Chapter 1 introduction

Chapter 1
Introduction
• Instructor: Engr. Sajid Yasin
• Department of Mechanical Engineering and Technology
MNS UET Multan

Introduction to Refrigeration
• Refrigeration is defined as the process of extracting heat
from a lower-temperature heat source, substance, or
cooling medium and transferring it to a higher-
temperature heat sink.
• Refrigeration maintains the temperature of the heat
source below that of its surroundings while transferring
the extracted heat, and any required energy input, to a
heat sink, atmospheric air, or surface water.
• A refrigeration system is a combination of components
and equipment connected in a sequential order to
produce the refrigeration effect.

Applications of Refrigeration
4
• Preservation of perishable food products by storing them
at low temperatures:
• Refrigerators
• Freezers
• Cold Stores
• Providing thermal comfort to human beings by means of
air conditioning:
• Window-type air conditioners
• Split-type air conditioners
• Chillers

Brief History
• Long back in 1748, William Coolen of Glasgow
university produced refrigeration by creating partial
vacuum over ethyl ether. But he could not implement his
experience in practice.
• The first development took place in 1834, when Parkins
proposed a hand-operated compressor machine working
on ether.
• In 1851 came Gorrie’s air refrigeration machine.
• In 1856, Linde developed a machine working on
ammonia.
• In 1898, Dewar made the famous Dewar flask to store
liquids.

 Food Storage and Distribution
Many meats, fish, fruits and vegetables are perishable, and their
storage life can be extended by refrigeration.
The frozen-food chain typically consists of the following links:
freezing, storage in a refrigerated ware houses, display in a
refrigerated case at food markets and finally storage in the home
freezer.
 Freezing
Air blast freezing: where air at approximately -30C is blown
with high velocity over packages of food.

• Contact Freezing: where food is placed between metal plates
and surfaces.
• Immersion Freezing: where food is placed in low temperature
brine
• Fluidized-bed freezing: where the individual particles are
carried along a conveyor belt and kept in suspension by an upward-
directed stream of cold air.
• Storage: Fruits and vegetables should be frozen quickly after
harvesting and meats frozen quickly after slaughter to maintain high
quality. These meats are stored at -20C t0 -23C, perhaps for many
months.

 Bakery Products:
The major reason for refrigerating bakery products is to provide a
better match between production and demand and thus prevent a
taste. Many breads and pastries are frozen following baking to
provide a longer shelf life before being sold to the consumer.
 Chemical and Process Industries
The chemical and process industries include the manufacturers of
chemicals, petroleum refiners, petrochemical plants and paper
industries etc.

• Distribution: Food moves from refrigerated ware houses to food
markets as needed to replenish to stock there. In the market food is
kept refrigerated in display cases held at 3 to 5C for dairy products
and at -20C for frozen food and ice cream. The consumer finally
stores the food in a domestic refrigerator or freezer until used.

 Food Processing
Some foods need operations in addition to freezing and refrigerated
storage and these process uses refrigeration as well.
 Dairy Products
The chief dairy products are milk, ice-cream and cheese. To pasteurize
milk, the temperature is elevated to approximately 73C and held for
about 20s. From the process, the milk is cooled and ultimately
refrigerated to 3 or 4C for storage.
 Beverages: Refrigeration is essential in the production of such
beverages as concentrated as concentrated fruit juices and beer etc.
The taste of many drinks can be improved by serving them cold.

Some important functions served by refrigeration in chemical and
process industries are
 Separation of gases
 Solidification of one substance in a mixture to
separate it from other
 Maintenance of a low temperature of stored liquid so
that the pressure will not be excessive
 Removal of heat of reaction

Special Applications of Refrigeration
 Drinking Fountains
Small refrigeration units chill drinking water for storage and use as
needed.
 Dehumidifiers
An appliance to dehumidify air in homes and buildings uses a
refrigeration unit by first passing the air to be dehumidified through
the cold evaporator coil of the system, where the air is both cooled
and dehumidified.
 Ice-makers
The production of ice may take place in domestic refrigerators, ice
makers serving restaurants and motels, and large industrial ice
makers serving food-processing and chemical plants.

 Ice-skating rinks
Skaters, hockey players and curlers cannot rely upon the weather to
provide the cold temperature necessary to freeze the water in their ice
rinks. Pipes carrying cold refrigerant are therefore embedded in a fill
of sand, over which water is poured and frozen
 Construction
Refrigeration is sometimes used to freeze soil. A further use of
refrigeration is in cooling huge masses of concrete. Concrete may be
cooled by chilling the sand, gravel, water and cement before mixing
and by embedding chilled-water pipes in the concrete.

 Desalting of Sea Water
One of the methods available for desalination of seawater is to
freeze relatively salt-free ice from the sea water, separate the ice
and re-melt it to redeem fresh water.

System, Surroundings and Boundary
 System: A quantity of matter or a region in
space chosen for study.
 Surroundings: The mass or region outside
the system
 Boundary: The real or imaginary surface
that separates the system from its
surroundings.

 Isolated system – neither
mass nor energy can cross
the selected boundary
 Example (approximate): coffee
in a closed, well-insulated
thermos bottle
Types of System (Isolated System)

 Closed system – only
energy can cross the
selected boundary
 Examples: a tightly capped cup
of coffee
Types of system (Closed system)

 Open system – both mass
and energy can cross the
selected boundary
 Example: an open cup of coffee
Types of System (Open System)

All the quantities which identify the state of thermodynamic
system are called Properties.
Properties may be intensive or extensive.
 Intensive – whose value for entire system doesn’t equal to sum
of value of individual parts.
e.g: Temperature, Pressure, and Density, Sp. Volume
 Extensive – whose value for entire system is equal to sum of
value of individual parts.
 e.g: Mass, Volume, Energy, Enthalpy
Properties of a system

Specific Properties – The ratio of any extensive property of a system
to that of the mass of the system is called an average specific value of
that property (also known as intensives property)
Properties of a System

 State – a set of properties that describes the conditions
of a system. Eg. Mass m, Temperature T, volume V
 Thermodynamic equilibrium -
system that maintains thermal,
mechanical, phase and
chemical equilibriums.
State, Equilibrium and Process

 Process – change from one equilibrium state to another.
Process Property held
constant
isobaric pressure
isothermal temperature
isochoric volume
isentropic entropy

The prefix iso- is often used to designate a process for which a
particular property remains constant.
Isobaric process: A process during which the pressure P
remains constant.
Pressure is Constant (ΔP = 0)

 Cyclic process - when a system in a given
initial state goes through various processes
and finally return to its initial state, the system
has undergone a cyclic process or cycle.
 Reversible process - it is defined as a
process that, once having take place it can
be reversed. In doing so, it leaves no change
in the system or boundary.
 Irreversible process - a process that cannot
return both the system and surrounding to
their original conditions
Types of Thermodynamics Processes

 Adiabatic process - a process that has no heat transfer
into or out of the system. It can be considered to be perfectly
insulated.
 Isentropic process - a process where the entropy of the
fluid remains constant.
 Polytropic process - when a gas undergoes a reversible
process in which there is heat transfer, it is represented with
a straight line, PVn = constant.
 Throttling process - a process in which there is no change
in enthalpy, no work is done and the process is adiabatic.
Types of Thermodynamics Processes

“ If two bodies are in thermal equilibrium with a third
body, there are also in thermal equilibrium with each
other.”
Zeroth Law of Thermodynamics

Q = ∆Ē + W
For Infinitesimal, Quasi-Static
Processes
đQ = dĒ + đW
Total Energy is Conserved
Heat absorbed
by the system
Work done
by the
system
Change in the
system’s internal
energy
The First Law of Thermodynamics

1st Law of Thermodynamics
“Energy can neither be
created nor destroyed.
It can only be changed
from one form to
another.”
Rudolf Clausius,
1850• The 1st Law of Thermodynamics is
Conservation of Total Energy!!!!
• It says nothing about
The Direction of Energy Transfer!

The Second Law of Thermodynamics
“The entropy of an isolated system increases
in any irreversible process and is unaltered in
any reversible process.”
• This is sometimes called
The Principle of Increasing Entropy
DS  0
• This gives the Preferred (natural)
Direction of Energy Transfer
• This determines whether a process can occur or not.
Change in entropy
of the system

Various Statements of the Second Law
1. “No series of processes is possible whose sole
result is the absorption of heat from a thermal
reservoir and the complete conversion of this
energy to work.” That is
There are no perfect engines!
2. “It will arouse changes while the heat transfers
from a low temperature object to a high
temperature object.”
Rudolf Clausius’
statement of the Second Law.

3. “It will arouse other changes while
the heat from the single thermal
source is taken out and is totally
changed into work.”
4. “It is impossible to extract an
amount of heat QH from a hot
reservoir and use it all to do work
W. Some amount of heat QC must
be exhausted to a cold reservoir.”
Lord Kelvin’s (William Thompson’s)
The Kelvin-Planck
Various Statements of the Second Law

The 2nd Law of Thermodynamics
Clausius’ statement for Refrigerators
• “It is not possible for heat to flow from a
colder body to a warmer body without
any work having been done to
accomplish this flow. Energy will not
flow spontaneously from a low
temperature object to a higher
temperature object.”
There are no perfect Refrigerators!
• This statement about refrigerators also applies to air
conditioners and heat pumps which use the same principles.

The Third Law of Thermodynamics
“It is impossible to reach a temperature of
absolute zero.”
On the Kelvin Temperature Scale,
T = 0 K
is often referred to as
“Absolute Zero”

Second Law of Thermodynamics
Alternative Statements
There is no simple statement that captures all aspects of
the second law. Several alternative formulations of the
second law are found in the technical literature. Three
prominent ones are:
►Clausius Statement
►Kelvin-Planck Statement
►Entropy Statement

Aspects of the
Second Law of Thermodynamics
The second law of thermodynamics has many
aspects, which at first may appear different in kind
from those of conservation of mass and energy
principles. Among these aspects are:
►Predicting the direction of processes.
►Establishing conditions for equilibrium.
►Determining the best theoretical performance
of cycles, engines, and other devices.
►Evaluating quantitatively the factors that
prevent achievement of the best theoretical
performance level.

Clausius Statement of the Second Law
It is impossible for self acting machine working in cyclic
process, to transfer heat from a body at lower
temperature to body at higher temperature without aid of
external agency.

Kelvin-Planck Statement of the Second Law
It is impossible to construct an engine that operate in a
thermodynamic cycle and deliver a net amount of
energy by work to its surroundings while receiving
energy by heat transfer from a single thermal reservoir.
Typical Engine Hypothetical Engine

Kelvin Temperature Scale
Consider systems undergoing a power cycle and a
refrigeration or heat pump cycle, each while
exchanging energy by heat transfer with hot and cold
reservoirs:
H
C
cycle
revH
C
T
T
Q
Q






The Kelvin temperature is defined so that

Third Law of Thermodynamics
• Third Law: The entropy of a perfect crystalline
substance is zero at T=0
• At T=0, all thermal motion has been quenched and in a
perfect crystal, all atoms are in a uniform array.

Reversible and Irreversible Processes
• A reversible process is one in which every state
along some path is an equilibrium state
– And one for which the system can be returned to its
initial state along the same path
• An irreversible process does not meet these
requirements
– Most natural processes are irreversible
• Reversible process are an idealization, but some
real processes are good approximations

Thermodynamic Functions
• Path Function whose value depends on the path
followed by the thermodynamic process irrespective
of the initial and final states of the process.
• Examples: Work and Heat.
• Point Function (State Function) is a function
whose value depends on the final and initial states
of the thermodynamic process, irrespective of the
path followed by the process.
• Examples: Temperature, Pressure, Density, Mass,
Volume, Enthalpy, Entropy, Internal Energy etc.

Thermodynamic Functions
• Processes A and B have same initial and final states,
hence, the change in volume (dVA & dVB) for both these
processes is same (3 m3), as volume is a point function,
• Whereas the work transferred (WA and WB) for the
processes is different since work is a path function.

Point Function Path Function
Its values are based on the state of the
system (i.e. pressure, volume, temperature
etc.)
Its values are based on how that particular
thermodynamic state is achieved.
No matter by which process the state is
obtained, its values will always remain the
same.
Different processes to obtain a particular
state will give us different values.
Only initial and final states of the process
are sufficient
We need to know exact path followed by
the process
Its values are independent of the path
followed
Its values are dependent on the path
followed
It is an exact or perfect differential It is an inexact or imperfect differential.
Its cyclic integral is always zero Its cyclic integral may or may not be zero
It is property of the system It is not the property of the system
Its examples are density, enthalpy, internal
energy, entropy etc.
Its examples are Heat, work etc.

• In thermodynamics, a quasi-static process is a
thermodynamic process that happens slowly enough for
the system to remain in internal equilibrium.
• Any reversible process is a quasi-static one.
However, quasi-static processes involving entropy
production are not reversible.
• Examples of quasi-static processes:
- isothermal: T = constant
- isovolumetric: V = constant
- isobaric: P = constant
- adiabatic: Q = 0
Quasi-Static processes
(QUASI-EQUILIBRIUM)

Quasi-static process
at each infinitesimal
movement
HAV  H
dH
dHAdV 

Work done by the
gas as its volume
changes from Vi to Vf

f
i
V
V
PdVW
dVP
dHAP
dHAP
dHFdW




)(
)( PdVdW 

Work done during volume changes

PdVdW 
• dV > 0: the work done on the gas is negative
• dV < 0: the work done on the gas is positive
In thermodynamics, positive work represents a transfer of energy out of the
system, and negative work represents a transfer of energy into the system.

f
i
V
V
PdVW i
f
P
V
Pi
Pf
Vi Vf
),( TVPP 
P-V diagram
The work done by a gas in the expansion
is the area under the curve connecting
the initial and final states
Work done during volume changes

)( iff VVPW 
a. isovolumetric
b. isobaric
a. isobaric
b. isovolumetric
)( ifi VVPW  
f
i
V
V
PdVW
isothermal
• Because the work done by a system depends on the initial and final states and
on the path followed by the systems between the states, it is not a state function.
• Energy transfer by heat also depends on the initial, final, and intermediate states
of the system, it is not a state function either.
a b c
Work and heat are not state functions

Internal energy
• All systems have Internal Energy (U)
• For example - kinetic energy of gas
molecules in random motion = ½ m v2
• If we add up all the kinetic energies of all
the molecules, we get the
 Internal Energy of the System:
• U cannot be measured directly,
2 2 2
1 1 2 2
1 1 1
2 2 2
N NU m v m v m v     
Box containing N molecules
all moving around randomly
The internal energy U is the sum of the energy of all the
molecules in the system

Internal Energy and Temperature
 Gas molecules
• Have energy because
• They are moving.
• The sum of all the energies of all the molecules is the
system’s Internal Energy
• The temperature of the system is a measure of the
average kinetic energy of the atoms,
• Temperature  Average Kinetic Energy

Temperature and Internal Energy
• Temperature, T, measures the average kinetic energy
(KE) of the molecules
• The internal energy, U, is the total energy of all of the
molecules
50° C
50° C
50° C
1 2 3
T1 = T2 = T3
U3 > U2 > U1

Heat
• Heat is the energy that flows from one system to
another because of their temperature difference.
• Heat stops flowing when the two systems come
to the same temperature.
• Heat was first thought to be an actual fluid
(caloric), but it is not a fluid- it is energy!
System A
at temp TA
System B
at temp TB

Quasi-static
process
Character UD WQ
adiabatic 0Q WU D
isothermal T = constant 0DU
isovolumetric
isobaric
V = constant
P = constant
QU D TCQ V D 0W
VPW DWQU D TCQ PD
1
2
ln
V
V
TNkW BWQ 
)
11
(
)1(
1
12
11 

 VV
VPW 

0Q
Summary

Work can change Internal Energy
• When one object is rubbed against another, work is
done, and heat is produced
• When a gas is compressed its internal energy is
increased; when it expands, its internal energy
decreases
• The internal energy of a system can change if work is
done on the system or heat is transferred to it. (1st Law
of Thermo.)

Absolute zero – as cold as it gets!
• There is nothing particularly significant about
0°C or 0°F.
• Is there a temperature scale where 0 really is
ZERO? It doesn’t get any colder than this!
• YES– It is called the KELVIN scale.
• At zero Kelvin, all molecular motion stops.
• We can see this from the behavior of gases,
where pressure decreases with temperature.

Approaching Absolute Zero
°C
Gas Pressure
273.15 °C
As a gas is cooled, its pressure decreases. If we
imagine continuing to cool it, the P vs T plot for
all quantities of gas extrapolate to - 273.15 C
This is absolute zero!

Temperature Measuring Scales
• Kelvin scale (where 0 means 0)
• TK = TC + 273.15°
• One degree K = one degree C
• There are NO negative Kelvin temperatures, zero is the
minimum.
0°
100°
32°
212°boiling
point
freezing
point
Celsius
scale
Fahrenheit
scale
180°100°
5 32
9C
T T
F
 
 
 
 
  
9
32
5
T
F C
T  
  
 


Thermodynamic Cycles
• A recurring series of thermodynamic processes through
which an effect is produced by transformation or
redistribution of energy and initial conditions are restored at
the end of process.
HEAT SOURCE
HEAT SINKPump
Engine W
Qin
Qout
Working
Substance

Five Basic Elements of all Cycles
• Working substance: transports energy within system
• Heat source: supplies heat to the working medium
• Engine: device that converts the thermal energy of the
medium into work
– Heated: heat added in engine itself
– Unheated: heat received in some device separate from engine
• Heat sink/receiver: absorbs heat from the working medium
• Pump: moves the working medium from the low-pressure
side to the high-pressure side of the cycle
HEAT SOURCE
HEAT SINKPump
Engine W
Qin
Qout
Working
Substance

Refrigerating Machines
There are essentially two categories
of thermal plants. These are:
• Thermal power plant or
work producing plants
• Refrigerating /heat pump plats or
work consuming plants

Refrigerating Machines
• The work producing plants or heat engines lead to the
conversion of heat to work.
• The work consuming plants (refrigerators or heat
pumps), are not those which are in any way related to
the conversion of work into heat.
• The objective of the work consuming plants, actually, is
to lead to the flow of heat from a low temperature body
to a high temperature body. The work is required to
achieve this.
• Examples of work consuming plants refrigerators ( Cold
storages, Domestic refrigerators, ice plants and food
freezing plants.

A Refrigerating Machine-
The Second law of Thermodynamics
• A refrigerating machine is device which will either cool or
maintain a body at a temperature below that of
surroundings. Hence, heat must be made to flow from a
body at low temperature to the surroundings at high
temperatures.
• However, this is not possible on its own. We see in
nature that heat flows from a high temperature body to a
low temperature body.
• Therefore, work is done to flow the heat from low
temperature to a high temperature.
• The vapor compression refrigeration cycle is a common
method for transferring heat from a low temperature to a
high temperature.

A Refrigerating Machine-
The Second law of Thermodynamics
• The purpose of a refrigerator is the removal of heat, called
the Cooling Load, from a low-temperature medium.
• The purpose of a heat pump is the transfer of heat to a
high-temperature medium, called the Heating Load.

Heat engine, Heat pump &
Refrigerating Machine.
Reversible heat engine may be converted into a refrigerating
machine by running it in reverse direction.
• For a Heat Pump, there is no difference in the cycle of
operation between a Refrigerator and a Heat pump. The
same machine can be utilized either
• To absorb heat from a cold body and reject it to the
surroundings (REFRIGERATING MACHINE)
• To absorb heat from the surroundings and reject it to a hot
body (HEAT PUMP)

The main difference between the refrigerating machine and
heat pump is in their operating temperatures.
• The Refrigerating Machine operates between the
ambient temperature and a low temperature.
• A heat pump operates between the ambient temperature
and high temperature.
Another essential difference in their useful function.
• In a Refrigerating Machine, the heat exchanger that
absorbs heat is connected to the conditioned space.
• In a Heat Pump, instead, the heat exchangers that rejects
heat is connected to the conditioned space.
The other heat exchanger in each case is connected to the surroundings.

Thus if a refrigerating machine, that is used for cooling
in summer, is to be used as a heat pump for heating in
winter, it will be necessary either
• To rotate the machine by 180˚ to interchange the
positions of the two heat exchangers between the space
and surroundings. Or
• To exchange the he functions of the two heat
exchangers by the operations of the of the valves

Energy Ratios or Coefficients of Performance
• The performance of a heat engine is described by its
thermal efficiency.
• The performance of a refrigerating machine or a heat
pump is expressed by the ratio of useful heat to work,
called the energy ratio or Coefficient of
Performance(COP).
• For a refrigerating machine, Cooling energy ratio or COP
for cooling
• For a heat pump, Heating energy ratio or COP for heating
Eq. 2.1
Eq. 2.2

Best Refrigeration Cycle: The Carnot Cycle Principle
• It is possible to show that the cooling energy ratio of a
refrigeration cycle working between the two temperatures
will be maximum when the cycle is reversible one.
• For example consider a reversible (R) and irreversible (I)
refrigerating machine , both working between two heat
reservoirs at temperatures at Temperatures To and Tk ,
and absorbing the same quantity of heat from the cold
reservoir at To as shown in Fig. 2.9(a)
Fig.2.9(a):
Reversible and
Irreversible Refrigerating machine

Best Refrigeration Cycle: The Carnot Cycle Principle
• To prove this, Let us assume that COP of the irreversible
machine is higher than the reversible machine. i.e.
• Hence,
• Also,
 Therefore,
• And
• Now, If the reversible refrigerating machine is made to
work as a heat engine and the irreversible refrigerating
machine continues to work as a refrigerating machine as
shown in Fig. 2.9(b).

Best Refrigeration Cycle:
The Carnot Cycle Principle
• The resultant combined system will work as a continuous
motion machine of second kind taking heat equal to
from the hot reservoir and converting it completely into work.
• Thus, violating the Kelvin-Planck statement of the second
law applicable to heat engines as shown in the Fig.2.10.
Fig.2.9(b):Reversible refrigerating machine working as a heat engine
In combination with irreversible refrigerating machine

Best Refrigeration Cycle:
The Carnot Cycle Principle
• It is therefore, concluded that a refrigeration cycle
operating reversibly between two heat reservoirs has the
highest coefficient of performance.
• All the reversible refrigeration cycles have the same
COP.
• These are the two corollaries of Second law comprising
the Carnot principle.
Fig.2.10: Combined system resulting in a perpetual motion machine
Thus violating the Second law

Reversed Carnot Cycle
• We know that reversible refrigeration has the maximum
COP.
• A reversible heat engine can be reversed in operation to
work as a refrigerating machine.
• Sadi Carnot, in 1824, proposed a reversible heat-engine
cycle as a measure of maximum possible conversion of
heat into work.
• A reversed Carnot cycle can therefore be employed as a
reversible refrigeration cycle, which would be a measure
of maximum possible COP of a refrigerating machine.
• This refrigerating machine operate between two
temperatures To of refrigeration and Tk of heat rejection.

Reversed Carnot Cycle … Contd.
A reversed Carnot Cycle is shown in the Fig.2.11.
Fig.2.11: A Reversed Carnot Cycle

• The areas on the T-s diagram, representing the heat
transfers and work done in the cycle as follows:
• Hence, we obtain Carnot values of COP for cooling and
heating as

Effect of Operating temperatures
To obtain the max. possible COP in any application,
• The cold body temperature should be as high as
possible.
• The hot body temperature should be as low as possible

The Inequality of Clausius
• The inequality of Clausius is a consequence of
the second law of thermodynamics.
• Q is the heat transfer to or from the system.
• T is the absolute temperature at the boundary.
• The symbol is the cyclic integral
0 T
Q


The Cyclic Integral
• The cyclic integral indicates
that the integral should be
performed over the entire
cycle and over all parts of
the boundary.
2 3 4 1
1 2 3 4
Q Q Q Q
T T T T
   
      
Q
T

Ñ

The Cyclic Integral
0 0H L
H L
Q Q
T T
   
Q
T

Ñ
2 3 4 1
1 2 3 4
Q Q Q Q
T T T T
   
      
H L
H L
Q Q
T T
 

Derivation of Clausius Inequality
IrreversibleReversible
Heat Engine
Refrigeration
Q
T

Ñ
0 T
Q

The Cyclic Integral of
Reversible Heat Engine
00 0H L
H L
Q Q
T T
   
H H
L L
Q T
Q T

Q
T

Ñ
2 3 4 1
1 2 3 4
Q Q Q Q
T T T T
   
      
H L
H L
Q Q
T T
 
Since

Irreversible Heat Engine
irr revW W
H L
H L
Q Q
T T

   H L H Lirr rev
Q Q Q Q  
Q
T

Ñ
H L
H L
Q Q
T T
 
We cannot use this
It is Irreversible
H L irr H L revQ Q Q Q  
L irr L revQ Q
H Lirr
H L
Q Q
T T
 0

Reversible Refrigerator
00 0L H
L H
Q Q
T T
   
H H
L L
Q T
Q T

Q
T

Ñ
2 3 4 1
1 2 3 4
Q Q Q Q
T T T T
   
      
L H
L H
Q Q
T T
 
Since

Irreversible Refrigerator
irr revW W
H L
H L
Q Q
T T

   H L H Lirr rev
Q Q Q Q  
Q
T

Ñ
H L
H L
Q Q
T T
  
We cannot use this
It is Irreversible
H irr L H rev LQ Q Q Q  
H irr H revQ Q
H irr L
H L
Q Q
T T
  0

Derivation of Clausius Inequality
IrreversibleReversible
< 00=Heat Engine
< 00=Refrigeration
Q
T

Ñ
0 T
Q
The equality in the Clausius inequality holds for totally or
just internally reversible cycles and the inequality for the
irreversible ones.

The Inequality of Clausius
• The Clausius inequality gives the basis for two
important ideas
– Entropy (S)
– Entropy generation (Sg)
• These two terms gives quantitative evaluations
for systems from second law perspective.

All paths are arbitrary
0
Q
T

Ñ
2 2
1 1A C
Q Q
T T
    
   
   
 Subtracting gives
2 1
1 2
0
C B
Q Q
T T
    
     
   
 
For reversible cycle A-B
2 1
1 2
0
A B
Q Q
T T
    
     
   
 
For reversible cycle C-B
0
Q
T

Ñ
Since paths A and C are arbitrary, it follows that the integral of Q/T
has the same value for ANY reversible process between the two sates.
Q
the quantity is independent of the path and dependent on the end states only
T

 
Derivation of Entropy (Reversible Process)

work & heat are dependent on path Path functions
Recall are independent of path
properties Point functions
and depend on state only





 
is a thermodynamic property
we call it entropy S
δQ
T
 
Entropy (the unit)
S = entropy (kJ/K); s = specific entropy (kJ/kg K)
 












2
1
12gintegratin
revrev T
Q
SS
T
Q
dS
 S2 – S1 depends on the end
states only and not on the path,
 it is same for any path
reversible or irreversible
Derivation of Entropy (Reversible Process)

2 1
1 2
for cycle A-B (reversible)
0
A B
Q Q Q
T T T
     
     
   
  Ñ
2 1
1 2
for path C-B (irreversible)
0
C B
Q Q Q
T T T
     
     
   
  Ñ
2 2
1 1
comparing gives
A C
Q Q
T T
 



    
   
   
 
{ {
2 2 2
1 1 1
reversible it is a
property
but A C
A
δQ
dS dS
T
 
  
 
  
in general
δQ
dS
T
 
2 2
1 1C
C
δQ
dS
T
 
   
 
 
2
2 1 1
or
δQ
S S
T
  
equality for reversible
inequality for irreversible
Consider 2 cycles AB is reversible and CB is irreversible
Derivation of Entropy (Irreversible Process)

2nd law of thermodynamics for a closed system
0 for irreversible process
entropy generation
0 for a reversible process
genS

 

In any irreversible process always entropy is generated (Sgen > 0)
due to irreversibility occurring inside the system.
gen
Q
dS S
T

 
2
2 1 1 gen
Q
S S S
T

   gen
for any process,
with S 0



This can be written out in a common form as an equality
or
Entropy Balance Equation for a closed system
δQ
dS
T

2
2 1 1
or
δQ
S S
T
  
equality for reversible
inequality for irreversible
Derivation of Entropy (Any Process)

Chapter 1 introduction

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Chapter 1 introduction