The Second Law of Thermodynamics

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Chapter 5
Department of Mechanical Engineering
Ir. Md. Mujibur Rahman

Chap. 5 The Second Law of Thermodynamics

• The Second Law of Thermodynamics

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Chapter Summary
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• Introduction to 2nd Law
• Definitions of thermal and work reservoirs, heat
  engines,thermal efficiency, heat pump and
  refrigerators and coefficient of performance
  (COP)
• 2nd law statement Kelvin-Planck and Clausius
• Perpetual Motion Machine
• Reversible and Irreversible Processes
• Carnot Cycle, Principles, Heat Engine and
  Refrigerators
• Thermodynamics Temperature Scale

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Introduction to the Second Law
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• 2nd Law states that processes occur in one
  direction, not just in any direction
• Physical processes in nature can proceed toward
  equilibrium spontaneously -
• water flow down a water fall
• Gas expands from high to low pressure
• Heat flows from a high temperature to low
  temperature
• Once taken place the process can be reversed but
  it will not reverse itself spontaneously. Some
  external input energy has to be expended to
  reverse the process

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Thermal Energy and Work Reservoirs
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• A heat or thermal reservoir -
• a sufficiently large system in stable equilibrium
  to which and from which finite amounts of heat
  can be transferred without any change in its
  temperature
• A high temperature heat reservoir from which heat
  is transferred is sometimes called a heat source.
  A low temperature heat reservoir to which heat
  is transferred is sometimes called a heat sink
• A work reservoir -
• is a sufficiently large system in stable
  equilibrium to which and from which finite
  amounts of work can be transferred adiabatically
  without any change in its pressure

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Work Vs Heat
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Work can be converted directly and completely to
heat but not the reverse
To convert heat to work requires special device
called Heat Engine
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Heat Engines
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• Characteristics of Heat Engines -
• Receive heat from a high temperature heat source
• Convert part of the this heat to work
• Reject the remaining waste heat to a low
  temperature sink
• Operate on a cycle
• A heat engine is a thermodynamic system operating
  in a thermodynamic cycle to which net heat is
  transferred and from which net work is delivered.
• The system, or working fluid, undergoes a series
  of processes that constitute the heat engine
  cycle.

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Steam Power Plant as a Heat Engine
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
As the plant is operating in a thermodynamics
cycle
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Thermal Efficiency, ?th
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• The thermal efficiency is the index of
  performance of a heat engine and is defined by

Where Wnet,out is the net work output
Qin is the net heat input at the heat source
Qout is the net heat rejected at heat
sink eg. The thermal efficiency this heat engine
is
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Heat Rejection..why??
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
A heat engine cycle must reject some heat to a
low temperature sink
A heat-engine cycle cannot be completed without
rejecting some heat to a low-temperature sink
Even the most efficient heat engines reject most
of the heat that they receive as waste heat
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Refrigerators and Heat Pumps
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• Heat pumps and refrigerator are a thermodynamic
  systems operating in a thermodynamic cycles which
  remove heat from a low temperature body and
  deliver heat to a high temperature body. To
  accomplish this energy transfer, they receive
  external energy in the form of work or heat from
  the surroundings
• The Refrigerator is a device that operates on a
  thermodynamic cycle and extracts heat from
  low-temperature media
• The Heat Pump also operates on a thermodynamic
  cycle but rejects heat to the high-temperature
  media

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Basic Components of a Refrigeration System in
Typical Conditions
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Vapour-compression refrigeration cycle
4 main components compressor, condenser,
expansion valve, evaporator
Working fluid Refrigerant R134a
Refrigeration R124a
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Coefficient of Performance
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• The index of performance of a refrigerator or
  heat pump is expressed in terms of the
  coefficient of performance, COP, the ratio of
  desired result to input. This measure of
  performance may be larger than 1 and we want the
  COP to be as large as possible.

For refrigeration or air conditioning
For heat pump
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Kelvin-Planck Statement of 2nd Law
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• It is impossible for any device that operates
  on a cycle, to receive heat from a single
  reservoir and produce a net amount of work
• In other words
• For a power plant to operate, the working fluid
  must exchange heat with environment as well as
  the furnace
• the maximum possible efficiency of a heat engine
  is less than 100
• ?th lt 100

Heat engine that violates Kelvin-Planck Statement
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Clausius Statement of the 2nd Law
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• It is impossible to construct a device that
  operates in a cycle and produces no effect other
  than the transfer of heat from a lower
  temperature body to a higher temperature body
• In other words -
• Heat will not flow by itself from a low
  temperature to a high temperature media
• Energy from the surroundings in the form of work
  or heat has to be expended to force heat to flow
  from a low temperature media to a high
  temperature media
• COP of a refrigerator or heat pump must be less
  than infinity .. COP lt ?

Refrigerator that violates Clausius Statement
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Equivalence of the Two Statements
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Proof that the violation of the Kelvin-Planck
statement leads to the violation of the Clausius
Statement
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Perpetual Motion Machines
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Any device that violates the first or second law
of thermodynamics is called perpetual-motion
machine (PPM). If the device violates the 1st
law, it is PMM of the 1st kind. If it violates
the 2nd law, it is PPM of second kind.
PPM of 1st Kind
PPM of 2nd Kind
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Reversible and Irreversible Processes
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• A process is said to be reversible if both the
  system and the surroundings can be restored to
  their original conditions. This process is
  quasi-equilibrium and have more restrictive
  requirements. Any other process is irreversible.
• Internally Reversible Process no
  irreversiblities occur within the boundaries of
  the system during the process.
• Externally Reversible Process no
  irreversiblities occur outside the boundaries of
  the system during the process.
• Totally Reversible no irreversiblities occur.
• All real processes are irreversible.
• Eg. of Irreversibilities friction, unrestrained
  expansion, heat transfer through a finite
  temperature difference, mixing of two substances,
  I2R losses, any deviation from quasi-equilibrium

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The Carnot Cycle
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
French military engineer Nicolas Sadi Carnot
(1769-1832) was among the first to study the
principles of the second law of thermodynamics.
Carnot was the first to introduce the concept of
cyclic operation and devised a reversible cycle
that is composed of four reversible processes,
two isothermal and two adiabatic.
Process 1-2 Reversible isothermal heat addition
at high temperature, TH gt TL to the working fluid
in a piston--cylinder device which does some
boundary work. Process 2-3 Reversible adiabatic
expansion during which the system does work as
the working fluid temperature decreases from TH
to TL. Process 3-4 The system is brought in
contact with a heat reservoir at TL lt TH and a
reversible isothermal heat exchange takes place
while work of compression is done on the
system. Process 4-1 A reversible adiabatic
compression process increases the working fluid
temperature from TL to TH
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Carnot Cycle P-v Diagram
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Carnot Cycle P-v Diagram Heat Engine
Reversed Carnot Cycle P-v Diagram Refrigeration
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The Carnot Principles
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• 1. The efficiency of an irreversible
• heat engine is always less than the
  efficiency of a reversible one operating between
  the same temperature reservoirs ?th lt ?th,carnot

2. The efficiencies of all reversible heat
engines operating between the same two reservoirs
are the same
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Proofs of Carnot Principles
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
22
The Thermodynamics Temperature Scale
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
Thermodynamics temperature scale is defined based
on Carnot Principles. The scale relate the heat
transfers between a reversible device and the
high- and low-temperature reservoirs by
Therefore, the QH/QL ratio can be replaced
by TH/TL for reversible devices, where TH and TL
are the absolute temperatures of the high- and
low-temperature reservoirs.
Heat Engine Arrangement for Developing
Thermodynamic temperature Scale
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The Carnot Heat Engine
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• A heat engine that operates on the reversible
  Carnot cycle is called a Carnot heat engine. The
  thermal efficiency of a Carnot heat engine, as
  well as all other reversible heat engines, is
  given byThis is the maximum efficiency a heat
  engine operating between two reservoirs at
  temperatures TH and TL can have.

No heat engine can have a higher efficiency than
a reversible heat engine operating between the
same high- and low-temperature reservoirs
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Carnot Refrigerators and Heat Pump
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• The COPs of reversible refrigerators and heat
  pumps are given in a similar manner
  asandAgain, these are the highest COPs a
  refrigerator or a heat pump operating between the
  temperature limits of TH and TL can have.

No Refrigerator can have a higher COP than a
Reversible Refrigerator operating between the
same temperature limits
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The Quality of Energy
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
The fraction of heat energy that can be converted
to work increases as the temperature of the heat
source increases
The higher the temperature of the thermal energy,
the higher its quality
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Household Refrigerators
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics
The cross section of a Refrigerator showing the
relative magnitudes of various effects that
constitute the predictable heat load
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Extra Examples
Department of Mechanical Engineering Ir. Md.
Mujibur Rahman
Chap. 5 The Second Law of Thermodynamics

• A steam power plant produces 50 MW of net work
  while burning fuel to produce 150 MW of heat
  energy at the high temperature. Determine the
  cycle thermal efficiency and the heat rejected by
  the cycle to surroundings. (efficiency)
• A Carnot heat engine receives 500 kJ of heat per
  cycle from a high-temperature heat reservoir at
  652 deg C and rejects heat to a low temperature
  heat reservoir at 30 deg C. Determine the thermal
  efficiency of this Carnot engine and the amount
  of heat rejected to the low temperature heat
  reservoir (Carnot Heat Engine)
• An inventor claims to have invented a heat engine
  that develops a thermal efficiency of 80 when
  operating between two heat reservoirs at 100 K
  and 300 K. Evaluate his claim. (Carnot Heat
  Engine)
• An inventor claims to have developed a
  refrigerator that maintains the refrigerated
  space at 2 deg C while operating in a room where
  the temperature is 25 deg C and has a COP of
  13.5. Is there any truth in his claim? (Carnot
  Refrigetor)
• A heat pump is to be use to heat a building
  during winter. The building is to be maintained
  at 21 deg C at all times. The building is
  estimated to be losing heat at a rate of 135,000
  kJ/hr when the outside temperature drops to -5
  deg C. Determine the maximum power required to
  drive the heat pump unit for this outside
  temperature. (Heat Pump)