into account
  directions.

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Problem Solving Thermodynamics

• Watch the units for work and heat work is most
  often expressed in joules, and heat in calories
  or kilocalories. Be consistent choose only one
  unit for use throughout a given problem.
• Temperatures must generally be expressed in
  kelvins temperature differences may be expressed
  in Co or K.
• Efficiency (or coefficient of performance) is a
  ratio of two energy transfers useful output
  divided by required input. Efficiency (but not
  coefficient of performance) is always less than 1
  in value and hence is stated as a percentage.

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Problem Solving Thermodynamics

• The entropy of a system increases when heat is
  added to the system, and decreases when heat is
  removed. Because entropy is a state variable,
  the range of change in entropy DS for an
  irreversible process can be determined by
  calculating DS for a reversible process between
  the same two states.

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Homework Problem 4

• A four-cylinder gasoline engine has an
  efficiency of 0.25 and delivers 180 J of work per
  cycle per cylinder. The engine fires at 25
  cycles per second. (a) Determine the work done
  per second. (b) What is the total heat input per
  second from the gasoline? (c) If the energy
  content of the gasoline is 130 MJ per gallon, how
  long does one gallon last?

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Homework Problem 13

• A nuclear power plant operates at 75 percent of
  its maximum theoretical (Carnot) efficiency
  between temperatures of 660oC and 360oC. If the
  plant produces electric energy at the rate of 1.1
  GW, how much exhaust heat is discharged per hour?

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Homework Problem 27

• An ideal engine has an efficiency of 35 percent.
  If it were run backward as a heat pump, what
  would be its coefficient of performance?

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Homework Problem 36

• If 1.00 kg of water at 100oC is changed by a
  reversible process to steam at 100oC, determine
  the change in entropy of (a) the water, (b) the
  surroundings, and (c) the universe as a whole.
  (d) How would your answers differ if the process
  were irreversible?

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Richard P. Feynman(1918-1988)Richard Chace
Tolman Professor of Theoretical
PhysicsCalifornia Institute of Technology
Finally may I add that the main purpose of
my teaching has not been to prepare you for some
examination. I wanted most to give you some
appreciation of the wonderful world and the
physicists way of looking at it, which, I
believe, is a major part of the true culture of
modern times. (There are probably professors of
other subjects who would object, but I believe
that they are completely wrong.) Perhaps you
will not only have some appreciation of this
culture it is even possible that you may want to
join in the greatest adventure that the human
mind has ever begun.
From The Feynman Lectures in Physics, 1963
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Physics is fun!