Basic Concept of Thermodynamics MORGAN

8/8/2019 Basic Concept of Thermodynamics MORGAN

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Koti Vidya Charitable Trusts

Alamuri Ratnamala Institute of Engineering And Technology,

A. S. Rao Nagar, Sapgaon.

1

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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Alamuri Ratnamala Institute of Engineeri

Basic Concept of Thermodynamics MORGAN

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