Analysis of Second Law

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Analysis of Second Law Reversible Cyclic
Machines

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Methods to Recognize Practicable Good
Innovations..
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Kelvin Planks postulate
Statements of Second Law of Thermodynamics

• It is impossible to construct a heat engine
  which produces no effect other than the
  extraction of heat from a single source and the
  production of an equivalent amount of work

Clausius postulate
The Clausius statement It is impossible to
construct a heat pump produces no effect other
than the transfer of heat from a cooler body to a
hotter body.
http//www.humanthermodynamics.com/2nd-Law-Variati
ons.html
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Discussion of Statements of Second Law

• Both are negative statements.
• They cannot be proved.
• They will remain correct till they are
  disproved.
• Violation of Kelvin Planks statement leads to
  violation of Clasius statement and vice versa.
• Can a heat engine be reversed to work as heat
  pump or refrigerator?
• If yes, what will be the COP of this reversed
  engine?
• Can a reversed heat pump perform same as forward
  engine between same reservoirs?

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Reversible Heat Pump
First law WLP QLP - QHP
First law WRHP QRHP - QRHP
?rev QHP/WHP
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Definition of Reversible Heat Pump
A Reversed heat pump works as a Heat Engine.
If A Heat Pump Reversed heat pump are working
between same reservoirs,
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Consequences of Second Law

• The performance of a reversed heat pumps is same
  as a heat engine.
• The performance of reversed heat engine is same
  as a heat pump.
• Heat engine and Reversed heat pump follow
  Kelvin-Plank statement.
• Heat pump and Reversed heat engine follow
  Clausius statement.
• All reversible heat engines working between same
  reservoirs should equally perform.
• It is impossible to construct a reversible heat
  engine better than another reversible machine
  working between same reservoirs.
• All reversible heat pumps working between same
  reservoirs should equally perform.
• It is impossible to construct a reversible Heat
  pump better than another reversible machine
  working between same reservoirs.

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A Compound Reversible Machine
Both Reversible Pump and Engine having same
performance
HTR (Sink)
QHE QHP
QHP
QHE
?rev 1/?rev
Wnet
Perpetual Motion Machine III
?
E
QLP
QLE
QLE QLP
LTR (Source)
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Liberal Market Innovation

• All innovations will perform equally, if each
  innovation is a reversible heat engine.
• All innovations will perform equally, if each
  innovation is a reversible heat pump.
• Innovation of reversible machines will lead to
  innovation of PMM III.
• There is no scope for further innovation after
  first innovation.
• No need to have many ideas for a given need
• What is this PMM-III?

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Models for Reversible Machines
A Blue Print for Construction of Reversible
Machine!!!!
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Famous Models for Reversible Machines

• The Stirling Cycle Reverend Robert Stirling
  patented a hot air engine in 1816 called The
  Economiser.
• The Carnot Cycle 1824 Réflexions sur la
  puissance motrice du feu et sur les machines
  propres à développer cette puissance which
  includes his description of the "Carnot cycle".
• The Regenerative Cycle

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The Reversible Cycles Carnot Cycle

• The first model (1824) for reversible machine is
  the Carnot cycle.
• This consists of two reversible isothermal
  processes and two reversible adiabatic processes.
• Hence Carnot Cycle is a Reversible Cycle.
• This mode can be used to construct either a heat
  engine or a heat pump.

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pv Diagram Gaseous (Single Phase) substance
executing a Carnot Cycle

• 1 2 Reversible Isothermal heat addition
• 2 3 Reversible Adiabatic Expansion
• 3 4 Reversible Isothermal Heat Rejection.
• 4 1 Reversible Adiabatic Compression.

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Carnot Gas Engine Crank-Slider Mechanism
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Carnot Engine using Phase Change Substance
Boiler
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Turbine
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Condenser
LTR
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pv Diagram
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1 2 Boiler Isothermal Heating T2 T1
QCV
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2

• No work transfer, change in kinetic and potential
  energies are negligible

Assuming a single fluid entering and leaving
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2-3 Turbine Reversible Adiabatic Process
No heat transfer. Change in kinetic and potential
energies are negligible
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3 4 Condenser Isothermal Cooling T3 T4
QCV
4
1
No work transfer, change in kinetic and potential
energies are negligible
Assuming a single fluid entering and leaving
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Compressor Reversible Adiabatic Compression
Process
4
1
SSSF Conservation of mass
First Law
No heat transfer, change in kinetic and potential
energies are negligible
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Analysis of Cycle

• A Cycles is a Control Mass Constant Mass Flow
  Rate
• First law
• Sqi Swi
• qbqc wtwc
• wnet qnet h2-h1 (h4-h1) Thigh (y2-y1)
  Tlow(y4-y1)
• Thigh (y2-y1) Thigh Dyboiler Tlow (y4-y1)
  Tlow Dycondenser
• wnet qnet h2-h1 (h4-h1) Thigh Dyboiler
  Tlow Dycondenser
• qboiler Thigh(y2-y1) Thigh Dyboiler

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• Efficiency of the cycle net work/heat input

• Dy is a change in a variable of a working
  fluid.
• Different working fluid will have different
  values of Dy at same Temperatures.
• However, the efficiencies of all reversible
  cycles operating between same reservoirs should
  have same efficiency!!
• The magnitude of Dy should be same at hot and
  cold reservoir conditions.

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Higher the temperature of heat addition, higher
will be the efficiency. Lower the temperature of
heat rejection, higher will be the
efficiency. Efficiency of a Reversible Engine is
independent of work fluid !!!!
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The Original Problem To be solved by Carnot

• What is the maximum work possible from a kg of
  steam?
• Is this also independent of substance ?

Dy is a change in property of a working fluid and
depends on substance!!! How to achieve required
temperature with a given substance?
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The Size of A Carnot Engine

• What decides the size (capital cost) of an engine?

Work done per unit change in volume of a
substance. Mean Effective Pressure.
A mathematical model for an engine is said to be
feasible iff both size and efficiency are
reasonable !!!!
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The Stirling engine and Stirling cycle
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The Stirling Cycle
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Ideal Regenerative Cycle
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