Second Law of
Thermodynamics
Anubhav Sinha
Assistant Professor
Department of Mechanical Engineering
Indian Institute of Technology (BHU)
anubhav.mec@iitbhu.ac.in 1
Syllabus
❑ Qualitative analysis of heat and work transfer;
❑ Heat engine and refrigerator;
❑ Kelvin Planck and Clausius statement;
❑ Efficiency and COP;
❑ Reversible and irreversible process; causes of irreversibility;
❑ Carnot cycle and Carnot’s theorem
❑ Carnot efficiency and Carnot COP
❑ Absolute thermodynamic temperature scale
2
Introduction
❑ What is the Second Law of Thermodynamics ?
❑ Why is it important ?
❑ Why is it required ?
❑ What are its implications ?
❑ How can we use it for practical applications ?
3
Examples
Q
Q
Hot Cold
Image- Google images 4
Hot Cold
❑ Natural processes take place in certain fixed direction and not in any random way.
❑ First law does not provide any directional constraint.
❑ We need a law/ rule to tell us how a natural process will proceed
❑ This directional constrain will be provided by the Second law.
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Thermal Energy Reservoir (TER)
• Large body with infinite heat capacity
𝑸
𝑸 = 𝒎𝒄∆𝑻 → ∆𝑻 =
𝒎𝒄
• It can absorb or reject unlimited amount of heat but its temperature will remain constant
• The TER from which heat is transferred to the system (Heat engine) is called the source
• The TER to which heat is rejected by the system (Heat engine) is called the sink
• E.g., atmosphere, large water bodies (lake, river, ocean)
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Heat Engine (HE)
• A device which converts heat to work
TH
• It receives heat from the high temperature reservoir (source)
𝑄𝐻
• Operates on a thermodynamic cycle and produces net work
𝑊𝑛𝑒𝑡 = 𝑄𝐻 − 𝑄𝐿
• Rejects some heat to the low temperature reservoir (sink)
𝑄𝐿 Net work output
Thermal Efficiency =
Total heat input
TL
𝑊𝑛𝑒𝑡 𝑄𝐻 − 𝑄𝐿 𝑄𝐿
𝜂𝑡ℎ = = =1−
𝑄𝐻 𝑄𝐻 𝑄𝐻
TH > TL
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Heat Engine – efficiency
𝑄𝐿
𝜂𝑡ℎ =1− Wastage of energy !
𝑄𝐻 TH
• Can we reduce this wastage of energy ? 𝑄𝐻
• Can we eliminate the heat rejection completely ?
𝑊𝑛𝑒𝑡 = 𝑄𝐻
0
𝜂𝑡ℎ = 1− = 100 % NO !
𝑄𝐻 𝑄𝐿 = 0
• Some heat will always be rejected – for the system to come
back to its initial stage (complete the cycle)
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Kelvin-Planck Statement
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.
❑ Heat engine producing net work and exchanging heat with a single reservoir - not allowed
❑ Some amount of heat must be rejected to sink !
❑ 100% efficient engine (complete conversion of heat to work in a cycle) - not allowed !
❑ This limitation is not because of friction or any other dissipative effects – This applies to both ideal
and practical engines.
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Heat and Work
❑ Can we completely convert work to heat ?
❑ But heat cannot be completely converted to work (in a cycle)
❑ Is there any qualitative difference in heat and work ?
❑ Heat is classified as Low grade energy
❑ Work is classified as High grade energy
❑ Complete conversion of low grade energy to High grade energy in a cycle is impossible !
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Heat Pump (HP)
TH
𝑄𝐻
𝑄𝐿
TL
TH > TL
Heat transfer from Colder body to Hotter body
Heat can be transferred from colder to hotter body
BUT
work input is required (electricity)
Image- Google images 12
Heat Pump (HP)
• A device which transfers heat from low temperature reservoir
TH
(TL) to high temperature reservoir (TH)
𝑄𝐻
• It works on a thermodynamic cycle
𝑊 = 𝑄𝐻 − 𝑄𝐿
• It requires Work input to function
• Efficiency is measured by Coefficient of Performance (COP)
𝑄𝐿
Desired Output
COP𝐻𝑃 =
TL Required input
𝑄𝐻 𝑄𝐻
TH > TL COP𝐻𝑃 = =
𝑊 𝑄𝐻 − 𝑄𝐿
Clausius Statement
It is impossible to construct a device that operates in a cycle and produces no effect
other than the transfer of heat from a cooler body to a hotter body.
❑ Natural/ spontaneous heat transfer from hot body to cold body !
❑ Processes which are not natural/ spontaneous need external aid – work !
❑ Refrigerator/ AC working without electricity (work input) – not allowed !
Hot Cold
14
Are these two statements for the
same law ?
15
Equivalence of both the statements
TH TH
𝑄𝐻 𝑄𝐻 + 𝑄𝐿 𝑄𝐿
𝑊 = 𝑄𝐻
Equivalent
Heat Pump
Heat Heat
Engine Pump
𝑄𝐿 𝑄𝐿
TL TL
Violation of Kelvin-Planck Violation of Clausius
statement statement
Equivalence of both the statements
TH
Equivalent Heat
𝑄𝐻 𝑄𝐻 Engine
𝑊 = 𝑄𝐻 − 𝑄𝐿 𝑊 = 𝑄𝐻 − 𝑄𝐿
Heat
Pump Heat
Engine
𝑄𝐻 𝑄𝐿
𝑄𝐻 − 𝑄𝐿
TL TL
Violation of Clausius Violation of Kelvin-Planck
statement statement
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❑ Both the statements are equivalent and concerned with the
same law.
❑ Is there any property involved ?
❑ Entropy (next chapter)
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Perpetual Motion Machine of the Second Kind (PMM2)
❑ PMM2 is a device which violates the Second law of
thermodynamics
❑ It is not possible to design a PMM2 which works
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Heat Pump (HP) and Refrigerator
• HP and Refrigerator are similar devices, causing the same
TH
effect (transfer of heat from cooler to hotter object)
𝑄𝐻
• The difference in their major objectives
𝑊 = 𝑄𝐻 − 𝑄𝐿
• Objective of the HP is to supply heat to high temperature (TH)
𝑄𝐿 (heat the hotter body)
• Objective of the Refrigerator is to extract heat from low
TL
temperature (TL) (cool the cooler body)
TH > TL
COP of HP and Refrigerator
Desired Output
𝐶𝑂𝑃 =
TH Required input
𝑄𝐻 𝑄𝐻 𝑄𝐻
COP𝐻𝑃 = =
𝑊 𝑄𝐻 − 𝑄𝐿
𝑊 = 𝑄𝐻 − 𝑄𝐿
𝑄𝐿 𝑄𝐿
COP𝑅𝑒𝑓 = =
𝑄𝐿 𝑊 𝑄𝐻 − 𝑄𝐿
TL COP𝐻𝑃 = COP𝑅𝑒𝑓 + 1
TH > TL
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What is thermodynamically more efficient ?
❑ 1 kW electrical heater
❑ Heat Pump that uses 1 kW
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Reversible and Irreversible
Process
23
Reversibility and Irreversibility
Pendulum in Vacuum Pendulum in air
Can keep oscillating indefinitely Will stop after some time
(no loss in energy with time)
No effect to the surroundings Affects the surroundings due to friction with air
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Reversibility and Irreversibility
Reversible Process
A process that can be reversed without leaving any trace on the surroundings
Irreversible Process
A process that can NOT be reversed without leaving any trace on the surroundings.
Irreversibility can occur due to:
• Lack of equilibrium during process
• Dissipative effects
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Irreversibility due to lack of Equilibrium
❑ Heat transfer through a finite temperature difference
❑ Lack of pressure equilibrium within the interior of the system or between system
and surroundings
❑ Free expansion
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Irreversibility due to Dissipative Effects
❑ Friction
❑ Paddle-wheel work transfer
❑ Transfer of electricity through a resistor
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Types of Irreversibility
Internal
Internal irreversibility is caused by internal dissipative effects like friction, electrical resistance, etc.,
within the system
External
External irreversibility refers to irreversibility occurring at the system boundary like heat transfer with the
surroundings at finite temperature gradient
A process is called totally reversible, or simply reversible, if it involves no irreversibilities within the
system or its surroundings
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Reversible process and time
❑ A reversible process is carried out infinitely slowly with an infinitesimal gradient, so that every state
passed through by the system is an equilibrium state
❑ A reversible process coincides with quasi static process
❑ If the time allowed for a process to occur is infinitely large, even through finite gradient, the process
can still be reversible.
❑ However, if the time for the process is small, the process is irreversible.
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Reversible process
A process is reversible if it is performed in such a way that
❑ the system remains infinitesimally close to a thermodynamic equilibrium state, at all the time
(quasi static)
❑ no dissipative effects are present, of any form.
❑ A reversible process is an ideal limiting case (theoretical)
❑ All natural/ practical processes are irreversible
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Carnot Cycle and
Carnot Theorem
31
Carnot Cycle
1-2 : Isothermal heat addition
𝑞𝐻
4-1 : Reversible adiabatic
(Isentropic) compression
𝑞𝐿
2-3 : Reversible adiabatic
(Isentropic) expansion
3-4 : Isothermal heat rejection
Thermodynamics, Cengel and Boles 32
Carnot Cycle
𝑞𝐻
1-2 : Isothermal heat addition
2-3 : Reversible adiabatic (Isentropic) expansion
3-4 : Isothermal heat rejection
𝑞𝐿
4-1 : Reversible adiabatic (Isentropic) compression
𝑞𝐻
Isothermal heat transfer
▪ Externally Reversible
𝑞𝐿
▪ is difficult to achieve in practical devices
Thermodynamics, Cengel and Boles 33
Reversed Carnot Cycle
TH
𝑄𝐻
𝑊 = 𝑄𝐻 − 𝑄𝐿
TH > TL
𝑄𝐿
1-2 : Reversible adiabatic (Isentropic) expansion
2-3 : Isothermal heat addition
TL
3-4 : Reversible adiabatic (Isentropic) compression
4-1 : Isothermal heat loss
Thermodynamics, Cengel and Boles 34
Carnot’s Theorem
Of all Heat Engines operating between a given constant temperature source, and a
given constant temperature sink, none has a higher efficiency than a reversible
engine
❑ A reversible engine will have the maximum efficiency for a given TH and TL
❑ For a fixed TH and TL, all irreversible engines will have lower efficiency than a reversible
engine
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Corollary of Carnot’s Theorem
The efficiency of all reversible heat engines operating between the same temperature levels is
the same
❑ For a fixed TH and TL, all reversible engines will have the same efficiency
❑ The efficiency of a reversible engine is independent of the nature or amount of the working
fluid 𝜂𝑖𝑟𝑟 < 𝜂𝑟𝑒𝑣
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Absolute thermodynamic temperature scale
• A temperature scale that is independent of the properties of the substances that are
used to measure temperature is called a thermodynamic temperature scale
• Lord Kelvin proposed a temperature scale such that
𝑄𝐿 𝑇𝐿
=
𝑄𝐻 𝑟𝑒𝑣
𝑇𝐻
• Triple point of water is fixed at 273.16 K
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Carnot Cycle -Efficiency
𝑊𝑛𝑒𝑡 𝑄𝐿
𝜂𝐶𝑎𝑟𝑛𝑜𝑡 = =1−
𝑄𝐻 𝑄𝐻
For isothermal heating process (1-2) :
𝑉2
𝑄1−2 = 𝑊1−2 = 𝑅 𝑇𝐻 𝑙𝑛 = 𝑄𝐻
𝑉1
𝑞𝐻
For isothermal cooling process (3-4) :
𝑉4
𝑄3−4 = 𝑊3−4 = 𝑅 𝑇𝐿 𝑙𝑛 = −𝑄𝐿
𝑉3
𝑉3
𝑄𝐿 = 𝑅 𝑇𝐿 𝑙𝑛 𝑞𝐿
𝑉4
Thermodynamics, Cengel and Boles 38
Carnot Cycle -Efficiency
For isentropic expansion (2-3) :
1/(𝛾−1) 1/(𝛾−1)
𝑉2 𝑇3 𝑇𝐿
= =
𝑉3 𝑇2 𝑇𝐻 𝑉2 𝑉1
=
𝑉3 𝑉4
→
For isentropic compression (4-1) :
1/(𝛾−1) 1/(𝛾−1)
𝑉1 𝑇4 𝑇𝐿
= = 𝑉2 𝑉3
𝑉4 𝑇1 𝑇𝐻 =
𝑉1 𝑉4
𝑉
𝑄𝐿 𝑅 𝑇𝐿 𝑙𝑛 𝑉3
𝑻𝑳
𝜂𝐶𝑎𝑟𝑛𝑜𝑡 =1−
𝑄𝐻
=1−
𝑉
4
𝑅 𝑇𝐻 𝑙𝑛 𝑉2
→ 𝜼𝑪𝒂𝒓𝒏𝒐𝒕 =𝟏−
𝑻𝑯
1
Thermodynamics, Cengel and Boles 39
The Quality of Energy
• Higher efficiency means that more percentage of that heat energy can be
converted to work
• It is better to have energy at higher temperature
• The higher the temperature, the higher the quality of energy
For 𝑻𝑳 =303 K
𝑻𝑳
𝜼𝑪𝒂𝒓𝒏𝒐𝒕 =𝟏−
𝑻𝑯
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Reversed Carnot cycle COP
Desired Output
TH 𝐶𝑂𝑃 =
Required input
𝑄𝐻 𝑄𝐻 𝑄𝐻 𝑄𝐿 𝑄𝐿
COP𝐻𝑃 = = COP𝑟𝑒𝑓 = =
𝑊 𝑄𝐻 − 𝑄𝐿 𝑊 𝑄𝐻 − 𝑄𝐿
𝑊 = 𝑄𝐻 − 𝑄𝐿
𝑇𝐻 𝑇𝐿
COP𝐻𝑃 = COP𝑅𝑒𝑓 =
𝑇𝐻 − 𝑇𝐿 𝑇𝐻 − 𝑇𝐿
𝑄𝐿
TL
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Reference Books
❑ “Engineering Thermodynamics” – P K Nag, Tata McGraw Hill (6th ed.)
❑ “Thermodynamics - An Engineering Approach” –Cengel and Boles, McGraw Hill
Publishers (8th ed., SIE)
❑ “Fundamentals of Thermodynamics” – Borgnakke and Sonntag, Wiley (7th ed.)
❑ “Principles of Engineering Thermodynamics” – Moran and Shapiro , Wiley (8th ed. SIE)
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Thank
You
anubhav.mec@iitbhu.ac.in
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