Physics 110 Lecture 40 from Chapter 12 Sections 3 and 4

1
Physics 110 Lecture 40 from Chapter 12
Sections 3 and 4

• Heat Engines
• and the
• 2nd Law of
• Thermodynamics

2
Homework Assignment 40

• Conceptual Question
• Chapter 12, CQ 2 on page 417
• Chapter 12, CQ 15 on page 418
• Problems
• Chapter 12, Problem 24 on page 420
• Chapter 12, Problem 29 on page 420

3
PV Diagrams

• Work done by a process is the area under the
  process line on the PV diagram.

Process to left Work on system Process to
right - Work on system
4
Cyclic Processes

• A cyclic process is one in which the process
  originates and ends at the same state
• The net work done per cycle by the gas is equal
  to the area enclosed by the path representing the
  process on a PV diagram

0
5
Heat Engine

• A heat engine is a machine or process that takes
  in energy by heat and partially converts it to
  work.
• In general, a heat engine carries some working
  substance through a cyclic process

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Heat Engine, cont.

• Three steps
• 1) Energy is transferred from a source at a high
  temperature (Qh)
• 2) Work is done by the engine (Weng)
• 3) Energy is expelled to a source at a lower
  temperature (Qc)

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Heat Engine, cont.

• Since it is a cyclical process, ?U 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

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Thermal Efficiency of a Heat Engine

• Thermal efficiency is defined as the ratio of the
  work done by the engine to the energy absorbed at
  the higher temperature
• eff 1 (100 efficiency) only if Qc 0
• No energy expelled to cold reservoir

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Heat Pumps and Refrigerators

• Heat engines can run in reverse
• Energy is injected
• Energy is extracted from the cold reservoir
• Energy is transferred to the hot reservoir
• This process means the heat engine is running as
  a heat pump
• A refrigerator is a common type of heat pump
• An air conditioner is another example of a heat
  pump

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Example

• A heat engine absorbs 20 kJ of energy from a heat
  source and is able to provide 12 kJ of work
  during a cycle that take 0.5 seconds to repeat.
• a) How much heat is lost as expelled heat?
• b) What is the efficiency of the machine?
• c) What is the power it is able to provide?

Qh20kJ
Weng 12kJ
QC?
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Example

• A heat engine absorbs 20 kJ of energy from a heat
  source and is able to provide 12 kJ of work
  during a cycle that take 0.5 seconds to repeat.
• a) How much heat is lost as expelled heat?

Qh20kJ
Weng 12kJ
QC?
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Example

• A heat engine absorbs 20 kJ of energy from a heat
  source and is able to provide 12 kJ of work
  during a cycle that take 0.5 seconds to repeat.
• b) What is the efficiency of the machine?

Qh20kJ
Weng 12kJ
QC8kJ
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Example

• A heat engine absorbs 20 kJ of energy from a heat
  source and is able to provide 12 kJ of work
  during a cycle that take 0.5 seconds to repeat.
• c) What is the power it is able to provide?

Qh20kJ
Weng 12kJ
QC8 kJ
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Carnot Cycle, PV Diagram

• Consider the cycle shown here.
• AB-- isothermal heat enters
• BC-- abiabatic expansion
• CD -- isothermal heat exits
• DA -- adiabatic compression
• The net work is equal to Qh - Qc
• This is the Carnot Cycle

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Carnot Engine

• A heat engine operating in an ideal, reversible
  cycle between two reservoirs is the most
  efficient engine possible
• Carnots Theorem No real engine operating
  between two energy reservoirs can be more
  efficient than a Carnot engine operating between
  the same two reservoirs

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Reversible and Irreversible Processes

• A reversible process is one in which every state
  along some path is an equilibrium state
• And one for which the system can be returned to
  its initial state along the same path
• An irreversible process does not meet these
  requirements
• Most natural processes are irreversible
• Reversible process are an idealization, but some
  real processes are good approximations

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Carnot Cycle
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Carnot Cycle, A to B

• A to B is an isothermal expansion at temperature
  Th
• The gas is placed in contact with the high
  temperature reservoir
• The gas absorbs heat Qh
• The gas does work WAB in raising the piston

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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

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Carnot Cycle, C to D

• The gas is placed in contact with the cold
  temperature reservoir at temperature Tc
• C to D is an isothermal compression
• The gas expels energy QC
• Work WCD is done on the gas

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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 WCD

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Carnot Cycle, PV Diagram

• Consider the cycle shown here.
• AB-- isothermal heat enters
• BC-- abiabatic expansion
• CD -- isothermal heat exits
• DA -- adiabatic compression
• The net work is equal to Qh - Qc
• This is the Carnot Cycle

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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

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Notes About Carnot Efficiency

• The Carnot cycle represents a frictionless engine
  at work. The processes are reversible.
• Efficiency is 0 if Th Tc
• Efficiency is 100 only if Tc 0 K
• Such reservoirs are not available
• The efficiency increases as Tc is lowered and as
  Th is raised
• Summary This is the best possible engine, and
  it will not be able to extract work from all the
  heat supplied to the system. No heat engine can
  be 100 efficient.

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2nd Law of Thermodynamics

• Several different formulations
• 1) No cyclic process is able to completely
  transform the heat flow into the system into
  useful work. Some of the energy associated with
  heat flow cannot be recovered as work.
• 2) All natural processes tend to move toward a
  state of greater disorder.
• 3) The total entropy of the Universe increases in
  all natural processes. ?S0.

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2nd Law of Thermodynamics

• In other words.
• 1) You can't ever extract more work than you put
  into a system, or even extract an equivalent
  amount of work equal to the heat flow into a
  system.
• 2) All process have a tendency to move toward
  uniform distribution.
• 3) Entropy usually increasesor at very best
  holds even

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Summary of the 1st and 2nd Laws

• First Law of Thermodynamics
• We cannot get a greater amount of energy out of a
  cyclic process than we put in
• Second Law of Thermodynamics
• We cant break even.

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Entropy

• A state variable related to the 2nd Law of
  Thermodynamics, is called entropy
• Let Qr be the energy absorbed or expelled during
  a reversible, constant temperature process
  between two equilibrium states. Then the change
  in entropy during any constant temperature
  process connecting the two equilibrium states can
  be defined as the ratio of the energy to the
  temperature

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Entropy, cont.

• When energy is absorbed, Q is positive and
  entropy increases.
• When energy is expelled, Q is negative and
  entropy decreases.however, there is a
  corresponding increase in the entropy of the
  environment at the same time.
• Irreversible processes cause greater increases of
  entropy than reversible ones.
• An isentropric process is a process where entropy
  remains constant. This can hold for an ideal,
  adiabatic, reversible process.

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Entropy and Disorder

• Entropy can be described in terms of disorder
• A disorderly arrangement is much more probable
  than an orderly one if the laws of nature are
  allowed to act without interference
• This comes from a statistical mechanics
  development

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Disorder to Entropy Concept
Assume you have a box of red and blue marbles.
All the red marbles are on the left side of an
internal partition. All the blue marbles are on
the right side of the partition. The marbles are
all very ordered.
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Disorder to Entropy Concept
Next you remove the partition and shake up the
box.
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Disorder to Entropy Concept
The marbles then to become more uniformly
distributed about the box...this reduction of
order is a measure can be described as an
increase of entropy.
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Disorder to Entropy Concept
How likely would it be to shake a box with
uniform distribution and have it go back to two
entirely seaparte sets of marbles?