Basic of thermodynamics section a

1
Section A
Basic Thermodynamics
By
Priyanka Singh
M.Tech (Applied Mechanics)
Motilal Nehru National Institute of Technology, Allahabad

Nomenclature
 A area (m2
)
 CP specific heat at constant
pressure (kJ/(kg⋅K))
 CV specific heat at constant volume
(kJ/(kg⋅K))
 COP coefficient of performance
 d exact differential
 E stored energy (kJ)
 e stored energy per unit mass
(kJ/kg)
 F force (N)
 g acceleration of gravity
( 9.807 m/s2
)
 H enthalpy (H= U + PV) (kJ)
 h specific enthalpy (h= u + Pv)
(kJ/kg)
 h convective heat transfer
coefficient (W/(m2
⋅K)
 K Kelvin degrees
 k specific heat ratio, CP/CV
 k 103
 kt thermal conductivity (W/(m-°C))
 M molecular weight or molar mass
(kg/kmol)
 M 106
 m mass (kg)
 N moles (kmol)
 n polytropic exponent (isentropic
process, ideal gas n = k)
 η isentropic efficiency for turbines,
compressors, nozzles
 ηth thermal efficiency (net work
done/heat added)
 P pressure (kPa, MPa, psia, psig)
 Pa Pascal (N/m2
)
2

Nomenclature con’t
 Qnet net heat transfer (∑Qin - ∑Qout)
(kJ)
 qnet Qnet /m, net heat transfer per
unit mass (kJ/kg)
 R particular gas constant
(kJ/(kg⋅K))
 Ru universal gas constant
(= 8.314 kJ/(kmol⋅K) )
 S entropy (kJ/K)
 s specific entropy (kJ/(kg⋅K))
 T temperature ( °C, K, °F, R)
 U internal energy (kJ)
 u specific internal energy
(kJ/(kg ⋅K))
 V volume (m3
)
 volume flow rate (m3
/s)
 velocity (m/s)
 specific volume (m3
/kg)
 v molar specific volume (m3
/kmol)
 X distance (m)
 X exergy (kJ)
 x quality
 Z elevation (m)
 Wnet net work done [(∑Wout -
∑Win)other + Wb] (kJ)where Wb =
for closed systems and 0 for
control volumes
 wnet Wnet /m, net work done per unit
mass (kJ/kg)
 Wt weight (N)
 δ inexact differential
 ε regenerator effectiveness
 ϕ relative humidity
 ρ density (kg/m3
)
 ω humidity ratio
3
V
V
v

Subscripts, superscripts
 A actual
 B boundary
 F saturated liquid state
 G saturated vapor state
 fg saturated vapor value
minus saturated liquid value
 gen generation
 H high temperature
 HP heat pump
 L low temperature
 net net heat added to system
or net work done by system
 other work done by shaft and
electrical means
 P constant pressure
 REF refrigerator
 rev reversible
 s isentropic or constant
entropy or reversible, adiabatic
 sat saturation value
 v constant volume
 1 initial state
 2 finial state
 i inlet state
 e exit state
 ⋅ per unit time
4

6
The study of thermodynamics is concerned with the ways energy is stored within a
body and how energy transformations, which involve heat and work, may take place.
One of the most fundamental laws of nature is the conservation of energy principle. It
simply states that during an energy interaction, energy can change from one form to
another but the total amount of energy remains constant. That is, energy cannot be
created or destroyed.
This review of thermodynamics is based on the macroscopic approach where a large
number of particles, called molecules, make up the substance in question. The
macroscopic approach to thermodynamics does not require knowledge of the
behavior of individual particles and is called classical thermodynamics. It provides a
direct and easy way to obtain the solution of engineering problems without being
overly cumbersome.
A more elaborate approach, based on the average behavior of large groups of
individual particles, is called microscopic approach or statistical thermodynamics.

Closed, Open, and Isolated Systems
7
A thermodynamic system, or simply system, is defined as a quantity of matter or a
region in space chosen for study.
The region outside the system is called the surroundings.
The real or imaginary surface that separates the system from its surroundings is
called the boundary. The boundary of a system may be fixed or movable.
Surroundings are physical space outside the system boundary.
System + Surroundings = Universe
Type of System Energy Transfer Mass Transfer Examples
Closed System Yes No Piston cylinder w/o valves
Open System Yes Yes Pump, Compressor, Boiler, Turbine
Isolated System No No Universe, Insulated coffee case

8
A closed system consists of a fixed amount of mass and no mass may cross the
system boundary. The closed system boundary may move.
Examples of closed systems are sealed tanks and piston cylinder devices (note the
volume does not have to be fixed). However, energy in the form of heat and work
may cross the boundaries of a closed system.

9
An open system, or control volume, has mass as well as energy crossing the
boundary, called a control surface. Examples of open systems are pumps,
compressors, turbines, valves, and heat exchangers.
An isolated system is a general system of fixed mass where no heat or work may
cross the boundaries. An isolated system is a closed system with no energy crossing
the boundaries and is normally a collection of a main system and its surroundings that
are exchanging mass and energy among themselves and no other system.
Isolated System Boundary
Mass
System
Surr 3
Mass
Work
Surr 1
Heat = 0
Work = 0
Mass = 0
Across
Isolated
Boundary Heat
Surr 2
Surr 4

10
Since some of the thermodynamic relations that are applicable to closed and open
systems are different, it is extremely important that we recognize the type of system
we have before we start analyzing it.
P
V
T
Smell
Taste
Not measurable
Gas
Any measurable characteristic of a system in equilibrium is called a property.
The property is independent of the path used to arrive at the system condition.
Some thermodynamic properties are pressure P, temperature T, volume V, and
mass m.
Properties may be intensive or extensive.
Extensive properties are those that vary directly with size and mass of the system.
Some Extensive Properties: mass, volume, total energy and mass dependent
property
Properties of a System

11
Intensive properties are those that are independent of size. Some Intensive
Properties: temperature, pressure, age, color and any mass independent property.
Note: Extensive properties per unit mass are intensive properties. For example, the
specific volume v, defined as






==
kg
m
m
V
mass
Volume
v
3
and density ρ, defined as






== 3
m
kg
V
m
volume
mass
ρ
are intensive properties.

12
State, Process and Equilibrium
Condition of a system that completely describes the system is known as state of the
system. At a given state all of the properties are known; changing one property
changes the state.
Any change of state is known as process.
Equilibrium
A system is said to be in thermodynamic equilibrium if it maintains thermal (uniform
temperature), mechanical (uniform pressure) and chemical equilibrium (uniform
chemical potential).

13
Process
Any change from one state to another is called a process. During a quasi-equilibrium
or quasi-static process the system remains practically in equilibrium at all times. We
study quasi-equilibrium processes because they are easy to analyze (equations of
state apply) and work-producing devices deliver the most work when they operate on
the quasi-equilibrium process.
In most of the processes that we will study, one thermodynamic property is held
constant. Some of these processes are
Constant Pressure
Process
Water
F
System
Boundary
Process Property held
constant
isobaric pressure
isothermal temperature
isochoric volume
isentropic Entropy

14
We can understand the concept of a constant pressure process by considering the
above figure. The force exerted by the water on the face of the piston has to equal
the force due to the combined weight of the piston and the bricks. If the combined
weight of the piston and bricks is constant, then F is constant and the pressure is
constant even when the water is heated.
We often show the process on a P-V diagram as shown below.

15
Cycle
A process (or a series of connected processes) with identical end states is called a
cycle. Below is a cycle composed of two processes, A and B. Along process A, the
pressure and volume change from state 1 to state 2. Then to complete the cycle, the
pressure and volume change from state 2 back to the initial state 1 along process B.
Keep in mind that all other thermodynamic properties must also change so that the
pressure is a function of volume as described by these two processes.
Process
B
Process
A
1
2
P
V

16
Temperature
Although we are familiar with temperature as a measure of “hotness” or “coldness,” it
is not easy to give an exact definition of it. However, temperature is considered as a
thermodynamic property that is the measure of the energy content of a mass. When
heat energy is transferred to a body, the body's energy content increases and so
does its temperature. In fact it is the difference in temperature that causes energy,
called heat transfer, to flow from a hot body to a cold body. Two bodies are in
thermal equilibrium when they have reached the same temperature
The temperature scales used in the SI and the English systems today are the Celsius
scale and Fahrenheit scale, respectively. These two scales are based on a specified
number of degrees between the freezing point of water ( 0°C or 32°F) and the boiling
point of water (100°C or 212°F) and are related by
T F T C° ° +=
9
5
32

If a body ‘A’ is in thermal equilibrium with body ‘B’ and body ‘B’ is
in thermal equilibrium ‘C’ separately. Then body ‘A’ and body ‘C’ are
in thermal equilibrium
if TA=TB and TB=TC,
then TA=TC
In zeroth law of thermodynamics one body acts as thermometer.
B
CA

Thermometric Principle
18
Type of Thermometer Thermometric Property
Resistance Thermometer Resistance
Thermocouple emf (Voltage)
Constant Volume Thermometer Pressure
Constant Pressure Thermometer Volume
PV= mRT
Since for a given gas m and R is constant. So now we can write:
T=ƒ (P,V)
If P= constant (say, P=2 bar), then T= (V)ɸ
In thermometric principle, the property which changes with temperature is
found first and with the help of this property temperature is found.
The property which helps in finding the temperature is known as thermometric
property.

19
Example 1-6
Water boils at 212 °F at one atmosphere pressure. At what temperature does water
boil in °C.
T = ( ) ( )T F F
C
F
C° − = − °
°
°
= °32
5
9
212 32
5
9
100
Like pressure, the temperature used in thermodynamic calculations must be in
absolute units. The absolute scale in the SI system is the Kelvin scale, which is
related to the Celsius scale by
T K T= C + 273.15°
In the English system, the absolute temperature scale is the Rankine scale, which is
related to the Fahrenheit scale by
= F+ 459.67T R T°
Also, note that
T R T K= 1.8

20
Below is a comparison of the temperature scales.
This figure shows that that according to the International Temperature Scale of 1990
(ITS-90) the reference state for the thermodynamic temperature scale is the triple
point of water, 0.01 °C. The ice point is 0°C, but the steam point is 99.975°C at 1
atm and not 100°C as was previously established. The magnitude of the kelvin, K, is
1/273.16 of the thermodynamic temperature of the triple point of water.
Triple
point of
water
Boiling
point
of water
at 1 atm
-273.15 0
0.01 273.16
99.975 373.125
°C K
0
32.02 491.69
211.95
5
671.62
5
°F R
-459.67
Absolute
zero

21
The magnitudes of each division of 1 K and 1°C are identical, and so are the
magnitudes of each division of 1 R and 1°F. That is,
∆
∆
∆ ∆
T K T T
T T T
T R T
= ( C + 273.15) - ( C + 273.15)
= C - C = C
F
2 1
2 1
° °
° ° °
°
=

Lecture-16
Energy, Energy Transfer, and First Law of
Thermodynamics
22
By
Vineet Kumar Mishra
M.Tech (Fluid and Thermal)
Indian Institute of technology Guwahati

Energy
Consider the system shown below moving with a velocity, at an elevation Z
relative to the reference plane.

V
Z
General
System
CM
Reference Plane, Z=0

V
The total energy E of a system is the sum of all forms of energy that can exist within
the system such as thermal, mechanical, kinetic, potential, electric, magnetic,
chemical, and nuclear. The total energy of the system is normally thought of as the
sum of the internal energy, kinetic energy, and potential energy. The internal
energy U is that energy associated with the molecular structure of a system and the
degree of the molecular activity.
23

The kinetic energy KE exists as a result of the system's motion relative to an external
reference frame. When the system moves with velocity the kinetic energy is
expressed as
KE m
V
kJ=
2
2
( )
The energy that a system possesses as a result of its elevation in a gravitational field
relative to the external reference frame is called potential energy PE and is expressed
as
PE mgZ kJ= ( )
where g is the gravitational acceleration and z is the elevation of the center of gravity
of a system relative to the reference frame. The total energy of the system is
expressed as
E U KE PE kJ= + + ( )
or, on a unit mass basis,

V
24

e
E
m
U
m
KE
m
PE
m
kJ
kg
u
V
gZ
= = + +
= + +
( )
2
2
where e = E/m is the specific stored energy, and u = U/m is the specific internal
energy. The change in stored energy of a system is given by
∆ ∆ ∆ ∆E U KE PE kJ= + + ( )
Most closed systems remain stationary during a process and, thus, experience no
change in their kinetic and potential energies. The change in the stored energy is
identical to the change in internal energy for stationary systems.
If ∆KE = ∆PE = 0,
∆ ∆E U kJ= ( )
25

Energy Transport by Heat and Work and the Classical Sign Convention
Energy may cross the boundary of a closed system only by heat or work.
Energy transfer across a system boundary due solely to the temperature difference
between a system and its surroundings is called heat.
Energy transferred across a system boundary that can be thought of as the energy
expended to lift a weight is called work.
Heat and work are energy transport mechanisms between a system and its
surroundings. The similarities between heat and work are as follows:
1.Both are recognized at the boundaries of a system as they cross the boundaries.
They are both boundary phenomena.
2.Systems possess energy, but not heat or work.
3.Both are associated with a process, not a state. Unlike properties, heat or work has
no meaning at a state.
4.Both are path functions (i.e., their magnitudes depends on the path followed during
a process as well as the end states.
26

Since heat and work are path dependent functions, they have inexact differentials
designated by the symbol δ. The differentials of heat and work are expressed as δQ
and δW. The integral of the differentials of heat and work over the process path gives
the amount of heat or work transfer that occurred at the system boundary during a
process. 2
12
1,
2
12
1,
(not Q)
(not )
along path
along path
Q Q
W W W
δ
δ
= ∆
= ∆
∫
∫
That is, the total heat transfer or work is obtained by following the process path and
adding the differential amounts of heat (δQ) or work (δW) along the way. The
integrals of δQ and δW are not Q2 – Q1 and W2 – W1, respectively, which are
meaningless since both heat and work are not properties and systems do not
possess heat or work at a state.
27

700
kPa
100
kPa
0.01 m3
0.03 m3
A sign convention is required for heat and work energy transfers, and the classical
thermodynamic sign convention is selected for these notes.
According to the classical sign convention, heat transfer to a system and work done
by a system are positive.
Heat transfer from a system and work done on system are negative. The system
shown below has heat supplied to it and work done by it.
In this study guide we will use the concept of net heat and net work.
The following figure illustrates that properties (P, T, v, u, etc.) are point functions, that
is, they depend only on the states. However, heat and work are path functions, that
is, their magnitudes depend on the path followed.
28

System
Boundary
Energy Transport by Heat
Recall that heat is energy in transition across the system boundary solely due to the
temperature difference between the system and its surroundings. The net heat
transferred to a system is defined as
Q Q Qnet in out= − ∑∑
Here, Qin and Qout are the magnitudes of the heat transfer values. In most
thermodynamics texts, the quantity Q is meant to be the net heat transferred to the
system, Qnet. Since heat transfer is process dependent, the differential of heat
transfer δQ is called inexact. We often think about the heat transfer per unit mass of
the system, Q. 29

q
Q
m
=
Heat transfer has the units of energy measured in joules (we will use kilojoules, kJ) or
the units of energy per unit mass, kJ/kg.
Since heat transfer is energy in transition across the system boundary due to a
temperature difference, there are three modes of heat transfer at the boundary that
depend on the temperature difference between the boundary surface and the
surroundings. These are conduction, convection, and radiation. However, when
solving problems in thermodynamics involving heat transfer to a system, the heat
transfer is usually given or is calculated by applying the first law, or the conservation
of energy, to the system.
An adiabatic process is one in which the system is perfectly insulated and the heat
transfer is zero.
30

Energy Transfer by Work
Electrical Work
The rate of electrical work done by electrons crossing a system boundary is called
electrical power and is given by the product of the voltage drop in volts and the
current in amps.
(W)eW V I=&
The amount of electrical work done in a time period is found by integrating the rate of
electrical work over the time period.
2
1
(kJ)eW V I dt= ∫
31

Mechanical Forms of Work
Work is energy expended by a force acting through a distance. Thermodynamic work
is defined as energy in transition across the system boundary and is done by a
system if the sole effect external to the boundaries could have been the raising of a
weight.
Mathematically, the differential of work is expressed as
δW F ds Fds= ⋅ =
 
cosΘ
here Θ is the angle between the force vector and the displacement vector.
As with the heat transfer, the Greek symbol δ means that work is a path-dependent
function and has an inexact differential. If the angle between the force and the
displacement is zero, the work done between two states is
∫ ∫==
2
1
2
1
12 FdsWW δ
32

Work has the units of energy and is defined as force times displacement or newton
times meter or joule (we will use kilojoules). Work per unit mass of a system is
measured in kJ/kg.
Common Types of Mechanical Work Energy (See text for discussion of these
topics)
•Shaft Work
•Spring Work
•Work done of Elastic Solid Bars
•Work Associated with the Stretching of a Liquid Film
•Work Done to Raise or to Accelerate a Body
Net Work Done By A System
The net work done by a system may be in two forms other work and boundary work.
First, work may cross a system boundary in the form of a rotating shaft work,
electrical work or other the work forms listed above. We will call these work forms
“other” work, that is, work not associated with a moving boundary. In
thermodynamics electrical energy is normally considered to be work energy rather
than heat energy; however, the placement of the system boundary dictates whether
33

Here, Wout and Win are the magnitudes of the other work forms crossing the
boundary. Wb is the work due to the moving boundary as would occur when a gas
contained in a piston cylinder device expands and does work to move the piston. The
boundary work will be positive or negative depending upon the process. Boundary
work is discussed in detail in Chapter 4.
to include electrical energy as work or heat. Second, the system may do work on its
surroundings because of moving boundaries due to expansion or compression
processes that a fluid may experience in a piston-cylinder device.
The net work done by a closed system is defined by
( ) botherinoutnet WWWW +−= ∑∑
( ) bothernetnet WWW +=
Several types of “other” work (shaft work, electrical work, etc.) are discussed in the
text.
34

Example 2-3
A fluid contained in a piston-cylinder device receives 500 kJ of electrical work as the
gas expands against the piston and does 600 kJ of boundary work on the piston.
What is the net work done by the fluid?
Wele =500 kJ Wb=600 kJ
( )
( )
( )
,
0 500 600
100
net net bother
net out in ele bother
net
net
W W W
W W W W
W kJ kJ
W kJ
= +
= − +
= − +
=
35

The First Law of Thermodynamics
The first law of thermodynamics is known as the conservation of energy principle. It states that
energy can be neither created nor destroyed; it can only change forms. Joule’s experiments
lead to the conclusion: For all adiabatic processes between two specified states of a closed
system, the net work done is the same regardless of the nature of the closed system and the
details of the process. A major consequence of the first law is the existence and definition of the
property total energy E introduced earlier.
The First Law and the Conservation of Energy
The first law of thermodynamics is an expression of the conservation of energy principle.
Energy can cross the boundaries of a closed system in the form of heat or work. Energy may
cross a system boundary (control surface) of an open system by heat, work and mass transfer.
A system moving relative to a reference plane is shown below where z is the elevation of the
center of mass above the reference plane and is the velocity of the center of mass.

V
Energyin
Energyout
z
System
Reference Plane, z = 0
CM

V
36

Normally the stored energy, or total energy, of a system is expressed as the
sum of three separate energies. The total energy of the system, Esystem
, is given as
For the system shown above, the conservation of energy principle or the first law
of thermodynamics is expressed as






=





−





systemtheofenergy
in totalchangeThe
systemtheleaving
energy
systemtheentering
energy TotalTotal
or
E E Ein out system− = ∆
E Internal energy Kinetic energy Potential energy
E U KE PE
= + +
= + +
Recall that U is the sum of the energy contained within the molecules of the system
other than the kinetic and potential energies of the system as a whole and is called
the internal energy. The internal energy U is dependent on the state of the system
and the mass of the system.
For a system moving relative to a reference plane, the kinetic energy KE and the
potential energy PE are given by
37

2
0
0
2
V
V
z
z
mV
KE mV dV
PE mg dz mgz
=
=
= =
= =
∫
∫



 
The change in stored energy for the system is
∆ ∆ ∆ ∆E U KE PE= + +
Now the conservation of energy principle, or the first law of thermodynamics for
closed systems, is written as
in outE E U KE PE− = ∆ + ∆ + ∆
If the system does not move with a velocity and has no change in elevation, it is
called a stationary system, and the conservation of energy equation reduces to
in outE E U− = ∆
Mechanisms of Energy Transfer, Ein and Eout
The mechanisms of energy transfer at a system boundary are: Heat, Work, mass
flow. Only heat and work energy transfers occur at the boundary of a closed (fixed
mass) system. Open systems or control volumes have energy transfer across the
control surfaces by mass flow as well as heat and work.
38

1. Heat Transfer, Q: Heat is energy transfer caused by a temperature difference
between the system and its surroundings. When added to a system heat transfer
causes the energy of a system to increase and heat transfer from a system
causes the energy to decrease. Q is zero for adiabatic systems.
2. Work, W: Work is energy transfer at a system boundary could have caused a
weight to be raised. When added to a system, the energy of the system increase;
and when done by a system, the energy of the system decreases. W is zero for
systems having no work interactions at its boundaries.
3. Mass flow, m: As mass flows into a system, the energy of the system increases
by the amount of energy carried with the mass into the system. Mass leaving the
system carries energy with it, and the energy of the system decreases. Since no
mass transfer occurs at the boundary of a closed system, energy transfer by mass
is zero for closed systems.
The energy balance for a general system is
( ) ( )
( ), ,
in out in out in out
mass in mass out system
E E Q Q W W
E E E
− = − + −
+ − = ∆
39

Expressed more compactly, the energy balance is
Net energy transfer Change in internal, kinetic,
by heat, work, and mass potential, etc., energies
( )in out systemE E E kJ− = ∆
14243 14243
or on a rate form, as
& & &E E E kWin out system− =
Rate of net energy transfer
by heat, work, and mass
Rate change in internal, kinetic,
potential, etc., energies
( )
1 24 34 124 34
∆
For constant rates, the total quantities during the time interval ∆t are related to the
quantities per unit time as
, , and ( )Q Q t W W t E E t kJ= ∆ = ∆ ∆ = ∆ ∆& & &
The energy balance may be expressed on a per unit mass basis as
( / )in out systeme e e kJ kg− = ∆
and in the differential forms as
40

( )
( / )
in out system
in out system
E E E kJ
e e e kJ kg
δ δ δ
δ δ δ
− =
− =
First Law for a Cycle
A thermodynamic cycle is composed of processes that cause the working fluid to
undergo a series of state changes through a process or a series of processes. These
processes occur such that the final and initial states are identical and the change in
internal energy of the working fluid is zero for whole numbers of cycles. Since
thermodynamic cycles can be viewed as having heat and work (but not mass)
crossing the cycle system boundary, the first law for a closed system operating in a
thermodynamic cycle becomes
net net cycle
net net
Q W E
Q W
− = ∆
=
41

Example 3-4
A system receives 5 kJ of heat transfer and experiences a decrease in energy in the
amount of 5 kJ. Determine the amount of work done by the system.
∆E= -5 kJ
Qin =5 kJ Wout=?
System
Boundary
We apply the first law as
( )
5
5
5 5
10
in out system
in in
out out
system
out in system
out
out
E E E
E Q kJ
E W
E kJ
E E E
W kJ
W kJ
− = ∆
= =
=
∆ = −
= − ∆
= − −  
=
42

The work done by the system equals the energy input by heat plus the decrease in
the energy of the working fluid.
Example 3-5
A steam power plant operates on a thermodynamic cycle in which water circulates
through a boiler, turbine, condenser, pump, and back to the boiler. For each kilogram
of steam (water) flowing through the cycle, the cycle receives 2000 kJ of heat in the
boiler, rejects 1500 kJ of heat to the environment in the condenser, and receives 5 kJ
of work in the cycle pump. Determine the work done by the steam in the turbine, in
kJ/kg.
The first law requires for a thermodynamic cycle
43

( )
Let and
2000 1500 5
505
net net cycle
net net
in out out in
out in out in
out in out in
out
out
Q W E
Q W
Q Q W W
W Q Q W
W Q
w q
m m
w q q w
kJ
w
kg
kJ
w
kg
− = ∆
=
− = −
= − −
= =
= − +
= − +
=
44
Energy Conversion Efficiencies
A measure of performance for a device is its efficiency and is often given the symbol
η. Efficiencies are expressed as follows:

Desired Result
Required Input
η =
How will you measure your efficiency in this thermodynamics course?
Efficiency as the Measure of Performance of a Thermodynamic cycle
A system has completed a thermodynamic cycle when the working fluid undergoes a
series of processes and then returns to its original state, so that the properties of the
system at the end of the cycle are the same as at its beginning.
Thus, for whole numbers of cycles
P P T T u u v v etcf i f i f i f i= = = =, , , , .
Heat Engine
A heat engine is a thermodynamic system operating in a thermodynamic cycle to
which net heat is transferred and from which net work is delivered.
45

The system, or working fluid, undergoes a series of processes that constitute the heat
engine cycle.
The following figure illustrates a steam power plant as a heat engine operating in a
thermodynamic cycle.
Thermal Efficiency, ηth
The thermal efficiency is the index of performance of a work-producing device or a
heat engine and is defined by the ratio of the net work output (the desired result) to
the heat input (the cost or required input to obtain the desired result).
46

ηth =
Desired Result
Required Input
For a heat engine the desired result is the net work done (Wout – Win) and the input is
the heat supplied to make the cycle operate Qin. The thermal efficiency is always
less than 1 or less than 100 percent.
ηth
net out
in
W
Q
=
,
where
W W W
Q Q
net out out in
in net
, = −
≠
Here, the use of the in and out subscripts means to use the magnitude (take the
positive value) of either the work or heat transfer and let the minus sign in the net
expression take care of the direction.
47

Example 3-7
In example 3-5 the steam power plant received 2000 kJ/kg of heat, 5 kJ/kg of pump
work, and produced 505 kJ/kg of turbine work. Determine the thermal efficiency for
this cycle.
We can write the thermal efficiency on a per unit mass basis as:
( )
,
505 5
2000
0.25 or 25%
net out
th
in
out in
in
w
q
kJ
w w kg
kJq
kg
η =
−
−
= =
=
Combustion Efficiency
Consider the combustion of a fuel-air mixture as shown below.
48

Air
Combustion
Chamber
Fuel
CnHm
CO2
H2O
N2
Qout = HVReactants
TR, PR
Products
PP, TP
Fuels are usually composed of a compound or mixture containing carbon, C, and
hydrogen, H2. During a complete combustion process all of the carbon is converted
to carbon dioxide and all of the hydrogen is converted to water. For stoichiometric
combustion (theoretically correct amount of air is supplied for complete combustion)
where both the reactants (fuel plus air) and the products (compounds formed during
the combustion process) have the same temperatures, the heat transfer from the
combustion process is called the heating value of the fuel.
The lower heating value, LHV, is the heating value when water appears as a gas in
the products.
2out vaporLHV Q with H O in products=
The lower heating value is often used as the measure of energy per kg of fuel
supplied to the gas turbine engine because the exhaust gases have such a high
temperature that the water formed is a vapor as it leaves the engine with other
products of combustion.
49

The higher heating value, HHV, is the heating value when water appears as a liquid
in the products.
2out liquidHHV Q with H O in products=
The higher heating value is often used as the measure of energy per kg of fuel
supplied to the steam power cycle because there are heat transfer processes within
the cycle that absorb enough energy from the products of combustion that some of
the water vapor formed during combustion will condense.
Combustion efficiency is the ratio of the actual heat transfer from the combustion
process to the heating value of the fuel.
out
combustion
Q
HV
η =
Example 3-8
A steam power plant receives 2000 kJ of heat per unit mass of steam flowing through
the steam generator when the steam flow rate is 100 kg/s. If the fuel supplied to the
combustion chamber of the steam generator has a higher heating value of 40,000
kJ/kg of fuel and the combustion efficiency is 85%, determine the required fuel flow
rate, in kg/s.
50

( )
100 2000
0.85 40000
5.88
steam outtosteamout
combustion
fuel
steam outtosteam
fuel
combustion
steam
steam
fuel
fuel
fuel
fuel
m qQ
HV m HHV
m q
m
HHV
kg kJ
s kg
m
kJ
kg
kg
m
s
η
η
= =
=
  
  
  =
 
  
 
=
&
&
&
&
&
&
Generator Efficiency:
electrical output
generator
mechanicalinput
W
W
η =
&
&
51

Power Plant Overall Efficiency:
, , ,
, ,
,
in cycle net cycle net electrical output
overall
fuel fuel in cycle net cycle
overall combustion thermal generator
net electricaloutput
overall
fuel fuel
Q W W
m HHV Q W
W
m HHV
η
η η η η
η
   
=       
   
=
=
& & &
& &&
&
&
Motor Efficiency:
mechanical output
motor
electricalinput
W
W
η =
&
&
52

Lighting Efficacy:
Amount of Light in Lumens
Watts of Electricity Consumed
Lighting Efficacy =
Type of lighting Efficacy, lumens/W
Ordinary Incandescent 6 - 20
Ordinary Fluorescent 40 - 60
Effectiveness of Conversion of Electrical or chemical Energy to Heat for
Cooking, Called Efficacy of a Cooking Appliance:
Useful Energy Transferred to Food
Energy Consumed by Appliance
Cooking Efficacy =
53

Lecture-17
The Second Law of Thermodynamics
By
Vineet Kumar Mishra

55
The second law of thermodynamics states that processes occur in a certain direction,
not in any direction. A process will not occur unless it satisfies both the first and the
second laws of thermodynamics. Physical processes in nature can proceed toward
equilibrium spontaneously:
Water flows down a waterfall.
Gases expand from a high pressure to a low pressure.
Heat flows from a high temperature to a low temperature.
The first law is concerned with the conversion of energy from one form to another.
Joule's experiments showed that energy in the form of heat could not be completely
converted into work; however, work energy can be completely converted into heat
energy. Evidently heat and work are not completely interchangeable forms of energy.
Furthermore, when energy is transferred from one form to another, there is often a
degradation of the supplied energy into a less “useful” form. We shall see that it is
the second law of thermodynamics that controls the direction processes may take and
how much heat is converted into work. A process will not occur unless it satisfies
both the first and the second laws of thermodynamics.
INTRODUCTION

© The McGraw-Hill Companies, Inc.,1998
Work Always Converts Directly and Completely
to Heat, But not the Reverse

57
Some Definitions
To express the second law in a workable form, we need the following definitions.
Heat (thermal) reservoir
A heat reservoir is a sufficiently large system in stable equilibrium to which and from which finite
amounts of heat can be transferred without any change in its temperature.
A high temperature heat reservoir from which heat is transferred is sometimes called a heat source.
A low temperature heat reservoir to which heat is transferred is sometimes called a heat sink.
Work reservoir
A work reservoir is a sufficiently large system in stable equilibrium to which and from which finite
amounts of work can be transferred adiabatically without any change in its pressure.

58
P P T T u u v v etcf i f i f i f i= = = =, , , , .
Heat Engine
A heat engine is a thermodynamic system operating in a thermodynamic cycle to
which net heat is transferred and from which net work is delivered.
The system, or working fluid, undergoes a series of processes that constitute the heat
engine cycle.
The following figure illustrates a steam power plant as a heat engine operating in a
Thermodynamic cycle
A system said to have undergone a cycle if the initial and final points are same, so
that the properties of the system at the end of the cycle are the same as at its
beginning. Thus, for whole numbers of cycles
Minimum number of process required for a cycle is Two.

59
Thermal Efficiency, ηth
The thermal efficiency is the index of performance of a work-producing device or a
heat engine and is defined by the ratio of the net work output (the desired result) to
the heat input (the costs to obtain the desired result).
ηth =
Desired Result
Required Input
For a heat engine the desired result is the net work done and the input is the heat
supplied to make the cycle operate. The thermal efficiency is always less than 1 or
less than 100 percent.

60
0 (Cyclic)
ηth
net out
in
W
Q
=
,
where
W W W
Q Q
net out out in
in net
, = −
≠
Here the use of the in and out subscripts means to use the magnitude (take the
positive value) of either the work or heat transfer and let the minus sign in the net
expression take care of the direction.
Now apply the first law to the cyclic heat engine.
Q W U
W Q
W Q Q
net in net out
net out net in
net out in out
, ,
, ,
,
− =
=
= −
∆
The cycle thermal efficiency may be written as

61
ηth
net out
in
in out
in
out
in
W
Q
Q Q
Q
Q
Q
=
=
−
= −
,
1
Cyclic devices such as heat engines, refrigerators, and heat pumps often operate
between a high-temperature reservoir at temperature TH and a low-temperature
reservoir at temperature TL.

62
The thermal efficiency of the above device becomes
ηth
L
H
Q
Q
= −1
Example:
A steam power plant produces 50 MW of net work while burning fuel to produce 150
MW of heat energy at the high temperature. Determine the cycle thermal efficiency
and the heat rejected by the cycle to the surroundings.
ηth
net out
H
W
Q
MW
MW
=
= =
,
.
50
150
0 333 or 33.3%
W Q Q
Q Q W
MW MW
MW
net out H L
L H net out
,
,
= −
= −
= −
=
150 50
100

63
Heat Pump
A heat pump is a thermodynamic system operating in a thermodynamic cycle that
removes heat from a low-temperature body and delivers heat to a high-temperature
body. To accomplish this energy transfer, the heat pump receives external energy in
the form of work or heat from the surroundings.
While the name “heat pump” is the thermodynamic term used to describe a cyclic
device that allows the transfer of heat energy from a low temperature to a higher
temperature, we use the terms “refrigerator” and “heat pump” to apply to particular
devices. Here a refrigerator is a device that operates on a thermodynamic cycle and
extracts heat from a low-temperature medium. The heat pump also operates on a
thermodynamic cycle but rejects heat to the high-temperature medium.
The following figure illustrates a refrigerator as a heat pump operating in a

64
Coefficient of Performance, COP
The index of performance of a refrigerator or heat pump is expressed in terms of the
coefficient of performance, COP, the ratio of desired result to input. This measure of
performance may be larger than 1, and we want the COP to be as large as possible.
COP =
Desired Result
Required Input

65
For the heat pump acting like a refrigerator or an air conditioner, the primary function
of the device is the transfer of heat from the low- temperature system.
For the refrigerator the desired result is the heat supplied at the low temperature and
the input is the net work into the device to make the cycle operate.
COP
Q
W
R
L
net in
=
,

66
Now apply the first law to the cyclic refrigerator.
( ) ( )
,
Q Q W U
W W Q Q
L H in cycle
in net in H L
− − − = =
= = −
0 0∆
and the coefficient of performance becomes
COP
Q
Q Q
R
L
H L
=
−
For the device acting like a “heat pump,” the primary function of the device is the
transfer of heat to the high-temperature system. The coefficient of performance for a
heat pump is
COP
Q
W
Q
Q Q
HP
H
net in
H
H L
= =
−,
Note, under the same operating conditions the COPHP and COPR are related by
COP COPHP R= +1

67
Second Law Statements
The following two statements of the second law of thermodynamics are based on the
definitions of the heat engines and heat pumps.
Kelvin-Planck statement of the second law
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.
The Kelvin-Planck statement of the second law of thermodynamics states that no
heat engine can produce a net amount of work while exchanging heat with a single
reservoir only. In other words, the maximum possible efficiency is less than 100
percent.
ηth < 100%

68
Heat engine that violates the Kelvin-Planck statement of the second law
Clausius statement of the second law
The Clausius statement of the second law states that it is impossible to construct a
device that operates in a cycle and produces no effect other than the transfer of heat
from a lower-temperature body to a higher-temperature body.

69
Heat pump that violates the Clausius statement of the second law
Or energy from the surroundings in the form of work or heat has to be expended to
force heat to flow from a low-temperature medium to a high-temperature medium.
Thus, the COP of a refrigerator or heat pump must be less than infinity.
COP < ∞

70
A violation of either the Kelvin-Planck or Clausius statements of the second law
implies a violation of the other. Assume that the heat engine shown below is violating
the Kelvin-Planck statement by absorbing heat from a single reservoir and producing
an equal amount of work W. The output of the engine drives a heat pump that
transfers an amount of heat QL from the low-temperature thermal reservoir and an
amount of heat QH + QL to the high-temperature thermal reservoir. The combination
of the heat engine and refrigerator in the left figure acts like a heat pump that
transfers heat QL from the low-temperature reservoir without any external energy
input. This is a violation of the Clausius statement of the second law.

71
Perpetual-Motion Machines
Any device that violates the first or second law of thermodynamics is called a
perpetual-motion machine. If the device violates the first law, it is a perpetual-motion
machine of the first kind. If the device violates the second law, it is a perpetual-
motion machine of the second kind.
Reversible Processes
A reversible process is a quasi-equilibrium, or quasi-static, process with a more
restrictive requirement.
Internally reversible process
The internally reversible process is a quasi-equilibrium process, which, once having
taken place, can be reversed and in so doing leave no change in the system. This
says nothing about what happens to the surroundings.
Totally or externally reversible process
The externally reversible process is a quasi-equilibrium process, which, once having
taken place, can be reversed and in so doing leave no change in the system or
surroundings.

72
Irreversible Process
An irreversible process is a process that is not reversible.
All real processes are irreversible. Irreversible processes occur because of the
following:
•Friction
•Unrestrained expansion of gases
•Heat transfer through a finite temperature difference
•Mixing of two different substances
•Hysteresis effects
•I2
R losses in electrical circuits
•Any deviation from a quasi-static process
The Carnot Cycle
French military engineer Nicolas Sadi Carnot (1769-1832) was among the first to
study the principles of the second law of thermodynamics. Carnot was the first to
introduce the concept of cyclic operation and devised a reversible cycle that is
composed of four reversible processes, two isothermal and two adiabatic.

73
The Carnot Cycle
Process 1-2:Reversible isothermal heat addition at high temperature, TH > TL, to the
working fluid in a piston-cylinder device that does some boundary work.
Process 2-3:Reversible adiabatic expansion during which the system does work as
the working fluid temperature decreases from TH to TL.
Process 3-4:The system is brought in contact with a heat reservoir at TL < TH and a
reversible isothermal heat exchange takes place while work of compression
is done on the system.
Process 4-1:A reversible adiabatic compression process increases the working fluid
temperature from TL to TH

74
You may have observed that power cycles operate in the clockwise direction when
plotted on a process diagram. The Carnot cycle may be reversed, in which it
operates as a refrigerator. The refrigeration cycle operates in the counterclockwise
direction.

75
Carnot Principles
The second law of thermodynamics puts limits on the operation of cyclic devices as
expressed by the Kelvin-Planck and Clausius statements. A heat engine cannot
operate by exchanging heat with a single heat reservoir, and a refrigerator cannot
operate without net work input from an external source.
Consider heat engines operating between two fixed temperature reservoirs at TH > TL.
We draw two conclusions about the thermal efficiency of reversible and irreversible
heat engines, known as the Carnot principles.
(a)The efficiency of an irreversible heat engine is always less than the
efficiency of a reversible one operating between the same two reservoirs.
η ηth th Carnot< ,
(b) The efficiencies of all reversible heat engines operating between the
same two constant-temperature heat reservoirs have the same efficiency.
As the result of the above, Lord Kelvin in 1848 used energy as a thermodynamic
property to define temperature and devised a temperature scale that is independent
of the thermodynamic substance.

76
The following is Lord Kelvin's Carnot heat engine arrangement.
Since the thermal efficiency in general is
ηth
L
H
Q
Q
= −1
For the Carnot engine, this can be written as
ηth L H L Hg T T f T T= = −( , ) ( , )1

77
Considering engines A, B, and C
Q
Q
Q
Q
Q
Q
1
3
1
2
2
3
=
This looks like
f T T f T T f T T( , ) ( , ) ( , )1 3 1 2 2 3=
One way to define the f function is
f T T
T
T
T
T
T
T
( , )
( )
( )
( )
( )
( )
( )
1 3
2
1
3
2
3
1
= =
θ
θ
θ
θ
θ
θ
The simplest form of θ is the absolute temperature itself.
f T T
T
T
( , )1 3
3
1
=
The Carnot thermal efficiency becomes
ηth rev
L
H
T
T
, = −1
This is the maximum possible efficiency of a heat engine operating between two heat
reservoirs at temperatures TH and TL. Note that the temperatures are absolute
temperatures.

78
These statements form the basis for establishing an absolute temperature scale, also
called the Kelvin scale, related to the heat transfers between a reversible device and
the high- and low-temperature heat reservoirs by
Q
Q
T
T
L
H
L
H
=
Then the QH/QL ratio can be replaced by TH/TL for reversible devices, where TH and TL
are the absolute temperatures of the high- and low-temperature heat reservoirs,
respectively. This result is only valid for heat exchange across a heat engine
operating between two constant temperature heat reservoirs. These results do not
apply when the heat exchange is occurring with heat sources and sinks that do not
have constant temperature.
The thermal efficiencies of actual and reversible heat engines operating between the
same temperature limits compare as follows:

79
Reversed Carnot Device Coefficient of Performance
If the Carnot device is caused to operate in the reversed cycle, the reversible heat
pump is created. The COP of reversible refrigerators and heat pumps are given in a
similar manner to that of the Carnot heat engine as
COP
Q
Q Q Q
Q
T
T T T
T
R
L
H L H
L
L
H L H
L
=
−
=
−
=
−
=
−
1
1
1
1
COP
Q
Q Q
Q
Q
Q
Q
T
T T
T
T
T
T
HP
H
H L
H
L
H
L
H
H L
H
L
H
L
=
−
=
−
=
−
=
−
1
1

80
Again, these are the maximum possible COPs for a refrigerator or a heat pump
operating between the temperature limits of TH and TL.
The coefficients of performance of actual and reversible (such as Carnot)
refrigerators operating between the same temperature limits compare as follows:
A similar relation can be obtained for heat pumps by replacing all values of COPR by
COPHP in the above relation.

81
Lecture-18
Entropy: A Measure of Disorder
By
Vineet Kumar Mishra

82
Entropy
The second law of thermodynamics leads to the definition of
a new property called entropy, which is a quantitative
measure of microscopic disorder for a system. Greater the
disorder greater is entropy and lesser will be efficiency.
The level of molecular disorder
(entropy) of a substance increases as it
melts and evaporates
S = K . ln(x)
S= entropy
K= Boltzmann constant
X= Disorder of molecule
Entropy is an extensive property. It
depends on number of molecules.

83
The definition of entropy is based on the Clausius
inequality, given by
where the equality holds for internally or totally reversible
processes and the inequality for irreversible processes.
Any quantity whose cyclic integral is zero is a property, and
entropy is defined as

84
Entropy change of a system
The entropy change of a system is the result of the process occurring within the
system.
Entropy change = Entropy at final state – Entropy at initial state
Mechanisms of Entropy Transfer, Sin and Sout
Entropy can be transferred to or from a system by two mechanisms: heat transfer
and mass flow. Entropy transfer occurs at the system boundary as it crosses the
boundary, and it represents the entropy gained or lost by a system during the
process. The only form of entropy interaction associated with a closed system is heat
transfer, and thus the entropy transfer for an adiabatic closed system is zero.
Heat transfer
The ratio of the heat transfer Q at a location to the absolute temperature T at that
location is called the entropy flow or entropy transfer and is given as

85
Entropy transfer by heat transfer S
Q
T
Theat: ( )= = constant
Q/T represents the entropy transfer accompanied by heat transfer, and the direction
of entropy transfer is the same as the direction of heat transfer since the absolute
temperature T is always a positive quantity.
When the temperature is not constant, the entropy transfer for process 1-2 can be
determined by integration (or by summation if appropriate) as
Work
Work is entropy-free, and no entropy is transferred by work. Energy is transferred by
both work and heat, whereas entropy is transferred only by heat and mass.
Entropy transfer by work Swork: = 0

Net Disorder (Entropy) Increases During Heat
Transfer
During a heat transfer process, the net disorder (entropy) increases (the increase
in the disorder of the cold body more than offsets the decrease in the disorder in
the hot body)
Entropy change is caused by heat transfer, mass flow, and irreversibilities. Heat
transfer to a system increases the entropy, and heat transfer from a system
decreases it. The effect of irreversibilities is always to increase the entropy.

The Entropy Change Between Two Specific States
The entropy change between two specific states is the same whether the process is
reversible or irreversible

The Entropy Change of an Isolated System
The entropy change of an isolated system is the sum of the entropy changes of its
components, and is never less than zero

The Entropy Change of a Pure Substance
The entropy of a pure substance is determined from the tables, just as for any
other property
Pure substances:
Any process: s = s2 - s1 [kJ/(kg-K)]
Isentropic process: s2 = s1
Incompressible substances:
Any process: s2 - s1 = Cav 1n [kJ/(kg-K)]
Isentropic process: T2 = T1
T2
T1

System Entropy Constant During Reversible-
adiabatic (isentropic) Process

91
Example:
Air, initially at 17o
C, is compressed in an isentropic process through a pressure ratio
of 8:1. Find the final temperature assuming constant specific.
For air, k = 1.4, and a pressure ratio of 8:1 means that P2/P1 = 8

92
Entropy Balance
The principle of increase of entropy for any system is expressed as an
entropy balance given by
or
S S S Sin out gen system− + = ∆
The entropy balance relation can be stated as: the entropy change of a system during
a process is equal to the net entropy transfer through the system boundary and the
entropy generated within the system as a result of irreversibilities.

Basic of thermodynamics section a

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