Chapter 5 The Classical Second Law of Thermodynamics

Chapter 5 The Classical Second Law of

Thermodynamics

1

A cup of hot coffee does not get hotter in a

cooler room.

Transferring heat to a wire will not

generate electricity.

The mechanical work done by the shaft is first

converted to the internal energy of the water.

This energy may then leave the water as heat.

It is known from experience that any attempt

to reverse this process will fail. That is,

transferring heat to the water does not cause

the shaft to rotate.

Some processes cannot occur even though they are not in violation with the first law.U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I

M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ

Spontaneity

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Processes occur in a certain direction (not over a certain path),

and not in the reverse direction. (Way or Direction nothing to

do with nature of the process nor they do decribe the process)

A process will not occur unless it satisfies both

the first and the second laws of thermodynamics.

U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I


MAJOR USES OF THE SECOND LAW

1. The second law may be used to identify the direction of processes.

2. The second law also asserts that energy has quality as well as quantity. The first law

is concerned with the quantity of energy and the transformations of energy from one

form to another with no regard to its quality. The second law provides the necessary

means to determine the quality as well as the degree of degradation of energy during

a process.

3. The second law of thermodynamics is also used in determining the theoretical limits

for the performance of commonly used engineering systems, such as heat engines

and refrigerators, as well as predicting the degree of completion of chemical

reactions.

3

HEAT ENGINES

Work can always be converted to

heat directly and completely, but the

reverse is not true.

Part of the heat received by a heat

engine is converted to work, while the

rest is rejected to a sink.



Heat engines are the devices that convert

heat to work and all can be characterized by

the following:

1. They receive heat ( 𝑄𝐻) from a high-

temperature source (𝑇𝐻) (solar energy,

coal or oil furnace, nuclear reactor, etc.).

2. They convert part of this heat to work

(usually in the form of a rotating shaft.)

3. They reject the remaining waste heat

( 𝑄𝐿) to a low-temperature sink (𝑇𝐿) (the

atmosphere, rivers, etc.).

4. They operate on a cycle.

Heat engines and other cyclic devices

usually involve a fluid to and from which heat

is transferred while undergoing a cycle. This

fluid is called the working fluid

A Simple Heat Engine

4



Why we cannot convert 𝑸𝑳 to work !?

5

A Heat Engine Involving Steady–State Processes

A Steam Power Plant

A portion of the work output of a

heat engine is consumed internally

to maintain continuous operation.



net out in T PW W W W W

net in out H LQ Q Q Q Q

:Energy equation for thecycle W Q net net H LW Q Q Q

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Thermal Efficiency

Some heat engines perform better

than others (convert more of the

heat they receive to work).



Thermal Efficiency

( )

( )

netthermal th

H

W Energy SoughtNetWork Output

Total Heat Input Q EnergyThat Costs

net net H LW Q Q Q

netthermal

H

W

Q

1H L Lthermal

H H

Q Q Q

Q Q

The transfer of heat from a low-temperature medium body to a high-temperature body

can be done with a Refrigerator or Heat Pump. The working fluid is the refrigerant,

such as R–134a or ammonia.

COP Desired Result

Required Input

Refrigerator Heat pump

7



Refrigerator & Heat Pump and Their Efficiency

Coefficient of Performance (COP or 𝜷)

RCOP '

HPCOP

A Simple Vapor–Compression Refrigeration Cycle.

L L

H L

Q QRefrigeration

Energy that Costs W Q Q

' H H

H L

Q QHeat Output

Energy that Costs W Q Q

The Second Law of Thermodynamics

There are two classical statements of the second law, known as the Kelvin–Planck

statement and the Clausius statement.

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The Kelvin–Planck Statement: It is impossible to construct a device that will operate in a

cycle and produce no effect other than the raising of a weight and the exchange of heat

with a single reservoir.

Implying that it is impossible to build a heat engine that has a thermal efficiency 100 %.

9



The 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 warmer

body.

This statement is related to the refrigerator or heat pump. In effect, it states that it is

impossible to construct a refrigerator that operates without an input of work.

This also implies that the coefficient of performance is always less than infinity.

Three Observations about These Two Statements

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Both are negative statements.

They are equivalent:

Any device that violates the Kelvin–Planck statement also violates the Clausius

statement, and vice versa.

They state the impossibility of constructing a perpetual–motion machine of the second

kind.

PMM of the first kind would create work from nothing or create mass or energy, thus

violating the first law.

PMM of the second kind would extract heat from a source and then convert this heat

completely into other forms of energy.

PMM of the third kind would have no friction, and thus would run indefinitely but produce

no work.

PMM is a device that violates one of the basic laws of thermodynamics.

The Reversible Process

Reversible Process: It is defined as a process that, once having taken place, can be

reversed and in so doing leave no change in either system or surroundings.

Irreversible Process: It is a process when reversed it will leave a sign.

• All the processes occurring in nature are irreversible to some extent. If so: Why are

we interested in reversible processes?

• (1) the resulting formulations are simpler and easier to analyze (compared with the

formulations involving irreversibilities).

• (2) they be viewed as theoretical limits for the corresponding irreversible ones.

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The question that can now logically be posed is this: If it is impossible to have a heat

engine of 100 % efficiency, what is the maximum efficiency one can have under a given

definite set of working conditions? The first step in the answer to this question is to

define an ideal process, which is called a reversible process .

Friction

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Factors That Render Processes Irreversible

There are many factors that make processes irreversible and they are called as

irreversibilities: friction, unrestrained expansion, mixing of two fluids, heat transfer

across a finite temperature difference, electric resistance, inelastic deformation of solids,

and chemical reactions.

Four of those factors – friction, unrestrained expansion, heat transfer through a finite

temperature difference, and mixing of two different substances – are considered here.

Unrestrained

Expansion

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Factors That Render Processes Irreversible

Heat Transfer Through a Finite Temperature Difference

Mixing

• Internally reversible process: If no irreversibilities occur within the boundaries of

the system during the process.

• Externally reversible: If no irreversibilities occur outside the system boundaries.

• Totally reversible process: It involves no irreversibilities within the system or its

surroundings.

Totally and internally reversible heat transfer processes.

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Internally and Externally Reversible Processes

15



The Carnot Cycle

1–2 A reversible isothermal process

in which heat transferred to or from

the high temperature reservoir.

2–3 A reversible adiabatic process in which the

temperature of the working fluid decreases

from the high temperature to low temperature.

3–4 A reversible isothermal process

in which heat transferred to or from

the low temperature reservoir.

4–1 A reversible adiabatic process in which the

temperature of the working fluid increases from

the low temperature to high temperature.

Execution of the Carnot cycle in a closed system.

P-V diagram of the Carnot cycle. P-V diagram of the reversed Carnot

cycle.

The Reversed Carnot Cycle

The Carnot heat-engine cycle is a totally reversible cycle.

Therefore, all the processes that comprise it can be reversed, in which case it

becomes the Carnot Refrigeration (or Heat Pump) Cycle.

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17



Example of a heat engine (and refrigerator) that operates on a Carnot cycle.

Two Propositions Regarding the Efficiency of a

Carnot Cycle

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First Proposition

It is impossible to construct an engine that operates between two given reservoirs and is

more efficient than a reversible engine operating between the same two reservoirs.

: any revProposition I

The proof is given in the textbook !

Second Proposition

All engines that operate on the Carnot cycle between two given constant–temperature

reservoirs have the same efficiency.

: any revProposition II

The proof proceeds with the same line of reasoning as in the first proposition.

Thermodynamic Temperature Scale

The zeroth law of thermodynamics provides a basis for temperature measurement, but

that a temperature scale must be defined in terms of a particular thermometer substance

and device.

A temperature scale that is independent of any particular substance, which might be

called an absolute temperature scale

The efficiency of a Carnot cycle is independent of the working

substance and depends only on the reservoir temperatures, i.e.,

if TH and TL are the same, then, 𝜂𝑡ℎ,𝐴 = 𝜂𝑡ℎ,𝐵.

This fact provides the basis for such an absolute temperature

scale called the thermodynamic scale. Since the efficiency of a

Carnot cycle is a function only of the temperature, it follows that

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1 1 ( , )Lthermal L H

H

QT T

Q

where ψ designates a functional relation.

There are many functional relations that could be chosen, for simplicity, the

thermodynamic scale is defined as

1 1L Lthermal

H H

Q T

Q T

For reversible cycles, the heat transfer ratio QH /QL can be

replaced by the absolute temperature ratio TH /TL. Then the

efficiency of a Carnot engine becomes

This temperature scale is called the Kelvin scale, and the

temperatures on this scale are called absolute

temperatures.

20



There are many functional relations that could be chosen, for simplicity, the

thermodynamic scale is defined as

Ideal versus Real Machines

24



,

,

,

th rev

th th rev

th rev

irreversibleheat engine

reversibleheat engine

impossibleheat engine

1 1L Lth real

H H

Q T

Q T

,

,

,

.

.

.

HP or Ref rev

HP or Ref HP or Ref rev

HP or Ref rev

COP irreversible HP or Ref

COP COP reversible HP or Ref

COP impossible HP or Ref

L Lreal

H L H L

Q T

Q Q T T

'

HPCOP

' H Hreal

H L H L

Q T

Q Q T T

.refCOP

Chapter 5 The Classical Second Law of Thermodynamics

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