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Transcript of Basic Concept of Thermodynamics MORGAN
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Alamuri Ratnamala Institute of Engineering And Technology,
A. S. Rao Nagar, Sapgaon.
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For ARMIET Students Only .
University of Mumbai
Class : F. E. (All Branches of Engineering) Semester III
SUBJECT: Mechanical (ATD)
Periods per week
(Each of 60 min.)Lecture
Practical
Tutorial
Hours Marks
Evaluation System Theory Examination
Practical
Oral Examination
Term Work
Total
Basic Concept of Thermodynamics
Thermodynamics is defined as science of energy transfer and
its effect on the physical properties of substances.
Thermodynamics forms the basis for the study of vast varietyof devices. The laws of thermodynamics govern the principles of
energy conversion. These laws have been formulated from common
experiences. The application of thermodynamics laws and
principles are found in all field of energy conversion like in steam
and nuclear power plant, internal combustion engines, gas turbines,
air conditioning, refrigeration, jet propulsion, compressor, chemical
process plant, direct energy conversion devices etc.
This subject mainly deals with relations between properties
of working substance and energy interaction.
MACROSCOPIC AND MICROSCOPIC VIEW
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There are two approaches to the study of thermodynamic.
They are known as microscopic approach and macroscopic
approach.
In microscopic approach, the matter is composed of atoms
and molecules. Hence changes of events taking place at molecular
level are observed. For example if it is a gas, then each molecule at
a given instant has certain position, velocity and energy. Hence
behavior of gas can be described by summing up behavior of each
molecule. Hence there is a statistic approach to simplify the
problem. This approached is used in kinetic theory of gases.
In microscopic approach a certain quantity of matter is
considered without taking into accounts the events occurring at
molecular level. In this approach time averaged effect of the
particles observed and measured by instruments.
For example pressure exerted by gas on wall. Pressure result
from change in momentum of gas molecules as they collide against
wall. Hence its approach, we are not concerned with collision of
molecule but with time averaged value of force exerted on a unit
area of surface of wall. This is measured by pressure gauge.
THERMODYNAMIC SYSTEM
A thermodynamic system is defined as quantity of matter or
region in space upon which attention is concentrated while
analysing a problem.
Surrounding: Every thing external to system is called surrounding
or environment.
System Boundary: A system is separated from its surrounding by
a system boundary. A system boundary maybe fixed or movable.
Universe:
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System and surrounding combines from a universe.
Boundary Surrounding
TYPES OF SYSTEM
1. Closed System : A closed system is a system in which only energycross the boundary of system but there is no mass transfer across
system boundary. Hence, closed system is a system of fixed mass.
Example:
Boundary
Work Weight Surrounding
Cylinder
Piston
System Boundary
Surrounding
Heat
As shown in figure above a gas enclose in a cylinder and
piston machine represents a closed system. If gas is heated it will
expand and piston will rise. As piston rises boundary of system
moves. Hence, energy in the form of heat and mechanical work
crosses system boundary. But mass does not.
The closed system can be subjected to change in volume if
boundary is flexible.
System
SystemE
E
Gas
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2. Open System: It is a system in which both mass as well as energycan cross system boundary. Hence system and surrounding can
interact in terms of both mass as well as energy.
High pressure Exhaust Gas
Out Out.Work
Heat Work
Air from Air Fuel Heat
Atmosphere INCompressor Engine
In a compressor air is taken inside at low pressure and leaves at
high pressure and there are energy transfers across system boundary.
Energy Mass Surrounding
BoundarySystem Energy
Mars
Isolated System: It is a system in which neither mass nor energy
crosses the system boundary. Hence, system and surroundings are
completely isolated from each other. Hence, this system is of fixed
mass and fixed energy. Example: A hot liquid once enclosed in a
thermos flask represents isolated system.
S
ystem Surrounding
AirSystem
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THERMODYNAMIC PROPERTICES :
Every system has certain characteristics by which its
physical condition may be described. Such as volume, pressure,
temperature etc. these characteristics are known as properties of
system.
STATE OF SYSTEM:
When all the properties of system have certain definite
values. Then the system is said to exist in a state.
Hence a property of system defines the state of system.
P2 2
V2Piston
V1 1V1 System
Let us consider a gas system in cylinder and piston with a
weight being placed on piston. The properties of system pressure
and volume have definite values P1 and V1 respectively. Hence,
system is said to exist in a definite state described by point 1.CHANGE OF STATE :
Any operation during which one or more of properties of
system changes isolatedchange of state.
If in above example, if the weight placed on piston is lifted,
gas will expand and pistonmoves to position (2). Where properties
of system have values P2 and V2.
Hence, they describe another state of system. Hence
properties are state variable of system. They are the space
coordinates to describe the state of system.
Gas
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PATH OF CHANGE OF STATE:
The succession of states passed through during a change of
state is called path of change of state.
Example: In previous example if instead of lifting the weight
placed on piston at once, if weight is made of number of small
weights and every piece of weight is removed one by one then the
properties of system at intermediate points between 1 and 2 i.e. a, b,
c, .asdescribed which are known as succession of state.
PROCESS :
If path of change of state is completely specified (i.e. its
nature) then change of state is called process. Ex: Process 12,
constant pressure process.
CYCLE:
A thermodynamics cycle is defined as series of change of
states (processes) performed in such a way that the final state is
identical with initial state.
In above example if at position (2) of piston if all weights
that were lifted of same magnitude (mass) are kept back on piston
in different way then system can be brought back to state 1 by
following another path 2-1. Then processes 1-2 and 2-1 combine
constitute a thermodynamic cycle.
TYPES OF PROPERTIES :
Thermodynamic properties of system are classified into two
categories.
1. Intensive properties:These properties are those which are independent of mass of system
i.e. they do not change with mass. e.g. Pressure, temperature,
density etc.
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2. Extensive properties:These are those properties which depends upon mass of the e.g.
Volume, energy etc.
Specific extensive properties i.e. extensive properties pert unit mass
of system are also called as intensive properties.
e.g. Specific volume, Specific energy.
PURE SUBSTANCE :
Substance may exist in various from A phase is any homogeneous
form of substance that is solid, liquid and gases.
A pure substance is one that is homogeneous and in variable in
chemical composition. It may exist is one or more phase but
chemical composition remain same in all phases.
Ex. Liquid water or solid (ice) or water vapour (steam) is pure
substance.
Mixture of gases such as atmospheric air comprising nitrogen and
oxygen and other few gases such as carbon dioxide, organ can be
treated as pure substance as long ad it remain gas. Since its
chemical composition is constant. But if there is change of phase
like mixture of gaseous and liquid air then it can not be considered
as pure substance, because chemical composition of air in liquid
phase is different from that in vapour phase.
Liquid nitrogen and gaseous nitrogen mixture can be called pure
substance.
HOMOGENEOUS AND HETROGENEOUS SYSTEM :
The quantity of matter homogeneous through chemical composition
and physical structure is called a phase. A system constituting
single phase is called homogeneous system. System constituting of
more than one phase is known as heterogeneous system.
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THERMODYNAMIC EQUILIBRIUM :
A system is said to be in a state of thermodynamic
equilibrium when there is no spontaneous change in any of property
of system. Hence the system behaves as it is isolated from
surrounding when it is in state of thermodynamics equilibrium.
A system will be called in a state thermodynamic equilibrium
if the conditions for the following three types of equilibrium are
satisfied.
1. Mechanical Equilibrium :-In absence of any unbalance force within system itself or between
system and surrounding the system is said is said to be in a state of
mechanical equilibrium.
In example discussed earlier the system is in state of
equilibrium when piston is at 1 As weight is lifted, it creates
mechanical unbalance between system and surrounding. This
causes spontaneous change in pressure. The system attains again
state of equilibrium when piston is at (2) and pressure is P2.
Thus if an unbalanced force exist, either system or both
system and surrounding will undergo a change of state till
mechanical equilibrium is attained.
2. Chemical Equilibrium :If there is no chemical reaction or transfer of matter from one part
of system to another such as diffusion, solution, the system is said
to exist in a state of chemical equilibrium.
If there is any chemical reaction then it will change state of the
system and hence system will be in non equilibrium state. Like
combustion of fuel mixed with air.
Spark
Air
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3. Thermal Equilibrium :
When a system existing in mechanical equilibrium is
separated from its surrounding by a diathermia wall (diathermia
mean which allow heat to flow) and even though there is no
spontaneous change in any property of system. Then system is said
to exist in a state of thermal equilibrium.
A B
Let a system separated from its surrounding first by
adiabatic wall (which restricts flow of heat). When insulation is
removed, due to temperature difference that will flow from system
to surrounding and causes change in temperature. Hence, it is in
state of non equilibrium. The thermal equilibrium will be attained if
both system and surrounding reaches to same temperature to stop
further heat flow.
When condition of any one type of equilibrium is not
satisfied then system is said to be in non equilibrium state.
When system is in state of non equilibrium there is no value
of property which is represented by whole system as single fixed
value. Because thermodynamic properties are co ordinates which
are defined and significant only for thermodynamic equilibrium
state.
Gas Gas
System
undermechanical
&c
hemicalequilibrium
System
undermechanical
&c
hemicalequilibrium
Adiabatic
Wall
Surrounding
300C
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QUASSI STATIC PROCEES
P
2 Final stage P1 Equilibrium StateP2 V2
Piston Initial stage
P1 V1
Equilibrium
System Cylinder State
P2V1 V2
Let us consider gas system shown above enclosed in cylinder
and piston machine. Initially system is in thermodynamic
equilibrium state defined by properties P1 and V1 if the weight on
the piston is removed the piston will be pushed by gas due to
mechanical unbalance between system and surrounding. System
again comes to state of equilibrium when piston hits stopper where
its thermodynamic properties are P2 and V2. But intermediate states
passed through by system are non equilibrium states. Hence system
is in thermodynamic equilibrium only at states 1 and 2. Hence they
are joined by dotted lines.
P
2 P2 V2 P1 aWeight of b Equilibrium States
small mass c1 P1 V1 d Quassi Static Process
e (Reversible Process)f
gh
P2 2
V1 V2
If in above system the single weight is made up of small
parts and each part is removed one by one very slowly then at every
instant the system will be in a state of thermodynamic equilibrium
shown by a, b, c, d .. etc. In such a case the departure of state of
system from thermodynamic equilibrium is infinitely small.
Gas
W
Gas
W
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Hence every state system passed through is a thermodynamically
equilibrium state. Such a process which is locus of all equilibrium
state passed through by system is kwon as quassi static process or
reversible process. The characteristic, of quassi static process is
infinite slowness.
ZEROTH LAW OF THERMODYNAMICS :
Temperature : Temperature is property of the system which
distinguishes thermodynamics from other science. Temperature is
used to distinguish hot from cold. When two bodies are maintained
at same temperature then they are said to exist in thermal
equilibrium.
The zeroth law of thermodynamics provides basis for the
temperature measurement equipments.
System 1 System 2 System 1 System 2
x1 y1 x2 y2 x1 y1 x2 y2
Adiabatic Wall Diathermia Wall
(a) (b)
When two system are interacting through by an adiabaticwall [shown in figure (a)], then they are really isolated systems.
Properties in either system can be varied independent of other
system. They do not affect each other.
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When two systems are interacting across a diathermia wall
then change of state of one affects change of state of other. When
equilibrium is attained then it is assumed that at least one property
acquire a common value for both system. This property is named as
temperature. Hence two systems will attain thermal equilibrium
when equality of temperature is attained between them.
The zeroth law of thermodynamic states that when a body A
is thermal equilibrium with a body B and A is also separately in
thermal equilibrium with body C then both B and C will be in
thermal equilibrium with each other.
Adiabatic Wall
Diathermia Wall
Body A is a reference body which establish the thermal
equilibrium first with body B. then it establish the thermal
equilibrium with C Then after comparing both, thermal
equilibrium between B and C can be proved. The body A can be
any temperature measurement device like thermometer.
This law forms the basis for all temperature measurement
devices.
Temperature Measurement:
To measure temperature a reference body is used and a
certain physical characteristic of this body which changes with
temperature is selected. The changes in that selected characteristics
is taken as indication of change in temperature. This selected
characteristics is called thermometric property and the reference
body itself used for measuring temperature is called thermometer
(or any temperature measurement device)
Body B Body C
Body A
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Example: In liquid filled in glass thermometer, displacement of
mercury is taken as thermometric property.
Hence, if x is the thermometric property of a reference body
then for all systems which are in thermal equilibrium with it, let
temperature (x) is linear function of x.i.e. temperature (x) x.(x) = a x
Where a is any constant.
Hence if this reference body is brought in contact with two
bodies maintained at two different temperatures then let x1 and x2
be change in thermometric property of ref. body with body 1 and
body 2 respectively.
Hence (x1) = ax1 a = (x2) = ax2
(x2) = =
Hence temperatures on linear scale are to each other as ratio
of corresponding thermometric properties.
To calibrate temperature measurement device some reference
point is considered. Hence triple point of water i.e. a state at which
liquid water, ice and water vapour co-exist in thermodynamic
equilibrium is chosen as fixed point. The temperature at which this
state exists is arbitrarily assigned the value 273.160
k.
If t is triple pt. of water and xt thermometric property of
reference body when it is brought in contact with water at its triple
point then,
t = a xt
a =
a =
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Now let the ref. Body is brought in contact with any body whose
temperature is to be measured then,
= ax = Temperature of body whose temperature to be
measured.
x = Value of thermometric property of ref. body when it is
brought in contact with body whose temperature is to be
measured
= x.
Now let the ref. Body is brought in contact with any body
whose temperature is to be measured then
= ax = Temperature of body whose temperature to be measured.
x = Value of thermometric property of ref. body when it is brought
in contact with body whose temperature is to measured.
=
= 273.16
= 273.16
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TYPES OF THERMOMETER
CONSTANT VALUE GAS THERMOMETER
Inconstant volume gas thermometer the change in pressure
of gas is thermometric property. The temperature which is function
of pressure of gas (p) is related to thermometric property as
(p) = 273.16
Po Capillarity twx
Mercury Manometer Hg
Bulb
Flexible tube
Where, pt = Pressure of gas when thermometer is brought in
contact with water at triple point. This thermometer consist of a
small amount of gas enclosed in bulb B which is in communication
via capillary tube with one limb of mercury manometer one limb of
Hg manometer is open to atmosphere and it can be moved
vertically to adjust the Hg level so that mercury just touches L of
capillary. The pressure in the bulb is calculated by equation.
P = po + pHg g Z
Po = Atmospheric pressure.
pHg = Density of mercury = 13600 kg/m3
Z = Difference in the leveret of mercury across two limbs.
When the bulb of thermometer is brought in contact with
body whose temperature is to be measured, then after some time
bulb comes in thermal equilibrium with body. The gas which
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S
receives heat from body expands pushing mercury downward. The
flexible limb of manometer is adjusted so that mercury level just
touches L. The difference in Hg level i.e. Z is recorded and pressure
of gas in bulb is calculated as volume remain constant.
Constant Pressure Gas Thermometer :
It uses change in volume of gas due to change in temperature
as thermometric property which is related to temperature by,
(v) = 273.16 x Where, V = Volume of gas when thermometer is brought in contact
with body whose temp is to be measured.
Vt = Volume of gas when thermometer is in contact with
water at triple point.
For constant pressure gas thermometer the Hg level as shown
in figure has to be adjusted to keep Z constant and hence volume V
of gas would vary with the temperature of body.
ELECTRICAL RESISTANCE THERMOMETER
Wheat stone bridge
R.
In this thermometer the change in resistance of a metal wire
due to its change in temperature is the thermometric property. The
wire used may be platinum. Wire is incorporate in a wheat stone
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bridge circuit. When the temp change in resistance of wire which is
governed by relation
R = R0 (1 + At + Bt2)
Where, R0 = Resistance of platinum wire when it is in contact
with water at ice point.
A = Constant measured at steam point.
B = Constant measured at sulphur point. (4440C)
The temperature measured by electric resistance thermometer
has high degree of accuracy and hence it is used as a standard for
calibration of other thermometers.
THERMO COUPLE
Wire A
To potentiometerWire B
Copper Wires
Test Junction
Ice water mixture
ReferenceJunction
A thermocouple is made by forming two junctions by two
wires A and B dissimilar metals. Due to set back effect an e.m.f. is
generated in the circuit which depends upon the temperature
difference between reference (cold) junction and (hot) junction.
Hence e.m.f. is the thermometric property.
The e.m.f. generated is measured by micro voltmeter. The
two metals used depend upon the temperature range. Generally
combinations of copper-constantan, chromel-alumel and platinum
rhodium are used.
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To calibrate thermocouple the thermal e.m.f. at various
known temperature is measured. The relationship between e. m. f.
and temperature can be given by equation.
= a + bt + ct2+ dt2
= Thermal e. m. f.a, b, c, d = constants to be find out at different known temperature
such as antimony point (630.5
0
C), silver point (960.
80
C), Goldpoint (1063.0
0C)
The advantage of thermocouple over other thermometer is
that is has quick response. Since its comes to thermal equilibrium
with the system whose temperature is to be measured very fast
because its mass is small.
WORK TRANSFER
Work is considered to one of basis mode of energy transfer,
it brings change in properties of system.
The work is said to be done by a force as it acts upon a body
moving in the direction of force. Forces never produce a physical
effect except when coupled with motion and hence force is not
energy. The action of force through a distance is called mechanical
work.
Fan
Work
+ Surrounding
System Boundary
Battery
Meter
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Thermodynamics looks the work transfer in a border sense.
In thermodynamics work transfer is considered to be occurring
between systems and surrounding. The work is said to be done by a
system if sole effect on the thing external to system can be
expressed to the raising of a weight.
Pulley
Disp.
System Boundary
WorkWork
System System
Surrounding Surrounding
[W is positive] [W is negative]
(a) (b)
When the work is done by the system it is taken as positive
work transfer. When work is done upon the system [shown in
figure (b)] it is taken as negative work transfer.
Unit of work 1 Joule = 1 Nm
Rate of work i.e. work per unit time is known as power. Its
unit in S. I. system is Nm/sec or Joule/sec or watt.1 watt = 1 Joule /sec.
In M.K.S. system unit of power is horse power. 1HP = 746 watts.
Battery
Meter
W
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P dv WORK OR DISPLACEMENT WORK
P
System P1 1Quassi Static Process
A
P2
W11 A 2
P1 V1 P P2 V2 2d V1 dv V2
V
Let us consider a gas enclosed in piston and cylinder
machine. The system is in a state of thermodynamic equilibrium at
1 defined by properties P1, V1. Let piston moves to final position 2
which is also equilibrium state of system defined by properties P2,
V2by following a quassi-static path.
At any intermediate state during travel of piston let pressure
is P and volume V which is also an equilibrium state. Let for this
state the piston has moved by an infinitely small distance dl, If a
is the cross section area of piston, the force F acting on piston is
given F = p x a. the small amount of work done by gas on piston.
dw = F x d/dw = p x a x d/ = P dv
Where dv = ad/ = infinitely small displacement volume.
Hence when piston moves from position 1 to 2 the work
done by gas on piston is given
By dw = P dv
The magnitude of work given by above equation is same as
area under the path 1-2 on P-v diagram.
Pdv Can be performed only on quassi static path.
W 1-2 = p (V2 V1)
Gas
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PATH FUNCTION
P
1P1
C
B
A
P2 2
V1 V2V
Let a system be taken from state 1 to state 2 by following
three different quassi-static paths A, B and C. Since area under the
curve for a path gives, the amount of work during that process,
hence from above it is clear that area under all three curves A, B
and C will be different. Hence, work done involved during each
path will be different although the end states for all the three paths
being same.
Hence work is a path function. Therefore dw is called an
inexact differential or imperfect differential.
Hence
dw = W1-2
dw W1 W2POINT FUNCTION :
For a given state there is a definite value for each of
thermodynamic property. The change in thermodynamic property
during a change of state depends only upon initial and final states
of system. It does not depend upon the path; the system follows
during change of state. Hence properties of the system are called
POINT FUNCTION. Hence are called exact or perfect differentials.
dv = V2 V1 for a change of statedv = 0 for cycle.
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I I
System Boundary
I I
W = E
E = Potential
ELECTRICAL WORK
When a current flows through a resistor which which is taken
as systemthere is work transfer to system. This is due to the fact
that current drive a motor, motor can drive a pulley and pulley can
raise a weight.
SHAFT WORK
SHAFT WORK
If shaft is considered as system is roted by motor there is
work transfer into the system. A shaft can roted pulley and pulley
can raise a weight.
If T is torque applied and is angular disp. of shaft then shaft
power =
Td
w =
MOTOR
Motor
W
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PADDLE WHEEL WORK
System
Pulley
Paddle
When the weight is moved the paddle will rotate and hence
there is work transfer into system. Here although volume of system
remains constant i.e.
= 0 but 0.If m is mass that is moved and dz is the distance through
which it is moved then work transfer to system
Dw = mgdz = Td
Where T Torque transmitted by shaft for rotating it through
an angle d.
W = dw = mgdz= Td
FLOW WORK
Flow work is the energy transferred across system boundary
which is imparted to fluid by a pump, or compressor to make it
flow across system boundary. Flow work is significant only in flow
process or for open system when mass transfer taken place across
system boundary.
W
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If p1 is fluid pressure exerted on an imaginary piston moving
with velocity V1, then work.
(dw) flow = p1dv
Where dv is the volume of fluid about to enter the system. If
dm1 is the mass flow rate of fluid across section (1) (1) then,
dw = P1 V1 dm1
Where, v = Specific volume of fluid.
1
FlowP1 V1
V1
1V1dt
OR
Force exerted by fluid on imaginary piston of area a1 = p1 x a1
Distance travelled by fluid in time, dt = V1dt. V1 Velocity of piston Work associated with fluid, dw = p1 a1 V1 dtwork/time = p1a1V1
From law of conversation of mass.
Mass flow rate dm1 = a1V1 = dm1v1
HEAT TRANSFER
Heat is a firm of energy that is transferred across the system
boundary the virtue of temperature difference. The heat in called
energy in transient just like work. Heat always flows from higher
(work /time) = p1v1 dm1 = (dw)Work /kg = (dw)flow = p1v1
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temperature system to lower temperature system. The temperature
difference between two systems is called potential and heat transfer
is called flux.
There are basically three modes of heat transfer. Heat
transfer due to condition, convection and radiation.
Heat transfer is a boundary phenomenon which takes place
only by the virtue of temperature difference. Heat transfer does not
necessarily result in change in temperature e.g. when heat is
transferred to mixture of ice and water is does not cause any change
in temperature unit ill ice is melted completely.
Similarly if a rotating wheel is stopped by applying break
the temperature of break surface increases. But this is not because
of heat transfer. Hence any rise in temperature of system is not
necessarily due to heat transfer only.
Heat transfer rate is transfer of heat per unit time. Heat
transfer is expressed by symbol Q.
Surrounding Q is Ve
Q Q
Q is + Ve Surrounding
When heat is absorbed by When heat is rejected by system
system is taken as positive. it is taken as negative.
Unit of heat transfer in S.I. system is Joule.
Heat transfer like work transfer is also a path function and
hence inexact differential.
Hence dQ = Q1-2
systemsystem
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FIRST LAW OF THERMODYNAMIC
FIRST LAW OF THERMODYNAMICS APPLIED TO CLOSE
SYSTEM FOR CYCLE:
The first law of thermodynamics is the law of conservation
of energy. Which states that energy can neither be created nor
destroyed but can only be transformed from one from to another.
This law is applied to thermodynamics for a closed system
undergoing a cycle by Joule. Heat and work are two different forms
of energy. Energy which enters a system as heat may leave the
system as work or energy which enters system as work may leave
as heat.
Thermometer Pulley
Weight
tSystem Water
Work
Surrounding 30 Q
(a) t = 30 (b)
Let us consider a closed system consisting of water in an
adiabatic vessel having paddle and thermometer. When weight is
moves a certain amount of work W1-2 is transferred in to system.
The system which was initially placed at temperature t1, after work
transfer reaches to temperature t2 due to temperature rise. Hence
system has gone through change of state 1-2 through work transfer
W1-2. This is represent on coordinate axes x-y.
1
Q21W12
2
W W
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Now if the insulation of vessel is removed the system is now
separated from surrounding by diathermia wall. This cause the heat
transfer from system to surrounding due to temperature different.
Thus the system again goes through change of state and thermal
equilibrium between system and surrounding is established when
system return back to original temperature t1
the 2 1 represent
another change of state brought in the system due to heat transfer
Q2-1
Thus 1-2-1 represents a thermodynamic cycle executed by
system which consist of work transfer W1-2 and a definite amount
of heat transfer Q2-1. This Q2-1is found to be proportional to Q2-1
i.e. W2-1 Q2-1W2-1 = JQ2-1When J = Joules equivalent or mechanical equivalent A heat.
If cycle involves more than one work and heat transfer then = J Cycle cycle
Or = J In S.I. system J = 1 Nm/J
Where O stand for cyclic integral.
Thus cyclic integral of heat transfer. This is known as
equation of first law of Thermodynamics applied to cycle exerted
by closed system.
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FIRST LAW FOR CLOSE SYSTEM UDERGOING PROCESS
In equation of first law for a cycle i.e., = thealgebraic sum of all energy transfer across system boundary isequal zero.
When a system undergoes a change of state during
which both heat and work transfer are involved then net energy
transfer I = Q W is stored with in the body of system itself.
Example: If a gas system is supplied with heat then piston will
move due give energy output as work. But according to Joule
during this change of state the net energy transfer i.e. Q W will be
stored within body of system. This energy in storage is neither heat
nor work and it is known as INTERNALENERGY of the system.
Work (W)
System
(1) (2)
Q Heat
i.e. Q W = E
where, E = Increase in Internal energy.
Or Equation of first law applied a process.
INTERNAL ENERGY IS PROPERTY OF SYSTEM
The internal energy i.e. energy in storage is a property of
system can be proved by considering following example.
PB C
A
V
Q E + W
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Let a system is taken from state 1 to state 2 by following path
A. Thus for change of state equation of first law is
Q1-2 = E + W1-2
Or
QA = EA + WA ----- (1)
The system is taken from state 2 to state 1 by following path
B. again for change of state 2-1 by path B equation of 1st
law is
QB = EB + WB ----- (2)
Adding equations (1) and (2)
QA + QB = (EA + EB) + (WA + WB) ----- (3)
But processes A and B constitute a thermodynamic cycle for
which equation of 1st
law is = Cycle cycle
i.e. QA + QB = WA + WB
equation (3) becomes 0 = EA + EB
EA = EB ----- (4)
Similarly if we consider that system is taken from state 2 to
state 1 by following path C instead of B then processes A and C
constitute a cycle for which we can say
EA = EC ----- (5)
From equation (4) and (5) we can say that
i.e. change in internal energy of system is same whether it follows
path C.
Hence internal energy is independent of path system follows
during change of state.
Hence, internal energy is a POINT FUNCTION and hence
A PROPERTY OF SYSTEM.
EB = EC
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PERPETUAL MOTION MACHINE OF I KIND (PM)
The first law of thermodynamics is the law of conservation
of energy which that energy can neither be created nor destroyed it
only transform from one to another.
Hence, there can not be any machine which continuously
supply the work without any other form of energy disappearing or
consuming simultaneously such machine is a fictitious machine
which is not possible since it will violates 1st
law and is called
perpetual motion machine of 1st
kind PMM1.
The converse of this i.e. there can be no machine consuming
work continuously without some other form of energy appearing
simultaneously is also true.
Q Q
Work Work
PMM1 Converse of PMM1
ENTHALPY
The enthalpy of a substance is the sum of internal energy and
product of pressure and volume. IT is denoted by H.
H = U + PV Joule
Since enthalpy comprises of all the properties i.e. u, p and v
hence it is also property of system.
Basically enthalpy is the sum of internal energy (u) and flow work (pv).
The specific enthalpy is given by
h = u + pv. J/kg.
Where, u and v are specific internal energy and specific
volume respectively.
Since internal energy is depend upon the temperature. H = f(T).
Machine
(Engine)Machine
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TYPES OF ENERGY
The total energy of system stored within its body, gets
stored in two ways i.e. microscopic mode and microscopic mode.
The microscopic mode of energy includes the energy of
system in the form of kinetic and potential energy.
The kinetic energy of system is the energy associated with a
fluid when following which is given by Ek = mV2
where m is
mass of fluid and v is fl0ow velocity.
The potential energy of system is the energy by virtue of its
position with reference to a datum surface given by Ep = mgz.
The microscopic mode of energy is the energy which is
stored in the atomic and molecular structure of the system and it is
known as internal molecular energy denoted by U.
The matter substances are composed of molecules which are
in thermal motion with certain velocity colliding with one another
and walls. Due to this collision molecules may be subjected to
rotation and vibration. Hence they can have translational kinetic
energy, rotational kinetic energy, vibration energy, nuclear energy
etc. if E is the total molecular energy of one molecule then.
If N is number of molecules the total internal energy is,
U = N
For ideal gas there are no inter molecular forces of attraction
and repulsion and hence internal energy depends only upon
temperature U = f(T) for ideal gasesHence, internal energy E = Ek + Ep + U
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Random Thermal Motion of Molecules
N
Flow (V)
Hence, change in internal energy
For a closed system going through change of state there is absence
and gravity changes. Hence for closed system K.E. = 0, P.E. = 0In differential forms, dE = dKE + dPE +dU
Hence, equation of 1st
law for a process.
Q = E + W Q = U + WdQ
dQ = dE + dw dQ = dU + dw
dQ = dE + pdv dQ = dU + pdv
= + = Q = E + Q = U + INTERNAL ENERGY OF AN ISOLATED SYSTEM
E = K.E. + P.E. + U
E = U
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IDEAL GASES
A perfect gas or ideal gas is the state of the substance whose
evaporation from its liquid state is complete and it follows all the
gas laws at all the condition of pressure and temperature. A perfect
gas is a gas having no forces of molecular attraction.
In actual practice there is no such gas exist in nature. All the
gases are real gases. But since at law pressure and high temperature
the molecules are far apart and hence force of attraction between
them tends to be small, some gas car be called perfect gases like
O2, N2 etc.
BOYLES LAW
It states for a gas going through change of state if temperature
remains constants then volume of varies inversely with absolute
pressure.
V if T = constantOr PV = C.i.e. PV1 = P2V2 = pnvn
CHARLES LAW:
It state that during a change of state of gas if pressure is kept
constant the volume of gas varies directly with temperature.
V t if P = constant. = C
Or =
= ----- =
GAY LUSSACS LAW
If states that during the change of state of a gas if the volume is
held constant then the pressure of the gas varies directly with
absolute temperature.
p T if V = constant. = C = = ----- =
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CHARACTERSTIC GAS EQUATION
This equation provides relationship between pressure, volume and
temperature of gas.
From Boyles law v if T = C.
From Charless law V T if P = C
Combining Bayles and Charless law.
v PV = CT
Or = C
Or
=
= ----- =
= RR = Characteristic Gas constant whose value is different for
different gases.
If m is the mass of gas then V = mv.
= mR
R = J/kg ok
R = 287 J/kg ok for air
AVOGADROS LAW
If state that one mole of all the gases occupies same volume
at NT.P which is equal to 22.4 m8/kg mole.
One mole of a gas has n mass equal to its molecular weight.
e.g. 1 kg mole of O2 weight 32 kg.
The characteristic gas equation is given by
PV = mRT
Or pv = RT
Multiplying equation by molecular weight M.
PV = mRT
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MPv = MRT
Where = Volume occupied by one mole of gas = Mv.Known as Molar volume = 22.4m
3/kg mole.
= Universal Gas constant whose value is same for all thegases = 8314.3 J/kg Mole ok. (RM).
SPECIFIC HEAT OF GAS :
The specific heat of a perfect gas is defined as the amount of
heat required by unit mass of the gas to rise its temperature by 10
C. it is denoted by C.
C =
J/kg okThe gases have to specific heat.
(I) Specific Heat at Constant Volume (CV)
It is the amount of heat required by unit mass of gas unit rise
in temperature when volume is held constant.
When the gas is heated at constant volume, all the heat
supplied is utilized to increase the internal energy of the gas as
energy in storage. There is no work done by gas.
Hence, specific heat at constant volume (Cv) is the rate of
change of internal energy with respect to temperature when volume
is held constant.
i.e. Cv = du = Cv dT
=
Joule/kg
Specific heat at constant volume is property of system since
T and V are properties.
P = T
u = Cv
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Specific Heat at Constant Pressure : (Cp)
It is the amount of heat required by unit mass of gas for its
unit rise in temperature when it is heated at constant pressure.
When a gas is heated at constant pressure the part of heat
supplied to it is used for moving piston to do some work and (flow
work) rest is stored within gas to increase its internal energy.
Hence specific heat at constant pressure is defined as rate of
change of enthalpy with respect to temperature when pressure is
held constant.
Cp = dh = Cp dT
=
= Cp (T2 T1) J/kgJust like Cv, Cp is also property of the system since h1 T and
P are all properties.
Value of Cp is always more that Cv since when a gas is
heated at cont. pressure some heat is utilized to do work apart from
increasing internal energy where as at constant volume all the heat
is utilized for increasing internal energy.
Enthalpy of gas h = u + pv
From characteristic gas equation Pv = RT h = u +RT Differentiating the equation.dh = dU + RdT
dh = CpdT CpdT = CvdT + Rdtdu = CvdT Cp = Cv + R
C p Cv = R
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The ratio of specific heat at constant pressure Cp and Sp heat
at constant volume (Cv) is known as adiabatic index (r)
= rCp Cv = R
Dividing equation by Cv
1 =
FIRST LAW APPLIED TO NON - FLOW PROCESSES
The thermodynamic processes are classified into two categories.
1) Non Flow Process: - i.e. takes place in a Closed System.
2) Flow process i.e. takes place in an open System.
CONSTANT VOLUME (ISOCHORIC) PROCESS
Let us consider a system of gas enclosed in piston and
cylinder machine. The state of the system which is thermodynamic
equilibrium state can be defined by properties p1, V1, t1.
When the gas it heated due to stopper piston can not
move up. Hence, the volume remains constant but pressure andtemperature of gas increase to let p2 and t2. Thus cont volume
process follows Charles law. i.e.
P T
= C or
=
= C
Stopper
Piston
Cylinder System
Cv =
V = C
P1, V1, t1
Gas
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P
P2 2
P1
V1 = V2
V
All the heat supplied to gas is stored within the body of gas
to increase its internal energy. Hence the work done or pdv work is
zero.
Work transfer : = = 0.Since = 0Change in Internal EnergyU = mCv dT
= mCv
Heat Transfer : From equation of 1st
law
Q = U + W
Q = U
Change in Enthalpy : dH = mcpdt
= mcpdt =(H2 H1 = H = mcp c T2 T1)
U = U2 - U1 = mCv (T2 T1)
W =0
Q = mCv(T2 T1)
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CONSTANT PRESSURE (ISOBARIC) PROCESS
W
(2) P2 V2 t2
Piston p1 = p2
System
Q
P1 = P2 1 2
W12 =
V1 V2
V
When a gas is heated at constant pressure the heat supplied to
it is utilized for two purposes.
1. Part of heat is used to overcome the resistance to the
movement of piston as work.
2. Rest of heat is stored within gas to increase its internal
energy.
Let p1, v1, t1 be the properties of system at equilibrium state 1.
P2, v2, t2 be the properties of system at equilibrium state 2.
For a quassi static path 1-2.
dw = pdV
= Work Transfer :
W1-2= = P (V2 V1)
W kg
Gas
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Change in Internal Energy :
Since temperature is changing from T1 to T2
dU = mCv dT
= mCv U = U2 U1 = mCv (T2 T1)
Heat Transfer : From equation of 1st
law.
Q = U + W
= mCv (T2 T1) + P (V2 V1)
= mCv (T2 T1) + P2 V2 P1 V1 P2= P1
= mCv (T2 T1) + mR (T2 T1) PV = mRT
= m (T2 T1) [Cv + R]
Q = mCp (T2 T1) Cp Cv = RCp = R + Cv
Changing Enthalpy :dH = mCp dT
=
Thus for cont. pressure process
H = H2 H1 = mCp (T2 T1)
H =Q
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CONSTANT TEMPERATURE (ISOTHERMAL) PROCESS
A process during which the temperature of system remains
constant either during expansion or compression is known as
isothermal process.
To carryout on isothermal process the system and
surrounding should be in perfect thermal contact with each other so
that any energy entering in to the system should be transferred by
the system to the surrounding in some other form at the process
takes place at a very slow rate.
Thus to carry out isothermal process if a system receiver or
reject the energy in the form of heat, it should be compensated
exactly for work done by system or upon the system respectively.
The isothermal process follows Boyles law.
PP1
Isothermal ExpansionP (Pv = C)
P2 2
V1 VV
Hence for isothermal process P1V1 = P2V2------- = PnVn = C
WORK Transfer for non flow process
dw = pdV
= = Let any instant pressure is & volume is V =
dv
Hence P1 V1 = P2V2 PV = C = C P = = P1 V1 = dV Since P1 V1 = cont. = P1V1Log
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W1-2 = P1V1
By refn =
As P1 V1 = P2 V2 = Where,
re =
=
=
=
Is known as expansion Ratio.
ADIABATIC PROCESS
[An adiabatic process is one during which system neither
receiver nor rejects the heat to surrounding during its expansion
or compression. This is possible when the system is perfectly
insulated from its surrounding so that no heat transfer is possible.]
[Thus when the system goes through expansion during this
process the work is done by the system at the cost of its internal
energy.]
[Similarly when the system is compressed adiabatically the
work done on system is used to increase its internal energy.]
Thus for adiabatic process, the change in internal energy of
the system is equal to work done by or upon the system.
PP1 1
Adiabatic Expansion
(Pvr= C)
P2 2
v1 v2V
W1-2 = P1V1 log e
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Let us consider m kg of gas, taken from state 1 to 2
adiabatically, p1, v1, t1 be the properties of system at state 1 and p2,
v2 t2 be the properties at state 2.
From equation of 1st
law for any process 12.
dQ = dU + dw
For adiabatic process dQ = 0.
0 = dU + dw
CvdT + PdV = 0
dT = --- (1)
Characteristics equation for a perfect gas PV = mRT
Differentiating above equation.
PdV + vdP = mRdT.
dT =
----- (2)
From equation (1) and (2) =
= =
=
= 1 Cp Cv = R = 1 r 1 = Cv =
r- 1 = 1
rpdv = vdp + = 0Integrating above equation:
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rloge v + log P = C
loge Vr + loge P = C
loge [PVr] = C
Hence above equation is the equation for an adiabatic process
in which r is called adiabatic constant (index). ----- = Relatio0nship between p1v1 and T for adiabatic process.
From general gas equation
Again
PVr= C
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WORK Transfer: for non flow process.
dw = pdv
Let at any equilibrium state during the process
Let pressure is p and volume is v.
Or OR
Change in Internal Energy dU = mCv dT Change in Enthalpy dH = mCpdT
Heat Transfer dQ = du + dw
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Hence heat transfer Q = 0 for adiabatic process.
POLYTROPIC PROCESS:
This is known as general law for expansion and compression.
It follows the law PVn
= C. where n is known as polytrophic index,
n can have any value from 0 to . Depending upon the manner inwhich expansion or compression takes place.
Constant pressuren = 0
Isothermal
n = 1 Polytrophic
r > n > 1 Adiabatic
r = n = r
V
PP1 1
Pvn C Polytrophic Expansion
P2 2
V1 V2
V
* When n = 0 i.e. p = constant. Hence it is a constant
pressure process.
* When n = 1, i.e. pv = constant it is an isothermal process.
Q 1-2 =0
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* When n = r i.e. PVr= C it is an adiabatic process.
* When n = i.e. V = constant it is 0 constant volumeprocess.
For a polytrophic expansion process 1 2 relation between P1V and
T is given by,
Work Transfer:
Work transfer during polytrophic process is given by,
OR
Change in internal energy:
U = U2 U1 = m (T2 T1)
Change in Enthalpy:
H = H2 H1 = m Cp (T2 T1)
Heat Transfer:
Q = U + W
= mCv ( T2 T1) + = mCv ( T2 T1) +
Cv =
=
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Q = mR ( T1 T2)
= mR ( T1 T2) = mR ( T1 T2)
Since W1-2 = for polytrophic processHence heat transfer
r 1 =
R= Cv(r 1)
OR
= change in internal energy
Prove that for a process governed by PVn
= C vdp = npdv
For process PVn
= C
Differentiating above equation
d (PVn) = 0
p x n Vn 1
dv + Vn
dp = 0
nPVn
x V- 1
dv + Vndp =0
npVn
1 dv + Vndp = 0
Q =
Q =
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Diving above equation by Vn 1
Npdv = vdp
Or
Control Volume:
The control volume is defined as the region or a certain
volume in space upon which concentration is focused to analyse an
open system. The control volume is bounded by a surface known as
control surface.
Both mass and energy crosses the control surface. The term
control volume is used in connection to the open system only.
Whenever the matter flows the system is considered to be a volume
of fixed identity known as control volume. Where as in close
system, the system is closed to flow of matter but volume can
change against flexible boundary.
High pressure air out
Heat
Control surface
Control volumeLow pressure air in
STEADY FLOW PROCESS:
The equation of 1st law applied to any process is Q = E + W
Where E = change in internal Energy of System.
= K. E + PE + U Q = K. E + P. E + U + W
Motor Air compressor
Vdp = np dv
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Flow process is a process executed in a system of flowing
mass. Thus the process takes place in an open system can be termed
as flow process since the open system is system of flowing mass.
Hence when there is mass transfer across the system
boundary system is called open system. Thus the above equation of
energy refers to a system having particular mass of substance and it
is free to move from one place to another.
Thus K. E, P.E can not be neglected as in case of close
system (non flow processes)
Steam in
W
Shaft
Control surface
Steam out
Let us consider a steam turbine through which steam is
flowing. Steam expands when it flows, through turbine. For this
energy equation is
Q = K. E + PE + U + W
To analyse open system two methods are followed.
1) According to Lagranges method a certain mass of substanceis considered and it is followed as it travels through device
(turbine) and considering the energy interaction involved
during its flow.
2) According to Eulers method which is most widely used,instead of concentrating a certain mass of moving substance
which can be called as moving system in flow process, the
attention is focused upon a certain region is space through
which substance flow known as control volume.
Turbine
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As the substance flows through control volume its properties
changes. e.g. pressure, volume and temperature, of steam when it
flows through (expands) turbine. The changes in properties takes
place as expansion (flow) proceeds, with respect to space co-
ordinates and time. But in most of flow device, constant rate of
flow mass and energy across control surface is maintained known
as steady flow device. Hence, the control volume in course of time
attains the steady state. At steady state, the thermodynamic property
has a fixed value at a particular location and dose not changes with
time. Hence, property changes only with respect to location or
space co-ordinates but not vary with time. Steady state means
invariant with time. Hence such a flow process is called steady flow
process.
STEADY, FLOW ENERGY EQUATION:
Q
Control surface
dm1 (1)
Flow in Control Volume
W
P1 (1) Aj
V1 m/sec. (2) dm2
Z2 v1 m3
1kg Flow out
u1 J/kg. A2 P2 m2
m1 kg/sec. 2 Z2 v2
v2
Datum Surface u2
Let,
A1, A2 = Cross sectional area of flow at inlet (1-1) and exit (2-2)
m1, m2 = Mass flow rate at inlet and exit respectively kg/sec.
P1, P2 = Pressure with which fluid enter and leave in N/m2
v1, v2 = Sp. Volume at inlet and exit respectively m3/kg.
Steady Flow Device
m
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V1, V2 = Velocity of flow at inlet and exit respectively m/sec.
u1, u2 = Specific internal energy of fluid at inlet and exit J/kg.
Z1, Z2 = Elevation of (1) - (1) & (2) - (2) from datum surface in
meter.
Ws = Work transfer in the form of shaft work through control
volume in J/kg.
Q = Heat transfer through control volume in J/kg.
Mass Balance:
According to law of conservation of mass since there is no
accumulation of mass inside control volume.
Mass flow rate at (1) (1) = Mass flow rate at (2) (2)
M = m1 = m2
Know as continuity Equation.
Energy Balance:
Equation of first law to flow device for a process.
Q = E + W ---- (1)
= (E2 E1) + W
Where E = change in internal Energy of system during process.
= E2 E1 E = KE + PE + U
= (KE2 + PE2 + U2) (KE2 + PE2 + U1)
---- (2)W = total work transfer during process. In above flow device
there are two types of work transfer present.
1) Shaft work (Ws)2) Flow Work
Let dm1 = mass of fluid at section (1) (1) at a given instant.
dm2 = mass of fluid at (2) (2) at same instant.
t = time in sec.
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Displacement or flow work done by fluid of mass dm1 when
it enters the flow device (control volume) is,
= P1v1dm1 joule = P1v1 Joule/kg. (For unit mass)
ve sign since work is done by fluid when it enters control volume.
Similarly when fluid leaves the control volume, displacement
or flow work done upon fluid.
= P2v2dm2 Joule,
For units mass = P2v2 Joule/kg
Total work transfer from control volume.
W = Ws + P2 V2 P1 v1
W = Ws + P2 v2 P1 v1 J/Kg 3
Substituting values of equation (2) and (3) in equation (1)
The above equation is known as steady flow energy Equation
applied to flow process. All terms are in Joule/kg.
Various forms of S.F.E.E.
Specific Enthalpy h = u + Pv J/kg.
S.F.E.E. Can be written as,
Writing Ws as W
Joule/kg
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Multiplying Equation by mass flow rate m = m1 = m2 =
Above equation represents S.F.E.E. in Joule/sec. Where is heattransfer rate and
is work transfer rate.Rewriting S.F.E.E. in J/kg as,
In differential form, S.F.E.E. is written as,
dQ = dh + dke +dpe +dw
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APPLICATION OF S.F.E.E. TO SOME FLOW DEVICES.
1) NOZZLE OR DIFFUSERA nozzle is device of varying cross sectional area in the
direction of flow which increases the kinetic energy or velocity of
fluid at the expense of its pressure energy.
Diffuser is also passage of varying cross section which
increases pressure of fluid at the expenses of its kinetic energy.
Adiabatic Wall
(1) Throat
(2)
P1V1
Flow m P2V2
Z2Z1 (1)
(2)
Convergent Portion Divergent Portion
Thermodynamically the expansion through nozzle to be
adiabatic is desirable.
S.F.E.E. is written as, Here, Q = 0, W = 0, P. E. = 0.
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2) TURBINE:Turbine is a device, which gives positive work output.
Whenever fluid flows through turbine it expands. There is
pressure drop. Thermodynamically it is desirable to have
adiabatic expansion through turbine.
m
WT1 1
Control surface
2 2
Here also Q = 0, K.E & PE are neglected.
S.F.E.E. becomesh1 = h2 + WWhere tone from turbine
3) PUMP FOR ROTARY COMPRESSORBoth pump and rotary compressor compress the fluid
to increase its pressure and deliver it. Hence both are power
consuming devices. Thermodynamically it is desirable to
have adiabatic compression process.
Control Surface(2) (2)
W
(1) (1)
Here also Q = 0, K.E & PE are neglected.
W = h1 h2 J/kg
Comp.Motor
Turbine
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S.F.E.E. becomes
h1 = h2 W (Compressor or pump consumes work
hence it is ve)
4) Reciprocating Compressor:Reciprocating Compressor takes in low pressure air or gas &
compresses it to deliver at high pressure. Thermodynamically
it is desirable that compression should follow isothermal law.
Hence during process, heat is rejected by working fluid to
surrounding.
Low pressure High pressureair in air out
Q
Control Surface
W
Here K.E and PE are neglected.
h1 + Q = h2 W
5) HEAT EXCHANGER (BOILER / CONDENSOR)The heat exchanger (boiler / condenser) are the devices
which transfer the heat from one fluid to another fluid. Let usconsider a steam condenser which condenses the steam by
using cold water. Water flows through tubes and team flows
over the tubes to cause the tubes to cause the heat transfer
when steam comes in contact with cold tube surface.
W = h2 h1 J/kg
W + Q = h2 h1
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Steam in
msiControl Surface
Water in Water outmwi mwo
mso
Condensate out
Let msi, mso = mass flow rate of steam entering and condensate
leaving kg/sec
mwi, mwo = mass flow rate of water entering and leaving kg/sec
For multi channel devices we use S.F.E.E. in rate form.
Here W = 0, K.E & P.E.
Q = 0 since there is no external heat interaction.
Heat interaction between steam and water is only within control
volume.
msi x his + mwi x hwi = mso x hso +mwo xhwo
msi = mso = ms and mwi = mwo = mw
or
WORK DONE IN STEADY FLOW PROCESS:
The S.F.E.E. in differential form is expressed as
dq = dh +dke + dpe +dw ---- (1)
The specific enthalpy h = u + pvDifferentiating above equation.
dh = du + d(pv)
dh = du + pdv + vdp ---- (2)
For closed system the equation of 1st
law is dq = du + pdv
ms (his hso) mw (hwo hwi)
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Equation (2) becomes
dh = dq + vdp
Substituting values of dh in equation (1)
dq = dq + vdp + dke + dpe + dw
0 = vdp + dke + dpe + dw --------- (3)
In most of engineering system changes in K. E. and P. E. are
negligible dke = 0 and dpe = 0
O = vdp + dw
This is work done for flow process.
P P1 1
Non flow process Flow process
2
2Work done for non process V Work done for flow process V
i.e. i.e. ve Sign in makes the above term positive forexpansion process. This is positive quantity andrepresents work done by system in flow process.
dw = -vdp
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PROPERTY RELATION FOR FLOW PROCESS:
Rewriting equation (3) of above article.
O = vdp + dke + dpe + dw
= KE + PE + W PE for most of Engg. Device is negligible.
= KE + W
For nozzle W = 0, = KE
For neglecting Velocity at inlet to nozzle.
For compressor K. E. = 0 CONSTANT PRESSURE FLOW PROCESS:
For flow process, work done is ,
W12 = Since dp = 0
S.F.E.E. is dq = h + KE + PE, if PE = 0 & KE = 0 then
CONSTANT VOLUME FLOW PROCESS:
W12 = and if KE = 0 & PE = 0= v [P2 P1]
S.F.E.E. is dq = u + pdv + vdp + KE + PE
{vdp =
CONSTANT TEMPRETURE (ISOTHERMAL) PROCESS:
W = 0
dq = h
dq = u
W12 = v[P1 P2]
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ADIABATIC (ISENTRPIC) PROCESS
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POLYTROPIC PROCESS:
As approved for adiabatic process, replaying by n.
Throttling Process:
Throttling is an reversible process in which a fluid flowing
across a restriction undergoes a drop in pressure. Such a pressure
occurs in flow through a porous plug, a partially closed valve and
very narrow orifice. During throttling process the fluid expands
from high pressure to low pressure with out doing work and there is
no change in kinetic energy and potential energy of fluid as also
there is no heat transfer.
The process can be best understood by an experiment known
as Joule Thompson porous plug experiment.
Porous Plug
Thermometer
Flow P1 P2
V1 V2
T1 T2
Insulation
Control Volume
Joule Thompson Porous Plug Experiment.
A steam of high pressure gas as P1 flow through an insulation
porous plug and cones out of lower pressure P2.
Energy entering control volume Energy leaving control
volume = Energy stored in control volume.
W12 = [P1V1 P2 v2]
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But steady flow energy equation is based on assumption that
sate of fluid at any point in control volume is maintained same.
Also control volume is equal to mass leaving. Hence there can not
be any accumulation f energy in control volume. Energy Entering Energy leaving = 0
For throttling K.E = 0 P.E = 0 Q = 0 W = 0
Hence
Hence enthalpy of fluid remains constant during adiabatic
throttling process.
P1 Q are inversion points.
P P, G are inversion points
Cooling Heating Inversion curve
T Constant Enthalpy Covers
G .
P
When series of experiments are performed by Joule
Thompson at same initial temperature T1 and pressure P1 but with
different flow rates and different downstream pressure. It was
found that T2 change up to some extent. The results are plotted as
constant enthalpy curves on temperature pressure diagram for
different flow rates at P1 and T1 condition, a series of constantenthalpy curves are obtained. Maximum point on each curve is
called inversion point. The locus of all such inversion points is
called inversion curve.
h1 = h2
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The slop of constant enthalpy curve is called Joule
Thompson Coefficient () and is given by is +ve on left hand side of inversion point and is ve onright hand side of inversion point. It is zero on inversion point.
Change in pressure P is always ve during throttling process.
Hence on L. H. S of inversion curve throttling produces coding
effect and on R. H. S. of inversion curve it produces heating effect.
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SECOND LAW OF THERMODYNAMICS
Limitations of1st
Law:
First law of thermodynamics states that when a system
undergoes a change of state a certain energy balance will hold work
and heat are mutually, convertible. But this law does not give any
clue on the direction of process.
Friction Brake
Fx
F
Flywheel
When a flywheel is stopped by a friction wheel (brake) the
brakes gets not from 1st
law the K. E. lost by flywheel will be equal
to heat gained by brake whose temperature increases 1st
law will be
equally satisfied if brakes were to cool and give back their internal
energy to flywheel to make it rotate. But this is not possible. Hence
action of brake in stopping flywheel is an irreversible process.
Hence there is directional law which imposes and limitation on
energy transformation which is provided by 2nd
law of
thermodynamics.
According to Joules experiment when energy is supplied to
system in the form of work it can be completely converted into
heat. But complete conversion of heat into work in a cycle is not
possible.
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Work is completely Heat is not completelyconverted into heat converted into work
Q02-1 W2-1
1 2 1
1 2 1
Q1-2
W1-2 W1-2 = Q2-1 Q1-2 > W2-1
Work is said to be high grade energy and heat as low grade
energy. Complete conversion of low grade energy into high grade
energy in a cycle is impossible.
CYCLE HEAT ENGINE:
A heat engine cycle is a thermodynamic cycle in which there
is net heat transfer to system and a net work transfer from system.
A system which executes heat engine cycle is called cycle heat
engine.
Q1
WE
WC
Q2
H2O (g) WtTurbine
Q1 CondenserBoiler
Q2
Furnace Sea or River
H2O (l) Pump
Cyclic Heat engine Wp(Open system)
A heat engine may be in the form of a mass of gas
enclosed in a cylinder and piston machine or a mass of water
moving in a steady flow through steam power plant.
System
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Net heat transfer to heat engine Qnet = Q1 Q2
Net transfer in cycle Wnet = WT WP or WE WP
From 1st
law : Q = Wcycle cycle
Qnet = Wnet
Q1 Q2
= WT WPQ1
B
WP P T WT
C
Q2
Function of heat engine cycle is to produce the work
continuously at the expense of heat input.
Efficient of Heat Engine:
It is definition of ration of total work (net work) out put of
cycle to total heat input to cycle.
= =
Also known as thermal efficiency of heat engine cycle.
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Heat Reservoir:
A heat reservoir is defined as a body of infinite heat
capacity which is capable of absorbing or rejecting an unlimited
quantity of heat without suffering any change in its
temperature.
SOURCE :
The heat reservoir from which heat Q1 is transferred to
system operating in heat engine cycle is called source.
SINK:
Heat reservoir to which heat Q2 is rejected from system
during cycle is called sink.
SOURCEHeat Reservoir
V
B
WP P T WT
C
Q2
SINK
Heat Reservoir
KELVIN-PLANCK Statement of II law
It states that It is impossible for a heat engine to produce
net work in a complete cycle if it exchanges the heat only with
bodies at a single fixed temperature.
Efficiency of heat engine is given by
Since heat input Q1 can never can be converted completely into
a work cycle. Hence Q1 > Wnet.
Hence < 100% i.e. a H. E. can never be 100% efficient.Hence > 0 i.e. there are always to be a heat rejection.
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It is impossible to construct a heat engine operating in a
cycle whose sole effect is to transfer heat from single heat reservoir
and its conversion into equal amount of work.
Hence to produce net work in a thermodynamic cycle heat
engine has to exchange heat with two reservoir maintained at
two different temperatures. i.e. source and sink.
Q1
Wnet = Q1 Q2
Q2
t1 > t2
t1
Q1
Wnet = Q1
Q2 = 0
PMM IIIf Q2 = 0 i.e. heat engine with produce net work in cycle
by exchanging heat with only one reservoir thus violating
Kelvin plank statement of II law of thermodynamics such a heat
engine is called perpetual motion machine of second PMM2
which is impossible.
PMM2 Violation of Kelvin planks state.
CLAUSIUS Statement:
Heat always flow from a body at height temperature to a
body at a lower temperature. The reverse process never occurs
spontaneously. Clausius statement states that If it is impossible
to construct a device which operating in a cycle will produce no
SOURCEat t
HE
HE
SINK
at t1
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effect body. Hence heat can not flow itself from a body work
must expended to achieve this.
It is impossible to construct device operating in a cycle
whose sole effect is to transfer heat from L.T.R. to H.T.R.
Refrigerator:
A refrigerator is a device which operating in a cycle
maintains a body at a temperature lowers than the temperature
of surrounding.
As shown in Figure body A is maintain at temperature t2
which is lower than surrounding temperature t1. Heat flow from
higher energy level. Hence there will be leakage of heat Q2 into
body from surrounding because of temperature difference. In
order to maintain body A at temperature t2 heat has to be
removed from body at the same rode at which it leaks into body.
This heat is discharged back to atmosphere which is done by
expenditure of work W. Supplied to a device known as
refrigerator which operates in a cycle.
There is performance parameter in refrigerator known as
coefficient of performance (C.O.P)
Atmosphereat temp. t1
Q1 = Q2 + W
W R
Q2
Q2
Surrounding at temp. t1
t1 > t2 Body A
Maintained at
temperature t2
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Heat Pump:
A heat pump is a device which operated in a cycle and
maintains a body at a temperature higher than the temperature of
surrounding.
Because of temperature difference heat Q1 leaks out of
body A. to maintain body A at temperature t1 the heat is
discharged into body at the same rate at which heat leaks out of
body. This heat is taken from surrounding (low temperature
reservoir) and discharged into body (higher temperature
reservoir) by expenditure of work W supplied to a device known
as heat temperature.
Q1
Q1 = Q2 + W
W HP
Q2
t1 > t2
Equivalence of Kelvin Planck and Clausius Statement:
The equivalence of Kelvin Planck and Clausius statementcan be proved by the fact that violation of one statement implies
violation of second.
Body A at temp. t1
Atmosphere at t2
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