The Carnot Cycle Part 1

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The Carnot Cycle - Part 1

• Physics 313
• Professor Lee Carkner
• Lecture 16

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Reversibility

• Consider a system where processes do work or
  exchange heat
• If the same amount heat and work are done with
  the reverse sign and no other changes in any
  other system takes place the process is
  reversible
• A reversible process must not change any other
  system
• No real process is reversible

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Mechanical Reversibility

• Most processes that convert work into heat are
  irreversible
• In order to reverse them you would have to
  completely convert heat into work
• Violates Kelvin-Planck statement
• Virtually every process converts some work into
  heat

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Isothermal Work

• Work done in contact with a reservoir
• Heat is produced but no temperature change
• To reverse must convert heat completely into work
• Example
• Friction, stirring, compression of a system in a
  large body of water

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Adiabatic Work

• Work done on insulated systems
• Heat and temperature changes are produced
• To reverse, must restore temperature by removing
  heat and converting to work
• Example
• Friction, stirring or compression of insulated
  systems

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Dissipation

• Converting work into internal energy is known as
  dissipation
• Dissipative effects produce external mechanical
  irreversibility
• Can reduce but can never eliminate dissipative
  effects
• Any real machine involves dissipation and is thus
  irreversible

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Thermal Irreversibility

• Heat flowing from hotter to cooler systems
• Changes internal energy
• Need to have heat flow from cool to hot
• violates Clausius statement
• Example
• melting ice
• can re-freeze, but that requires work

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Perpetual Motion Machines
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Perpetual Motion

• Three kinds of perpetual motion
• 1st kind
• Machine that creates energy
• violates 1st law
• 2nd kind
• Machine that converts heat completely into work
• violates 2nd law
• 3rd kind
• Machine with no dissipation
• violates 2nd law

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Ideal and Real Systems

• Real systems are not reversible
• not quasi-static
• dissipative
• Can approximate an ideal system with a heat
  reservoir
• Can also approach reversibility by reducing
  dissipation

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Carnot Cycle

• A Carnot engine is a device that operates between
  two reservoirs (at high and low T) with adiabatic
  and isothermal processes
• An adiabatic rise from TL to TH
• An isothermal addition of heat QH
• An adiabatic fall from TH to TL
• An isothermal subtraction of heat QL
• Engine Applet

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Carnot Info

• Carnot cycles can operate with many different
  systems
• gas, liquid-vapor, paramagnetism, battery
• Operates with only 2 reservoirs (only two
  temperatures)
• Cycle is reversible
• All other cycles involve heat transfers across
  temperature changes and thus are irreversible

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Carnot Refrigerator

• If you reverse a Carnot engine, you get a Carnot
  refrigerator
• Isothermal absorption of heat QL
• Adiabatic rise from TL to TH
• Isothermal subtraction of heat QH
• Adiabatic fall from TH to TL
• If the two reservoirs are the same, the heats and
  work are the same from a Carnot refrigerator and
  engine

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Carnots Theorem

• The Carnot cycle is the most efficient cycle
  operating between two reservoirs
• Reversible processes are the most efficient
• The Carnot efficiency is the maximum efficiency
  and engine can have
• Carnot efficiency is an upper limit for any engine

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Corollary

• All Carnot engines operating between the same two
  reservoirs have the same efficiency
• Efficiency only depends on the temperatures of
  the reservoirs
• Maximum efficiency of any engine depends only on
  the temperatures of the reservoirs

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Comparison with Other Engines

• In other engines heat exchange occurs at several
  temperatures
• For Carnot heat exchange occurs at max and min
  temperatures of system
• This makes heat transfer and thus work easier
• Can never achieve true reversibility due to
  dissipation
• Carnot efficiency is upper limit