The Second Law of
Thermodynamics
Cengel & Boles,
Chapter 5
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The Second Law of
Thermodynamics
• So far we have studied:
– conservation of energy (i.e., First Law
of Thermodynamics)
– conservation of mass
– tabulated thermodynamic properties
and equations of state (e.g., ideal gas
law)
• There is a need for another law – one
that tells us what sort of processes
are possible while satisfying
conservation principles
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Second Law Statements
• Like the 1st Law, the 2nd Law of
Thermodynamics is based upon a long
history of scientific experimentation
• There is no single verbal or math
statement for this Law - instead, there
is a collection of statements,
deductions, and corollaries regarding
thermodynamic processes that
together form the 2nd Law
• Two popular statements:
– Clausius statement
– Kelvin-Planck statement
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Kelvin-Planck Statement
• “It is impossible for any device
that operates as a cycle to
receive heat from a single
thermal reservoir and produce
an equivalent amount of work”
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Clausius Statement
• “It is impossible to construct a
device that operates as a cycle
whose sole effect is the transfer
of heat from a lower temperature reservoir to a higher
temperature reservoir”
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Thermodynamic Cycles
• Cycle energy balance
Qcycle  Wcycle  Ecycle
 Qcycle  Wcycle
• Types of cycles
– heat engines, (aka power cycles)
– refrigeration and heat pump cycles
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Heat Engines
• Net (cycle) work output:
Wcycle  Qcycle
or
Wnet ,out  Qin  Qout
 QH  QL
• Thermal efficiency
desired output Wnet ,out
th 

required input
QH
QH  QL
QL

 1
QH
QH
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Refrigeration & Heat
Pump Cycles
• Net work input:
 Wnet ,in  Qin  Qout
or
Wnet ,in  QH  QL
• Coefficient of performance (COP)
desired output
required input
Q
QL
COPR  L 
Wnet ,in QH  QL
COP 
QH
QH
COPHP 

Wnet ,in QH  QL
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(refrigera tor)
(heat pump)
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Reversible Processes
• Reversible Process: a process that
can be reversed, allowing system
and surroundings to be restored to
their initial states
– no heat transfer
– no net work
– e.g., adiabatic compression/expansion
of a gas in a frictionless piston device:
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Reversible Processes, cont.
• Reversible processes are considered
ideal processes – no energy is
“wasted”, i.e., all energy can be
recovered or restored
– they can produce the maximum amount
of work (e.g., in a turbine)
– they can consume the least amount of
work (e.g., in a compressor or pump)
– they can produce the maximum KE
increase (e.g., in a nozzle)
– when configured as a cycle, they
produce the maximum performance
(i.e., the highest th or COP)
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Irreversible Processes
• Irreversible Process - process that
does not allow system and surroundings to be restored to initial state
– such a process contains “irreversibilities”
– all real processes have irreversibilities
– examples:
•
•
•
•
•
•
•
•
heat transfer through a temperature difference
unrestrained expansion of a fluid
spontaneous chemical reaction
spontaneous mixing of different fluids
sliding friction or viscous fluid flow
electric current through a resistance
magnetization with hysteresis
inelastic deformation
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Internally Reversible
Processes
• A process is called internally
reversible if no irreversibilities occur
within the boundary of the system
– the system can be restored to its initial
state but not the surroundings
– comparable to concept of a point mass,
frictionless pulley, rigid beam, etc.
– allows one to determine best theoretical
performance of a system, then apply
efficiencies or correction factors to
obtain actual performance
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Externally Reversible
Processes
• A process is called externally
reversible if no irreversibilities occur
outside the boundary of the system
– heat transfer between a reservoir and a
system is an externally reversible
process if the outer surface of the
system is at the reservoir temperature
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The Carnot Principles
• Several corollaries (the Carnot
principles) can be deduced from the
Kelvin-Planck statement:
– the thermal efficiency of any heat
engine must be less than 100%
th 
Wnet ,out
QH
 1
QL
QH
– th of an irreversible heat engine is
always less than that of a reversible
heat engine
– all reversible heat engines operating
between the same two thermal
reservoirs must have the same th
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The Kelvin
Temperature Scale
• Consider a reversible heat engine
operating between TH and TL :
th,rev
QL
 f1 (TL , TH )  1 
QH
 QL
 
 QH

  1  f1 (TL , TH )
 rev
 f 2 (TL , TH )
• Kelvin proposed a simple relation:
 QL 
T
   L
 QH  rev TH
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The Kelvin Temperature
Scale, cont.
• Kelvin’s choice equates the ratio of
heat transfers in a reversible heat
engine to a the ratio of absolute
temperatures
• Need a reference to define the
magnitude of a kelvin (1 K) - the
triple point of water is assigned
273.16 K:
 QH 

 TH  273.16 
Q 
 L,tp  rev
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Maximum Performance
of Cycles
• Carnot Heat Engine:
th,rev  1 
TL
TH
• Carnot Refrigerator:
COPR ,rev
TL
1


TH  TL TH / TL  1
• Carnot Heat Pump:
COPHP,rev
TH
1


TH  TL 1  TL / TH
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The Carnot Cycle
• The Carnot cycle is the best-known
reversible cycle, consisting of four
reversible processes:
– adiabatic compression from
temperature TL to TH
– isothermal expansion with heat input
QH from reservoir at TH
– adiabatic expansion from temperature
TH to TL
– isothermal compression with heat
rejection QL to reservoir at TL
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The Carnot Cycle, cont.
• Note:
– the heat transfers (QH , QL) can only be
reversible if no temperature difference
exists between the reservoir and system
(working fluid)
– the processes described constitute a
power cycle; it produces net work and
operates clockwise on a P-v diagram
– The Carnot heat engine can be reversed
(operating counter-clockwise on a P-v
diagram) to become a Carnot
refrigerator or heat pump
– the thermal efficiency and coefficients
of performance of Carnot cycles
correspond to maximum performance
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