Reversible Processes

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Reversible Processes

• The second law of thermodynamics state that no
  heat engine can have an efficiency of 100.
• Then one may ask, what is the highest efficiency
  that a heat engine can possibly have.
• Before we answer this question, we need to define
  an idealized process first, which is called the
  reversible process.
• The processes discussed earlier occurred in a
  certain direction. They can not reverse
  themselves irreversible processes.

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Reversible Processes

• A reversible process is defined as a process that
  can be reversed without leaving any trace on
  either system or surroundings.
• This is possible if the net of heat and net work
  exchange between the system and the surrounding
  is zero for the combined process (original and
  reverse).

Quasi-equilibrium expansion or compression of a
gas
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• Reversible processes actually do not occur in
  nature.
• They are simply idealization of actual processes.
• Reversible processes can never be achieved.
• You may be wondering, then, why we are bothering
  with such fictitious processes
• Easy to analyze
• Serve as idealized model

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• Engineers are interested in reversible processes
  because
• when Reversible processes are approximated
  instead of the Actual ones
• Work-producing devices such as car engine and gas
  or steam turbine deliver the most work, and
• Work-consuming devices such as compressors, fan,
  and pumps consume the least work.

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• Reversible processes can be viewed as theoretical
  limits for the corresponding not reversible ones.
  
• We may never be able to have a reversible
  process, but we may certainly approach it.
• The more closely we approximate a reversible
  process, the more work delivered by a
  work-producing device or the less work required
  by a work-consuming device.
• Processes that are not reversible are called
  Irreversible processes.

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• Reversible processes
• Ideal processes

• Irreversible processes
• Actual processes

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Irreversible Process

• If the process leaves any trace on either system
  or surroundings, then it is an irreversible.
• The factors that cause a process to be
  irreversible are called irreversibilities. They
  include

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1- Friction

• Work is done to raise the block and overcome
  friction.
• Block is getting hotter due to friction.
• In the reverse process, the block is getting even
  hotter due to friction.
• Heat should be rejected to the surrounding to
  bring it back to its initial position.
• Hence, irreversible process.

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2- Unrestrained expansion

• Unrestrained expansion means W0
• To bring the gas back to its initial pressure and
  Temperature, work must be supplied by
  surrounding.
• Hence irreversible process.

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3- Mixing of two gases,

• Work should be supplied from the surrounding to
  separate the two gases.
• Hence, irreversible process.

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4- Heat transfer through a finite temperature
difference

1. A system at a high temperature body and a low
   temperature body, let heat be transferred from TH
   to TL .
2. The only way to bring the system back to TL is to
   cool it by refrigerator.
3. The refrigerator requires work from the
   surrounding Winput.
4. The net effect is extra heat rejected to the
   surrounding equal in magnitude to the work.
5. Hence it is an irreversible process.

High Temperature
Q
Q
Low Temperature
Ref
W
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1. Since the surrounding is permanently affected,
   heat transfer through a finite temperature
   difference is an irreversible process.
2. The smaller the temp difference the smaller the
   irreversibility.
3. As ?T approaches zero, the process can be
   reversed in direction (at least theoretically)
   without requiring any refrigeration.
4. This is a conceptual process and can not be done
   in real world.

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Internally and Externally Reversible Process

• A process is called internally reversible if no
  irreversibility occur within the boundaries of
  the system during the process.
• A process is called externally reversible if no
  irreversibility occur outside the system
  boundaries during the process.
• A process is called totally reversible or simply
  reversible if it involves no irreversibility
  within the system or its surroundings during the
  process.

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Heat transfer process and finite temperature
difference process

• For a Heat transfer process to be revisable
  process it has to be an Isothermal process.
• For a finite temperature difference process to be
  revisable process it has to be an adiabatic
  process.

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• Cycles that are composed of reversible processes
  will give the maximum net work and consumes the
  minimum work.
• One of these cycles is the
• Carnot Cycle.
• Named for French engineer Nicolas Sadi Carnot
  (1769-1832)
• It is composed of four processes as follows

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Process 1-2 A reversible isothermal expansion

• The gas is allowed to expand isothermally by
  receiving heat ( QH) from a hot reservoir.

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Process 2-3 A reversible adiabatic expansion

• The cylinder now is insulated and the gas is
  allowed to expand adiabatically and thus doing
  work on the surrounding.
• The gas temperature decreases from TH to TL.

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Process 3-4 A reversible isothermal compression
The insulation is removed and the gas is
compressed isothermally by rejecting heat (QL) to
a cold reservoir.
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Process 4-1 A reversible adiabatic compression

• The cylinder is insulated again and the gas is
  compressed adiabatically to state 1, raising its
  temperature from TL to TH

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Net work done by Carnot cycle is the area
enclosed by all process
The Carnot cycle is the most efficient cycle
operation between two specified temperatures
limits.
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Carnot cycle can be executed in many different
ways
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Reversed Carnot Cycle
Process 1-2 The gas expands adiabatically
(throttling valve) reducing its temp from TH to
TL.
Process 2-3 The gas expands isothermally at TL
while receiving QL from the cold reservoir.
Process 3-4 The gas is compressed adiabatically
raising its temperature to TH.
Process 4-1 The gas is compressed isothermally
by rejecting QH to the hot reservoir.
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Reversed Carnot Cycle
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Carnot principles

1. No heat engine is more efficient than a
   reversible one operating between the same two
   reservoirs.
2. The thermal efficiencies of all reversible heat
   engines operating between the same two reservoirs
   are the same.

Low temperature reservoir at TL
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The Thermodynamic Temperature Scale
The second Carnot principle state that the
thermal efficiencies of all reversible heat
engines operating between the same two reservoirs
are the same.
hth, rev f (TH,TL)
A temperature scale that is independent of the
properties of the substances that are used to
measure temperature is called a thermodynamic
temperature scale. That is the Kelvin scale, and
the temperatures on this scale are called
absolute temperatures.
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Efficiency of a Carnot Engine

• For a reversible cycle the amount of heat
  transferred is proportional to the temperature of
  the reservoir.

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COP of a Reversible Heat Pump and a Reversible
Refrigerator
Only true for the reversible case
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How do Reversible Carnot Heat Engine compare with
real engines?
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How do Carnot Refrigerator compare with real
Refrigerator?
COP of Carnot Refrigerator
COP of Refrigerator
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How do Carnot Heat Pump compare with real one?
COP of Carnot Heat Pump
COP of real Heat Pump
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How to increase the efficiency of a real heat
engine?
1- Increase TH but you are limited with melting
temperature of the engine material.
2- Decrease TL but you are limited with your
environment.
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Example (5-8) Heating a House by a Carnot Heat
Pump
A heat pump is to be used to heat a house during
the winter, as shown in the figure at right. The
house is to be maintained at 21oC at all times.
The house is estimated to be losing heat at a
rate of 135,000 kJ/h when the outside temperature
drops to -5oC. Determine the minimum power
required to drive this heat pump. Sol
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Example (1)
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Example (2)
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Example (3)
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Example (4)