Thermodynamics

UNIT-I: BASIC CONCEPTS OF THERMODYNAMICS
Department of Mechanical Engineering
Course: BASIC THERMODYNAMICS

BASIC THERMODYNAMICS
UNIT-I
BASIC CONCEPTS OF THERMODYNAMICS
1. INTRODUCTION TO THERMODYNAMICS
 Thermodynamics is a science that deals with energy, transformation of energy and the
effects of transfer of energy on properties of substances. .
 Thermodynamics is the study of energy and the ways in which it can be used to
improve the lives of people around the world.
 The word “thermo-dynamics,” used first by Thomson (later Lord Kelvin)
 The word thermodynamics was derived from two Greek words, therme (means hot or
heat) and dynamikos (means power). Thermodynamics is the study of various
processes that change energy from one form (thermal energy) into another (work) and
uses variables such as pressure, volume and temperature.
 The basis of thermodynamics is primarily experimental observation. The outcome of
observations and logical reasoning have been formalized into certain basic laws, which
are known as zeroth, first, second and third laws of thermodynamics.
Zeroth law of thermodynamics − Fowler and Guggenheim in 1939
First law of thermodynamics − Joule, Mayer, and Colding in about 1845
Second law of thermodynamics − Carnot in 1824
Third law of thermodynamics − Nerst in 1907
 Engineers are creating things intended to meet human needs by using the principles
drawn from thermodynamics.
 Thermodynamics can also be defined as the science of Energy, Entropy and
Equilibrium.
 Engineering thermodynamics is the part of the science that applies to the design and the
analysis of devices and systems for energy conversion.
 Engineering Thermodynamics is related to the study of
 Interaction between system and its surroundings
 Energy and its transformation
 Relationship between heat, work and physical properties of the substance such as
pressure, volume, temperature etc.
 Feasibility of a process and the concept of equilibrium.

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2. THERMODYNAMIC SYSTEM
The objects studied in mechanics are called bodies, and we analyze them through the use of
free body diagrams. The objects studied in thermodynamics are called systems, and the free
body diagrams of mechanics are replaced by system diagrams in thermodynamics. The system
sketch in thermodynamics is equivalent to the free body diagram sketch in mechanics. The
term “system” is used to identify the subject of the analysis in thermodynamic study. Once the
system is defined then it is possible to study the relevant interactions with other systems.
The study of a thermodynamics problem starts with the identification of the system
involved in the problem. Every system is associated with boundary and surroundings. These
terms are discussed below.
Thermodynamic system:
A thermodynamic system may be defined as a region in space containing certain quantity
of matter whose behavior is being investigated.
An arbitrary thermodynamic system can be represented as shown in figure.
Surroundings:
Everything external to the system is called surroundings or environment
Boundary:
 The interface separating the system and its surroundings is known as system boundary.
 The boundary may be a physical boundary (such as the walls of a container) or some
imaginary surface enveloping the region.
 The boundary may be either fixed or moving.
 In fact, the boundary is the contact surface which is shared by both the system and the
surroundings.

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Universe:
 A system and its surroundings together comprise a Universe.
System + Surroundings = Universe
 The size of the Universe is infinite and it has no boundaries.
 The energy of Universe remains constant.
3. TYPES OF THERMODYNAMIC SYSTEMS
The investigation of the behavior of a system is mainly focused on interaction between the
system and surroundings. The interaction is usually in the form of mass transfer or energy
transfer. On the basis of mass transfer and energy transfer, there are three types of
thermodynamic systems namely closed system, open system and isolated system.
1. Closed System:
 The closed system is a system of fixed mass.
 There is no mass transfer across the system boundary. There may be energy transfer
into or out of the system.
 There is no mass transfer across the system boundary. There may be energy transfer
into or out of the system.
No Mass transfer
Examples:
 A certain quantity of fluid in a cylinder bounded by a piston constitutes a closed
system.
 The gas inside a closed balloon is a closed system.
Note:
i) The mass within the closed system remains the same and constant, though its volume can
change
ii) The physical nature and chemical composition of the mass may change.

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2. Open System:
 The open system is a system in which matter crosses the boundary of the system.
There may be energy transfer also.
 An open system has mass exchange with the surroundings along with the transfer of
energy in the form of heat and work.
 The mass within the system may change depending upon mass inflow and mass
outflow.
 Most of the engineering devices are generally open systems.
Examples: Air compressor, Boiler, Nozzles, turbines etc.
For example, an air compressor in which air enters at low pressure and leaves at high
pressure and also energy transfers take place across the system boundary.
3. Isolated System:
 Isolated system is a system in which there is no interaction between the system and
the surroundings.
 It is of fixed mass and energy, and there is no mass or energy transfer across the
system boundary.
 Example: Fluid enclosed in a perfectly
insulated closed vessel. (Thermos flask).

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4. PHASE
 If a quantity of matter is uniform or homogeneous throughout in physical structure and
chemical composition, it is called a phase.
 Uniformity of chemical composition means that the chemical composition does not
vary from one part of the system to another.
 Uniformity of physical structure means that the material is all gas or all liquid or all
solid.
 Based on phase change, a system may be classified as
(i) Homogeneous system
(ii) Heterogeneous system
(i) Homogeneous System: A system consisting of a single phase is called homogeneous
system.
Examples: Mixture of air and water vapour, Solution of ammonia in water,
Water + Nitric acid, Octane + Heptane.
(ii) Heterogeneous system: A system consists of more than one phase is called heterogeneous
system.
Examples: Water + steam, Water + gasoline, Water + mercury.
Note: In the case of heterogeneous system, the mass content is non-uniform.
5. CONTROL VOLUME
 A control volume is defined as any region in space which is separated from its
environment by a control surface which may be either physical or imaginary.
 The control surface is normally taken to be fixed in shape, position and orientation
relative to the observer.
 Heat and work interactions are present across the control surface and matter flows
continuously in and out of the control volume.
Consider a steam generator with water being fed to it at one side and steam being taken out of
it from the other side. During the continuous operation of steam formation, the region has a
constant volume. Its boundary does not change even though there occurs mass flow across the
control surface. Since the mass crosses the system boundary, this arrangement represents an
open system.

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If the volume of the open system remains constant, then this volume is called control volume.
Note: In the case of control volume, both position and volume are fixed whereas in the case of
open system both position and volume could be changed.
6. MACROSCOPIC APPROACH AND MICROSCOPIC APPROACH
There are two approaches for investigating the behavior of a thermodynamic system.
(a) Macroscopic Approach
(b) Microscopic Approach
(a) Macroscopic Approach:
In the macroscopic approach
 Structure of the matter is not considered.
 No attention is focused on the behaviour of individual particles constituting the matter.
 The volumes considered are very large compared to molecular dimensions and the
system is regarded as continuum.
 Study is made of overall effect of several molecules.
 Only a few variables are used to describe the state of the matter under consideration.
 The values of the variables used to describe the state of the matter are easily
measurable.
For example under macroscopic approach, consider a certain amount of gas is trapped in a
circular cylinder, one can measure the volume occupied by the gas by measuring the diameter
and height of the cylinder. The pressure exerted by the gas can be measured with the help of a
pressure gauge. Its temperature can be measured with the help of a thermometer or a thermo
couple. Then the state of the gas can be described by specifying the pressure, volume and
temperature. Such a study is made in macroscopic approach. When we consider matter from
the macroscopic point of view, the subject is called Classical thermodynamics.

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Dr.K.G.DURGA PRASAD Page 7
PROFESSOR OF MECHANICAL ENGINEERING
ENGINEERING & TECHNOLOGY PROGRAM
GVP COLLEGE FOR DEGREE & P.G.COURSES (A), VISAKHAPATNAM, INDIA
(b) Microscopic Approach:
In the microscopic approach
 The complete knowledge of the structure of matter is necessary.
 Attention is focused on the behaviour of individual particles constituting the matter.
 The matter is considered to be comprised of a large number of tiny particles called
molecules.
 The overall behaviour of the matter is predicted by statistically averaging the behaviour
of individual particles.
 A large number of variables are needed for a complete specification of the state of
matter.
 Easy and precise measurement is not possible for the variables used to describe the
state of matter.
For example under microscopic approach, consider the same gas that is trapped in a circular
cylinder. The gas consists of a large number of small particles (molecules), each of which
moves at random with independent velocity. The state of each particle can be specified in
terms of the position coordinates and the momentum components .The position, velocity and
energy for each particle changes frequently as result of collisions. For each and every particle it
is required to find out position coordinates and momentum components to specify the state of
the whole gas. The behaviour of the gas is predicted by statistically averaging the behaviour of
individual particles. Such a study is made in microscopic approach.
When we consider matter from the microscopic point of view, the subject is called Statistical
thermodynamics.
Note:
(i) The results of microscopic and macroscopic analysis must not be different.
(ii) Engineering thermodynamics analysis is macroscopic and not microscopic.
(iii) Microscopic approach is complex, cumbersome and time consuming.
(iv) Macroscopic approach is more practical
(v) Microscopic view helps to explain certain phenomena which cannot be analyzed by
macroscopic approach.

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Differences between Macroscopic and Microscopic Approaches
Sl.
No
Macroscopic approach Microscopic approach
1 Structure of the matter is not considered
Complete structure of the matter should
be considered
2 No attention is focused on the behaviour
of individual particles
Attention should be focused on the
behaviour of individual particles
3 Study is made of overall effect of several
molecules
The overall behaviour of the matter is
predicted by statistically averaging the
behaviour of individual particles.
4 Less number of variables are needed to
describe a system.
More number of variables are needed to
describe a system
5 Properties considered in this approach are
easily measurable
Properties considered in this approach are
not easily measurable
6 Simple to study a system
Complex and time consuming to study a
system
7. CONCEPT OF CONTINUUM
The concept of continuum is very useful in dealing with Classical Thermodynamics. From
the macroscopic point of view, we are always concerned with volumes that are very large
compared to molecular dimensions. In fact, systems may contain several molecules. But under
macroscopic point of view, we are not concerned with the behavior of individual molecules
and we can treat the substance as being continuous, disregarding the action of individual
molecules. Therefore, it is always convenient to consider the system as a continuous
distribution of matter. This continuous distribution of matter is known as continuum.
Note:
This continuum concept is only a convenient assumption that loses validity when the mean free
path of the molecules approaches the order of magnitude of the dimensions of the vessel.
8. THERMDYNAMIC PROPERTY
 A thermodynamic property refers to the characteristic which can be used to describe the
condition or state of a system.
 In other words, thermodynamic properties are the coordinates to describe the state of a
system.
 Examples: pressure, volume, temperature, entropy etc.

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The salient aspects of a thermodynamic property:
 It is a measurable characteristic describing a system and helps to distinguish from one
system to another.
 It has a definite unique value when the system is in a particular state.
 It depends only on the state of the system.
 Thermodynamic properties are the state variables of the system.
 It does not depend on the path followed by the system.
 The differentials of a thermodynamic property are exact.
 Since a thermodynamic property is a function of the state of the system, it is referred to
as a state function or point function
9. TYPES OF THERMDYNAMIC PROPERTIES
There are two types of thermodynamic properties
1. Intensive properties
2. Extensive properties
1. Intensive properties:
The properties which are independent of the mass of the system are known as intensive
properties.
Examples: pressure, temperature, density, viscosity, thermal conductivity etc.
2. Extensive properties:
The properties which are depending on the mass of the system are known as extensive
properties. If mass is increased, the value of the extensive properties also increases.
Examples: volume, internal energy, entropy, enthalpy, weight etc.
Let us consider a system with the value of a property X
If 1 2 3
, ,
X X X etc denote the values of that property for various parts of the system, then
For an as intensive property, 1 2 3
X X X X
      
For an as extensive property, 1 2 3
X X X X
      
Note:
(i) An extensive property is additive in the sense that its value for the whole system is the
sum of the values for its parts
(ii) Extensive properties per unit mass are called specific extensive properties.
Examples: specific volume, specific enthalpy, specific internal energy etc.

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(iii) A given expression dZ Mdx Ndy
  would be a thermodynamic property if its
differential is exact. This means that it has to satisfy the following condition of exactness.
y
x
M N
y x
 
 
 

   
 
 
 
10. PROPERTIES COMMONLY USED IN THERMODYNAMICS
1. Pressure:
 Pressure is defined as the force per unit area
 If a force F is applied on an area A, and if this force is uniformly distributed over the
area, then the pressure P exerted is given by ,
F
P
A

 It is intensive property
 Units of pressure: CGS  dyne /cm2
, MKS  2
kgf/m
SI  2
N/m
 2
1N/m =1Pa
5 2
1bar = 10 N/m
1torr = 1 mm of Hg
2
1 mm of Hg = 133.4N/m
 Pressure exerted by a fluid column is given by P g h


Where ρ = density of the fluid
g = acceleration due to gravity
h = height of the fluid column
 The atmospheric air exerts a normal pressure upon all surfaces with which it is in
contact and it is known as atmospheric pressure.
 Atmospheric pressure is also known as barometric pressure. The atmospheric pressure
varies with the altitude and it can be measured by means of Barometer.
 The atmospheric pressure at sea level is called standard atmospheric pressure. The
value of standard atmospheric pressure is 1 atmosphere (1atm.).
 1 atm. = 760 mm of Hg = 10.3 m of water = 101.3 kPa
 Gauge pressure is the pressure more than atmospheric pressure
 Manometers, Pressure gauges are used to measure the pressure of fluids.

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 Vacuum pressure is the pressure below the atmospheric pressure. It is the negative
gauge pressure
 The state of zero pressure, where there is no matter in any form is called perfect
vacuum.
 Any pressure less than perfect vacuum is never possible.
 If the perfect vacuum is taken as reference point for the measurement of pressure is
referred to as the absolute zero pressure.
 Pressure is measured with respect to absolute zero pressure is known as Absolute
pressure.
 Absolute pressure = Atmospheric pressure + gauge pressure
abs atm gauge
P P P
 
Vacuum pressure = Atmospheric pressure – Absolute pressure
vacuum atm abs
P P P
 
2. Volume:
 Volume is the quantity of three-dimensional space enclosed by a closed surface.
 It is an extensive property. It is denoted by V
 Units of volume: CGS cm3
, MKS  3
m , SI  3
m
 The volume may also be expressed in litre (L)
 3 3
1L=10 m

3. Specific Volume:
 The specific volume is the volume per unit mass of the substance.
 It is intensive property
 It is defined by ratio of the volume occupied (V) and the mass of substance (m).
 It is denoted by v

V
v
m

 Units of volume : CGS cm3
/g , MKS  3
m / kg , SI  3
m / kg
4. Temperature:
 Temperature may be defined as the physical quantity which determines the degree of
hotness of a body and the direction of heat flow.

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 It is the property which is used to measure the degree of relative hotness or coldness of
a body.
 It is an intensive property of the system
 The unit of temperature in S.I. system: Kelvin (K)
 The temperature at which pressure and volume of the gas becomes zero is called
Absolute zero temperature.” It is equal to 273.16°C 273°C
   .
 Absolute zero temperature = 273.16°C 273°C
   = 0K
 No molecular activity takes place in the body at absolute zero temperature.
 The relation helps to convert a centigrade scale of temperature ( °C
t ) to absolute scale
of temperature (T) is  
C 273 K
T t
  
5. Density:
 It is defined as the mass of the fluid per unit volume. =
m
V

 The unit of density in S.I system is 3
kg/m
 It is the reciprocal of specific volume
 It is intensive property of the system
 Density of a fluid decreases with the increase of temperature.
11. STATE:
 The unique condition of a system is known as the state of the system. In other words,
state is the condition of a system at an instant of time, described by its thermodynamic
properties such as pressure, volume, temperature, density etc.
 By using thermodynamic properties as coordinates, the state of the system can be
represented by a point on property diagram.
Let us assume that the initial state of a system is described by  
1 1
,
P V and the final state of the
system is described by  
2 2
,
P V .Then the initial and
final states of the system can be represented on property
diagram as shown in figure.

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12. CHANGE OF STATE:
 Any operation in which one or more of the properties of the system changes is called
the change of state.
 When a system changes its state, then the properties of the system changes.
13. PATH:
 A thermodynamic system passing through a series of states constitutes a path.
 In other words, the locus of the series of states through which a system passes in going
from initial state to its final state constitutes the path followed by the system.
14. PROCESS:
 A complete specification of the path is referred to as a process.
 For example, let us assume that a system is initially at state 1. Due to the expansion of
the system, assume that it reaches the final state 2. Then, the line 1-2 represents the
process that has taken place.
15. CYCLE (CYCLIC PROCESS):
A thermodynamic cycle or cyclic process is defined as a series of state changes such that
the final state is identical with the initial state.

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Figure shows a thermodynamic cycle1 2 3 1
   consisting of the processes 1 2,2 3
A B
   
and 3 1
C
 
 An essential feature of the cycle is that the initial condition of the system is restored after
the process.
 The cyclic integral of any property of the system is equal to zero.
0
dX 


Where X  Any property of the system
16. THERMODYNAMIC EQUILIBRIUM:
A system is said to be in thermodynamic equilibrium only, if the system is incapable of
undergoing a spontaneous change in any macroscopic property when it is isolated.
When a system is in thermodynamic equilibrium, the value of the property is the same at all
points in the system.
A system will be in a state of thermodynamic equilibrium, if the conditions for the following
three types of equilibrium are satisfied.
(a) Mechanical equilibrium
(b) Chemical equilibrium
(c) Thermal equilibrium
 In the absence of any unbalanced force within the system itself and also between the
system and surroundings, the system is said to be in a state of mechanical equilibrium.
 If there is no chemical reaction or transfer of matter from one part of the system to another,
the system is said to exist in a state of chemical equilibrium.
 A system is said to be in thermal equilibrium, there should not be any temperature gradient
in the system.
When a system satisfies the above conditions of mechanical equilibrium, chemical equilibrium
and thermal equilibrium, then it is said to be in a state of thermodynamic equilibrium.
Whenever the conditions for any one of the three types of equilibrium are not satisfied, the
system is said to be in a state of non-equilibrium.
17. QUASI-STATIC PROCESS:
 If a process is carried out in such a way that at every instant, the system departs only
infinitesimally from the state of thermodynamic equilibrium, such a process is known
as Quasi-static process.

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Let us consider a system of gas contained in a cylinder. The system is initially in equilibrium
state which is represented by the properties 1 1 1
, ,
P V T .
The weight on the piston just balances the upward force exerted by the gas. If the weight is
removed, there will be an unbalanced force between the system and the surroundings. Because
of the gas pressure, the piston will move up till it hits the stopper or stops. The system again
comes to an equilibrium state, being described by the properties 2 2 2
, ,
P V T . But the intermediate
states passed through by the system are non-equilibrium states which cannot be described by
thermodynamic coordinates (properties).
Now, if the single weight on the piston is made up of several small pieces of weights and these
weights are removed one by one very slowly from the top of the piston.
At any instant of the upward travel of the piston, if the gas system is isolated, the departure of
the state of the system will be infinitesimally small. So every state passed through by the
system will be an equilibrium state.

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The locus of the series of such equilibrium states is called a quasi-static process or quasi-
equilibrium process and can be represented graphically by a continuous solid line as shown in
figure.
Hence a quasi-static process is a succession of equilibrium states.
 Infinite slowness is a characteristic feature of the quasi-static process
 A quasi-static process is also called a reversible process
18. REVERSIBLE PROCESS:
A reversible process is one which can be stopped at any stage and reversed so that the system
and surroundings are exactly restored to their initial states.
Figure shows a reversible process on X Y property diagram, which follows the path is1 2
 . If
the process is reversed, the path 2 1
 will be followed and that will restore the system and their
surroundings back to their respective initial states.
Conditions of Reversibility:
The following conditions need to be followed for a process to be reversible:
 There should be no friction
 The heat exchange to or from the system should be only through infinitely small
temperature difference
 The process should be Quasi-static
Note: In fact no real process is truly reversible, but some processes may approach reversibility.
Examples: (i) Motion of a body without friction (ii) expansion and compression of spring (iii)
Isothermal expansion or isothermal compression (iv) electrolysis

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19. IRREVERSIBLE PROCESS:
If a system passes through a sequence of non-equilibrium states during a process, then such
process is called an irreversible process. These non-equilibrium states cannot be located on
any property diagram, because each property does not have a unique value in the entire
system.
When an irreversible process is made to proceed in the back ward direction, the original state
of the system is not restored.
Irreversible process may be represented on property diagram by a broken line joining the initial
and final states as shown in figure.
Characteristics of Irreversible process:
 Irreversible process can be carried out in only one direction
 Irreversible process occurs at a finite range
 At any instant the system is never in equilibrium state during an irreversible process.
Examples: (i) spontaneous chemical reaction (ii) viscous flow of fluid (iii) free expansion
process (iv) throttling process (v) plastic deformation (vi) combustion of air and fuel
(vii) diffusion of gases (viii) flow of electricity through a resistance
Causes of Irreversibility:
The irreversibility for a process may be caused due to either one or both of the following
(i) Lack of thermodynamic equilibrium during the process
(ii) Involvement of dissipative effects during the process
20. ENERGY
Energy is the capacity to do work.
 Energy is a scalar quantity
 The S.I. unit of energy is Joule (J

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 Energy cannot be observed but can be recorded and evaluated by indirect
measurements
 When energy is added to or subtracted from the system, there occurs a change in one or
more properties of the system
21. CLASSIFICATION OF ENERGY
Energy may be broadly classified as follows:
22. STORED ENERGY (ENERGY IN STORAGE):
Stored energy is the energy contained within the system boundaries. Some of the examples of
stored energy are potential energy, kinetic energy, internal energy etc.
Potential Energy:
 The energy possessed by a system due to its position with respect to earth is known as
potential energy.
 When a body (system) of mass m is kept at an elevation z , then the potential energy of
the system is P.E m g z

Kinetic Energy:
 The energy possessed by a system by virtue of its motion is known as kinetic energy.
 The energy available for the system due to its motion is the kinetic energy.
 When a body (system) of mass m is moving with velocityc relative to the earth, then the
kinetic energy of the system is 2
1
K.E
2
mc

Note: Both potential energy and kinetic energy are the external forms of energies. They do not
depend up on the composition of the substance comprising the system.

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Internal Energy:
 Internal energy of a system is defined as the energy associated with the configuration
and motion of its molecules, atoms and sub atomic particles relative to its centre of
mass.
 Internal energy includes internal potential energy and internal kinetic energy. Internal
potential energy is the energy stored within the molecules, atoms and ions of the
substance and it is equal to the work done in separating them against binding forces of
mutual attraction. Internal kinetic energy is the energy of the particles which are moving
randomly in translation, rotation, vibration and spin.
23. ENERGY IN TRANSITION:
 Energy that is transferred to or from a system is referred to as energy in transit. It is the
energy which crosses the system boundaries.
 Energy can be transferred only when a driving force (potential) exists to cause the
transfer to take place.
 Energy in transit may be classified as below on the basis of potentials associated with
it.
Energy in transit Potential difference (Driving force)
Work (Mechanical) Pressure difference
Work (Electrical) Electrical potential difference
Heat Temperature difference
Note: The existence of a potential difference does not give guarantee that energy is being
transferred, because a path for the flow of energy must also exist simultaneously.
24. WORK TRANSFER:
 Work is one of the basic modes of energy transfer.
 In Mechanics, work is defined as the product of force  
F and displacement  
x in the
direction of the force. W F x
 
 In Thermodynamics, the work may be defined as follows:
“Work is said to be done by a system if the sole effect on things external to the system
can be reduced to the raising or lowering of a weight”.
Consider an electric storage battery as a system, whose terminals are connected to an electrical
resistance coil through a switch as shown in figure. The circuit external to the battery

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constitutes the surroundings. When the switch is closed for a certain period of time, the current
flows through the resistance coil, and as a result the resistance coil (surroundings) becomes
warmer. This clearly shows that, system has interaction with the surroundings.
Energy transfer takes place between the system and surroundings because of the potential
difference (not the temperature difference). Now according to the definition of work given in
Mechanics, there is no force which moves through a distance. Thus, no work is done by the
system. But according to the definition of work given in Thermodynamics, the work is done by
the system. Because , assume that the resistance coil is replaced by an electric motor with a
pulley on its shaft to wind up the rope on which a weight is suspended as shown in figure.

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If the current flow is the same as when the resistance coil was there, then there is absolutely no
difference between the two systems. If we assume the friction in the motor bearings is
negligible, the sole effect on things external to the system is then the raising of the weight.
Hence the system has done certain work.
 In Thermodynamics, work can also be defined as follows:
“Work is defined as the energy transferred across the boundary of a system, because of
only an intensive property difference other than temperature difference that exists
between the system and the surroundings”.
Note: In most of the engineering problems, the pressure difference is considered as intensive
property difference for work transfer.
Salient Aspects of Work Transfer:
 Work is energy in transit and can be identified only when the process is being executed
 Work does not exist either or after the interaction
 Work is never contained in a system
 Work is a boundary phenomenon. It is observed at the boundaries of the system
 Work is not a property of the system
 Work is a path function, because it is depending on the path followed by the system
 Work is an inexact differential
 As the work is an inexact differential, it is represented as W
 instead of dW
Note:
2
2 1
1
W W W
  
 but
2
1 2
1
W W
 
 or 1 2
W 
Sign Convention for Work Transfer:
 When work is done by the system , it is arbitrarily taken to be positive
 When work is done on the system , it is taken to be negative

UNIT-I
25. FORMS OF WORK:
The following forms of work may be considered in Thermodynamics:
1) Non- Flow work ( PdV work or Piston displacement work)
2) Flow work
3) Shaft work
4) Paddle wheel work or Stirring work
5) Electrical work
1. Non-Flow work:
The work done during a non flow process is called non-flow work. Non-flow process is the
process associated with the closed systems.
Let us considered a piston cylinder arrangement as shown in figure
Let the gas in the cylinder be a system having a state of thermodynamic equilibrium in the
initial position (1) described by the properties 1 1
,
P V . Let the piston move out to a new final
position (2), which is also a state of thermodynamic equilibrium described by the properties
2 2
,
P V .
At any intermediate position (state) in the travel of the system
Let P  Pressure of the gas (system)
V Volume of the gas
This intermediate state is also an equilibrium state.
Let A  Cross-sectional area of the piston
dl  Infinitesimal distance moved by the piston
Now force F PA

The infinitesimal amount of work done by the gas on the piston is W F dl
  
 
W PA dl
  

UNIT-I
 
W P Adl

    
W P dV

  
Where dV  infinitesimal displacement volume
The work done by the system during the process 1 2
 is
 
2 2
1 2
1 1
W W P dV

   
   
2
1 2
1
W P dV
 
This process is represented on P V
 diagram as shown in figure.
The term  
2
1
P dV
 represents the area under P V
 diagram. Therefore, the area under P V

diagram represents the magnitude of the work done during the process 1 2

The equation  
2
1 2
1
W P dV
  is valid when
 the system is a closed system
 the process should be quasi-static ( reversible)
 there are no viscous effects within the system
 the effects due to gravity, electric current and magnetism are negligible
Note:
 For any reversible process,  
2
1 2
1
W P dV
 
For any irreversible process,  
2
1 2
1
W P dV
 
 To calculate the work done by using  
2
1 2
1
W P dV
  , we should know the relationship
between pressure P and volume V

UNIT-I
2. Flow work:
 In any process, if there is a continuous mass flow rate across a system boundary,
then such a process is called flow process and the work done in such a process is
known as flow-work.
 The flow work is the work required to cause the flow of fluid in any passage. It
represents the work necessary to advance a fluid against the existing pressure.
Consider an open system as shown in Figure.
Let P be the pressure of the fluid in the plane of the imaginary piston, which acts in a
direction normal to it.
The work done on this imaginary piston is W PdV
 
Where dV  volume of the fluid element about to enter into the system
We know that, the specific volume
dV
v
dm
 dV vdm
 
Flow work    
flow
W P vdm
 
Flow work per unit mass is  flow
w Pv
 
3. Shaft work:
Consider a shaft which undergoes an angular displacement when it is subjected to a
constant torque.
Let   Angular displacement
T  Torque applied

UNIT-I
Then shaft work
2
1 2
1
W Td
 
Note: Shaft power T

N  Speed of the shaft in rpm.
  Angular velocity
We know
2
60
N

 
Therefore, Shaft power
2
60
NT


4. Paddle - wheel Work or Stirring Work:
Consider a fluid system which is stirred by means of a paddle wheel as shown in
figure.
As soon as the mass m moves downwards, the paddle wheel rotates. Then there is a
work transfer into the fluid system which gets stirred. Since, the volume of the fluid
system remains constant, 0 0
dV PdV
  

But, the differential work transfer equal to decrease in potential energy of the mass.
 
W mg dz
 
 
2
1 2 1 2
1
W W W mg dz

  
 

UNIT-I
5. Electrical work:
When a current flows through a resistor taken as a system, there is work transfer
into the system. This is because the current can drive a motor, the motor can drive a
pulley and the pulley can raise a weight.
Let C  Electric charge
I  Electric current
  Time taken for flow of current
Then
dC
I
d

Where dC is the charge crossing a boundary during time d . If E is the voltage
potential, then the work is  
W E dC
   
W EI d
 
   
2
1 2
1
W EI d
  
26. HEAT TRANSFER
 Heat is defined as the form of energy that is transferred across a system boundary by
virtue of a temperature difference.
 For heat transfer, the temperature difference is the driving force or the potential.
 Like work transfer, heat transfer depends only on the path followed by the system and
not on the end states and hence heat transfer is a path function.
 The unit of heat transfer in S.I. system is Joule 
J . Heat transfer is usually denoted by
the letter Q
Sign Convention for Heat Transfer:
 When heat flows into the system , the heat transfer is arbitrarily taken to be positive
 When heat flows out of the system , the heat transfer is taken to be negative

UNIT-I
27. COMPARISION BETWEEN HEAT AND WORK
Similarities:
 Heat and work are path functions
 They are not the properties of the system
 Both represent transient phenomenon. These energy interactions occur only
when a system is undergoing a change of state. They do not exist either before
or after the interaction.
 They represent the energy crossing the system boundary and hence they are a
boundary phenomenon.
 In S.I. system both have same units.
Dissimilarities:
 Pressure difference is the cause for work transfer, where as temperature
difference is the cause for heat transfer.
 Work is high grade energy, whereas heat is low grade energy.
28. ENTHALPY:
The sum of the internal energy and the product of pressure and volume is called enthalpy.
It is denoted by H . It is the property of a system.
Mathematically H U PV
 
The unit of enthalpy in S.I system is J
Specific enthalpy of a system is the enthalpy of the substance per unit mass.
Specific enthalpy,
H
h
m

The unit of specific enthalpy in S.I system is J/kg
29. SPECIFIC HEAT:
The amount of heat required to raise the temperature of unit mass of substance through 1°C is
called specific heat of the substance.
Gases possess two specific heats
(i) Specific heat at constant pressure  
p
C and
(ii) Specific heat at constant volume  
v
C

UNIT-I
Specific heat at constant pressure 
p
C : The amount of heat required to raise the temperature
of unit mass of gas through 1°C at constant pressure is called specific heat of the gas at
constant pressure.
The specific heat of a gas at constant pressure can also be defined as
p
p
h
C
T

 
  

 
It can be written as p
dh
C
dT

p
dh C dT
 
p
mdh mC dT
 
p
dH mC dT
 
Now integrating on both sides,
2 2
1 1
p
dH mC dT

   
2 1 2 1
p
H H mC T T
   
Thus, for a system undergoing a change of state from 1 to 2 through any process, the change in
enthalpy is given by  
2 1
p
H mC T T
  
Specific heat at constant volume  
v
C : The amount of heat required to raise the temperature
of unit mass of gas through 1°C at constant volume is called specific heat of the gas at
constant volume.
The specific heat of a gas at constant volume can also be defined as
v
v
u
C
T

 
  

 
It can be written as v
du
C
dT

v
du C dT
  v
mdu mC dT
 
v
dU mC dT
 
Now integrating on both sides,
2 2
1 1
v
dU mC dT

   
2 1 2 1
v
U U mC T T
   
Thus, for a system undergoing a change of state from 1 to 2 through any process, the change in
internal energy is given by  
2 1
v
U mC T T
  

UNIT-I
30. POINT AND PATH FUNCTIONS
Point Function:
If z is a function of two independent variables, x and y , expressed by the notation  
,
z f x y
 ,
then z is called a point function, because at each point on a plane of x y
 coordinates there is
a discrete value of z . The differential dz of a point function is an exact differential, and it can
be written as  
,
z f x y

y x
z z
dz dx dy
x y
 
 
 
   
 
 
   
This may be written as dz Mdx Ndy
 
Where M 
y
z
x

 
 

 
and N 
x
z
y
 

 

 
Then
2
(1)
M z M z
y y x y y x
    
 
     
 
     
 
2
(2)
N z N z
x x y x x y
 
    
     
 
     
 
As we know
2 2
z z
x y y x
 

   
Therefore from equations (1) and (2)
M N
y x
 

 
A differential in the form dz Mdx Ndy
  is an exact differential if and only if
M N
y x
 

 
For an exact differential dz ,
2
2 1
1
dz z z
 

Where  
2 2 2
,
z f x y
 and  
1 1 1
,
z f x y

The value of the integral is independent of the path followed on xy coordinates in going from
 
1 1
,
x y to 
2 2
,
x y . It would be the same for any of the path.
As the initial and end states are identical, 0
dz 


All thermodynamic properties are point functions. Therefore, the cyclic integral of property is
always zero. For any cyclic path if 0
dz 

 , z must be a property.

UNIT-I
Path Function:
If any quantity that depends on the path followed by the system when it is going from one
state to another, then such quantity is known as a path function.
If G is a path function, it is a quantity that depends on the path followed in going from state 1
 
1 1
,
x y to state 2  
2 2
,
x y , and no relation of the form ( , )
G f x y
 exists, because specifying a
value of x and a value of y does not determine a value of G .
The notation 1
G or 2
G should not be used and the value of G corresponding to a particular path
between states 1and 2 is not as the change in G , but simply as the value of G for that
particular path. This value of G is equal to the sum of the G values for any number of
segments into which the path may be divided. If these segments are made smaller and smaller,
the limiting value of G for one segment can be represented as G
 .
For any specific path between states 1 and 2, because of that a path function cannot be
evaluated in terms of end states alone and we may write
2
1 2
1
G G
 


Also for a path function,
2
2 1
1
G G G
  

Let us assume that there may be a relationship of the form G Mdx Ndy
  
As G is a path function, G
 is an inexact differential and hence
M N
y x
 

 
Note: (i) In general the cyclic integral of a path function is not equal to zero. 0
G
 


(ii) The heat and work are path functions
WORK IS A PATH FUNCTION:
Let us consider several reversible processes such as , and
A B C from state 1 to state 2 as shown
in figure.

UNIT-I
The work done in each case is represented by the area under the corresponding path. The path
followed by the system depends on the nature of the process. From the P-V diagram it is clear
that the areas under each path between the state points 1 and 2 are different. Therefore, the
work is different in each case and hence work transfer is depending on the path followed by the
system in between the state points 1 and 2. This suggests that work is not a property or a state
function, but it is a path function. The infinitesimal increment of work is an inexact
differential.
Hence work is a path function and is expressed by
2
1 2
1
W W

  and 1 2 2 1
W W W
 
Normal Temperature and Pressure (N.T.P.):
The conditions of temperature and pressure at 0°C (273K) and 760 mm of Hg respectively are
called normal temperature and pressure (N.T.P.)
Standard Temperature and Pressure (S.T.P.):
The temperature and pressure of any gas, under standard atmospheric conditions are known as
standard temperature and pressure. The standard temperature and pressure are taken as 15°C
(288K) and 760 mm of Hg respectively. Some countries take 25°C (298K) as temperature.

Thermodynamics

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