Iit k Thermo Part 1 - Copy

8/13/2019 Iit k Thermo Part 1 - Copy

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The lecture deals with

Introduction Areas of Application of Thermodynamics Different Approaches in the study of Thermodynamics SI Units

Introduction

The most of general sense of thermodynamics is the study of energy and its relationship to theproperties of matter. All activities in nature involve some interaction between energy and matter.Thermodynamics is a science that governs the following:

Energy and its transformation easibility of a process involving transformation of energy

easibility of a process involving transfer of energy E!uilibrium processes

"ore specifically# thermodynamics deals with energy conversion# energy e$change and the direction ofe$change.

Areas of Application of Thermodynamics:

All natural processes are governed by the principles of thermodynamics. %owever# the following engineeringdevices are typically designed based on the principles of thermodynamics.

Automotive engines# Turbines# &ompressors# 'umps# ossil and (uclear 'ower 'lants# 'ropulsion systems for theAircrafts# Separation and )i!uefication 'lant# *efrigeration# Air+conditioning and %eating Devices.

The principles of thermodynamics are summari,ed in the form of a set of a$ioms. These a$ioms are -nown as fourthermodynamic laws:


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The ,eroth law# the first law# the second law and the third law.

The eroth )aw deals with thermal e!uilibrium and provides a means for measuring temperatures.

The irst )aw deals with the conservation of energy and introduces the concept of internal energy.

The Second )aw of thermodynamics provides with the guidelines on the conversion of internal energy ofmatter into wor-. It also introduces the concept of entropy.

The Third )aw of thermodynamics defines the absolute ,ero of entropy. The entropy of a pure crystallinesubstance at absolute ,ero temperature is ,ero.


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Different Approaches in the Study of Thermodynamics

Thermodynamics can be studied through two different approaches:

/a0 "acroscopic Approach and

/b0 "icroscopic Approach

"acroscopic Approach

&onsider a certain amount of gas in a cylindrical container. The volume /10 can be measured bymeasuring the diameter and the height of the cylinder. The pressure /'0 of the gas can be measured bya pressure gauge. The temperature /T0 of the gas can be measured using a thermometer. The state ofthe gas can be specified by the measured '# 1 and T . The values of these variables are spaceaveraged characteristics of the properties of the gas under consideration. In classical thermodynamics#we often use this macroscopic approach. The macroscopic approach has the following features.

The structure of the matter is not considered. A few variables are used to describe the state of the matter under consideration. The values of these variables are measurable following the available techni!ues of

e$perimental physics.

"icroscopic Approach

2n the other hand# the gas can be considered as assemblage of a large number of particles each ofwhich moves randomly with independent velocity. The state of each particle can be specified in terms ofposition coordinates / xi # yi# zi0 and the momentum components / pxi# pyi# pzi0. If we consider a gas

occupying a volume of 3 cm4at ambient temperature and pressure# the number of particles present in itis of the order of 3565. The same number of position coordinates and momentum components areneeded to specify the state of the gas. The microscopic approach can be summari,ed as:

A -nowledge of the molecular structure of matter under consideration is essential. A large number of variables are needed for a complete specification of the state of the matter.

SI Units

SI is the abbreviation of Syst7me International d8 Unit9s. The SI units for mass# length# time and force are -ilogram#meter# second and newton respectively. The unit of length is meter# m# defined as

3 ;5


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The unit for temperature is =elvin# = . 2ne = is the fraction 3B6


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The smaller or bigger !uantities are e$pressed using the following prefi$es

Factor Prefix Symbol Factor Prefix Symbol

1012 tera T 10-2 centi c

109 giga G 10-3 milli m

106 mega M 10-6 micro

103 kilo k 10-9 nano n

102 hecto h 10-12 pico p

Pressure

'ressure is the normal force e$erted by a system against unit area of the boundary surface.

where A approaches ,ero.

The unit for pressure in SI is pacsal# 'a

1 Pa = 1 N/m2

Two other units are widely used1 bar = 105Pa = 100 kPa = 01 !Pa

and the standard atmosphere# where

3 atm 353.46; -'a 3.5346; bar pressure e$erted by a columan of


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System Surroundings Types of Systems

Intensive and E$tensive 'roperties

System

A thermodynamic system is defined as a definite !uantity of matter or a region in space upon which attention isfocussed in the analysis of a problem. e may want to study a !uantity of matter contained with in a closed rigidwalled chambers# or we may want to consider something such as gas pipeline through which the matter flows. Thecomposition of the matter inside the system may be fi$ed or may change through chemical and nuclear reactions. Asystem may be arbitrarily defined. It becomes important when e$change of energy between the system and theeverything else outside the system is considered. The Gudgement on the energetics of this e$change is veryimportant.

Surroundings

Everything e$ternal to the system is surroundings. The system is distinguished from its surroundings by a specifiedboundary which may be at rest or in motion. The interactions between a system and its surroundings# which ta-eplace across the boundary# play an important role in thermodynamics. A system and its surroundings togethercomprise a universe.

Types of systems

Two types of systems can be distinguished. These are referred to# respectively# as closed systems and opensystems or control volumes. A closed system or a control mass refers to a fi$ed !uantity of matter# whereas acontrol volume is a region in space through which mass may flow. A special type of closed system that does notinteract with its surroundings is called an Isolated system .

Two types of e$change can occur between the system and its surroundings:

3.energy e$change /heat or wor-0 and6.e$change of matter /movement of molecules across the boundary of the system and surroundings0.

@ased on the types of e$change# one can define

isolated systems: no e$change of matter and energy

closed systems: no e$change of matter but some e$change of energy

open systems: e$change of both matter and energy

If the boundary does not allow heat /energy0 e$change to ta-e place it is called adiabatic boundary otherwise it isdiathermal boundary.

Property

To describe a system and predict its behaviour re!uires a -nowledge of its properties and how those properties arerelated. 'roperties are macroscopic characteristics of a system such as mass# volume# energy# pressure andtemperature to which numerical values can be assigned at a given time without -nowledge of the past history of thesystem. "any other properties are considered during the course of our study.

The value of a property of a system is independent of the process or the path followed by the system inreaching a particular state.


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The change in the value of the property depends only on the initial and the final states.

The word state refers to the condition of a system as described by its properties.

"athematically# if ' is a property of the system# then the change in the property in going from the initial state 3 tothe final state 6 is given by

If ' ' /$# y0 then#

where#

If # then d' is said to be an e$act differential# and ' is a point function. A thermodynamic property

is a point function and not a path function. 'ressure# temperature# volume or molar volume are some of the

!uantities which satisfy these re!uirements.

Intensive and Extensive Properties

There are certain properties which depend on the si,e or e$tent of the system# and there are certainproperties which are independent of the si,e or e$tent of the system. The properties li-e volume# whichdepend on the si,e of the system are called e$tensive properties. The properties# li-e temperature andpressure which are independent of the mass of the system are called intensive properties. The test foran intensive property is to observe how it is affected when a given system is combined with some

fraction of e$act replica of itself to create a new system differing only by si,e. Intensive properties arethose which are unchanged by this process# whereas those properties whose values are increased ordecreased in proportion to the enlargement or reduction of the system are called e$tensive properties.

Assume two identical systems S3and S6as shown in igure 6.3. @oth the systems are in identicalstates.)et S4be the combined system. Is the value of property for S4same as that for S3/and S60H


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igure !"#

If the answer is yes# then the property is intensive

If the answer is no# then the property is e$tensive

The ratio of the e$tensive property to the mass is called the specific value of that property

specific volume# v 1Bm 3B / is the density0

specific internal energy# u UBm

Similarly# the molar properties are defined as the ratios of the properties to the mole number /(0 of thesubstance

"olar volume 1B(

"olar internal energy UB(


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Energy "acroscopic modes of Energy "icroscopic modes of Energy Thermodynamic E!uilibrium 'rocess

Energy

Energy is often defined as the capacity to produce wor-. %owever# this JcapacityJ has a special significance. Thecapacity represents a combination of an effort and the change brought about by the effort. %owever# the effort ise$erted in overcoming resistance to a particular type of change.

The effort involved is measured !uantitatively as a Jdriving forceJ in thermodynamics. A driving force is a propertywhich causes and also controls the direction of change in another property. The !uantitative value of this change iscalled a JdisplacementJ. The product of a driving force and its associated displacement represents a !uantity ofenergy# but in thermodynamics this !uantity has meaning only in relation to a specifically defined system.

*elative to a particular system there are generally two ways of locating a driving force and the displacement itproduces. In one way# the driving force and the displacement are properties of the system and are located entirelywithin it. The energy calculated from their product represents a change in the internal energy of the system.

Similarly# both the driving force and its displacement could be located entirely within the surroundings so that thecalculated energy is then a change in the total energy of the surroundings.

In another way# the displacement occurs within the system but the driving force is a property of the surroundingsand is applied e$ternally at the system boundary. @y definition# the boundary of a system is a region of ,erothic-ness containing no matter at all so that the energy calculated in this way is not a property of matter either in thesystem or in its surroundings but represents a !uantity of energy in transition between the two. In any !uantitativeapplication of thermodynamics it is always important to ma-e a careful distinction between energy changes within asystem or within its surroundings and energy in transition between them.

$acroscopic modes of energy

=inetic Energy /=E0

If a body is accelerated from its initial velocity to final velocity # the total wor- done onthe body is

The wor- done on a body in accelerating it from its initial velocity to a final velocity # is e!ual to the change inthe -inetic energy of the body. If the body is decelerated from a velocity to a velocity by the application ofresisting force# the wor- done by the body is e!ual to decrease in its -inetic energy.


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'otential Energy /'E0

A body of mass mis moved from an initial elevant 3to a final elevation 6/ig 4.30

igure %"#

The force on the body# mgThis force has moved a distance / 6+ 30 . Therefore# the wor- done on the body

The -inetic energy and potential energy are also called organi,ed form of energy that can be readily converted intowor-.

$icroscopic modes of energy

The microscopic modes of energy refer to the energy stored in the molecular and atomic structure of the system.

The molecules are in random motion. A molecule possesses energy in several forms.

Translational energy# *otational energy# 1ibrational energy.Electronic energy# &hemical energy# (uclear energy.

If K represents energy of one molecule# then

If ( is the total number of molecules in the system# then the total amount of microscopic form of energy

U ( K e may also call this as I(TE*(A) E(E*LM of the system. The internal energy# U is due to random motions ordisorgani,ed motions of molecules. The internal energy cannot be readily converted into wor-. 2ne of the maGortas-s involved in thermodynamics is devising means for converting disorgani,ed internal energy into useful ororgani,ed wor-.

Thermodynamic E&uili'rium

Steady state

Under the steady state condition# the properties of the system at any location are independent of time.

E!uilibrium

At the state of e!uilibrium# the properties of the system are uniform and only one value can be assigned to it.


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In thermodynamics# e!uilibrium refers to a state of e!uilibrium with respect to all possible changes# thermal#mechanical and chemical.

aThermal e!uilibrium

A state of thermal e!uilibrium can be described as one in which the temperature of the system is uniform.b"echanical e!uilibrium

"echanical e!uilibrium means there is no unbalanced force. In other words# there is no pressure gradient within thesystem.

c&hemical e!uilibrium

The criterian for chemical e!uilibrium is the e!uality of chemical potential

Superscripts A and @ refers to systems and subscript i refers to component

If Libbs function is given by L# L U N '1 O TS

where niis the number of moles of substance i . The composition of a system does not undergo any change

because of chemical reaction

ProcessIn thermodynamics we are mainly concerned with the systems which are in a state of e!uilibrium. henever asystem undergoes a change in its condition# from one e!uilibrium state to another e!uilibrium state# the system issaid to undergo a process.

&onsider a certain amount of gas enclosed in a piston+cylinder assembly as our system. Suppose the piston movesunder such a condition that the opposing force is always infinitesimally smaller than the force e$erted by the gas.The process followed by the system is reversible .

A process is said to be reversible if the system and its surroundings are restored to their respective initial states byreversing the direction of the process. A reversible process has to be !uasi+static# but a !uasi + static process is notnecessarily !uasi+static.


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igure %"!

The process is irreversible if it does not fulfil the criterion of reversibility. "any processes are characteri,ed by thefact that some property of the system remains constant. These processes are:

A process in which the volume remains constantconstant volume process. Also called isochoric process B isometric process

A process in which the pressure of the system remains constant.

constant pressure process. Also called isobaric process

A process in which the temperature of the system is constant.

constant temperature process. Also called isothermal process

A process in which the system is enclosed by adiabatic wall.

Adiabatic process


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or- Thermodynamic Definition of or- %eat

(or)

or- is one of the basic modes of energy transfer. The wor- done by a system is a path function# andnot a point function. Therefore# wor- is not a property of the system# and it cannot be said that the wor-is possessed by the system. It is an interaction across the boundary. hat is stored in the system isenergy# but not wor-. A decrease in energy of the system appears as wor- done. Therefore# wor- isenergy in transit and it can be indentified only when the system undergoes a process.

or- must be regarded only as a type of energy in transition across a well defined# ,ero thic-ness#boundary of a system. &onse!uently wor-# is never a property or any !uantity contained within asystem. or- is energy driven across by differences in the driving forces on either side of it. 1arious-inds of wor- are identified by the -ind of driving force involved and the characteristic e$tensive propertychange which accompanied it. or- is measured !uantitatively in the following way. Any driving forceother than temperature# located outside the system on its e$ternal boundary# is multiplied by atransported e$tensive property change within the system which was transferred across the systemboundary in response to this force. The result is the numerical value of the wor- associated with thissystem and driving force. In static E!uilibrium# 'A /ig P.30. The dQ is small so that ' does notchange. The change in volume of the gas AdQ. The elemental wor-#

ddQ'AdQ'd1


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igure *"#

$odule # :

+ecture * : (or) and ,eat

Thermodynamic Definition of (or)

In thermodynamics# wor- done by a system on its surroundings during a process is defined as thatinteraction whose sole effect# e$ternal to the system# could be reduced as the raising of a massthrough a distance against gravitational force. )et us consider the raising of mass m from an initial

elevation ,3to final elevation ,6against gravitational force. To raise this mass# the force acting on themass is given by mg . The wor- done on the body is mg/ , 6+ ,30

An e$ternal agency is needed to act on the system It can be seen that e$pansion of the gas gets reduced to raising a mass against gravitational

force /igure P.60

dW = F dX = P A dX = P dV


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igure *"!

During this e$pansion process# the e$ternal pressure is always infinitesimally smaller than the gaspressure.

igure *"%

&ompare two systems shown in the figure P.4. )et the resistor be replaced by a motor drawing thesame amount of current as the resistor. The motor can wind a string and thereby raise the masswhich is suspended. As far as the battery is concerned# the situations are identical. So# according tothermodynamic definition of wor-# the interaction of a battery with a resistor is called wor-. @y

manipulating the environment# that is e$ternal to the battery /system0# the effect can be reduced toraising of a mass against the gravitational force and that is the only effect on the surroundings. ecan see that the thermodynamic definition of wor- is more general than that used in mechanics.

Situation in which ( - P d.


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igure *"*

)et the initial volume be 13and pressure '3

)et the final volume be 16and pressure '6

hat should be the wor- done in this caseH Is it e!ual to R' d1 H

"' d1 area under the curve indicating the process on '+1 diagram.The e$pansion process may be carried out in steps as shown in figure P.P. It is possible to draw a smooth curvepassing through the points 3bcde6 . Does the area under the curve /figure P.;0 represent wor- done by thesystemH The answer is no# because the process is not reversible. The e$pansion of the gas is not restrained by ane!ual and opposing force at the moving boundary.

# "P dV

igure *"/

(o e$ternal force has moved through any distance in this case# the wor- done is ,ero. Therefore# we observe that

R ' d1 only for reversible process R ' d1 for an irreversible process

Another e$ceptional situation

The piston is held rigid using latches /igure P.0d1 5

or- done on the gas is e!ual to the decrease in the potential energy of mass m

A situation where d1 5 and yet d is not ,ero


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such wor- can be done in one direction only. or- is done on the system by the surroundings

igure *"0

,eat

%eat is energy transfer which occurs by virtue of temperature difference across the boundary. %eat li-ewor-# is energy in transit. It can be identified only at the boundary of the system. %eat is not stored inthe body but energy is stored in the body. %eat li-e wor-# is not a property of the system and hence itsdifferential is not e$act. %eat and wor- are two different ways of transferring energy across theboundary of the system.

The displacement wor- is given by /figure P.


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product of the intensive property ' and the differential change in the e$tensive property# d1 .

Fust li-e displacement wor-# the heat transfer can also be written as

The !uantity dC is an ine$act differential.

dQ = TdX Q is an e$tensive property and dQ is an e$act differential. The e$tensive property is yet to be defined.e shall see later that Q is nothing but the entropy# S of a system.

It is possible to write

or#

where is integrating factor.


Introduction to state postulate

eroth )aw of Thermodynamics

Temperature Scale

'erfect Las Scale

Introduction to state postulate

Since every thermodynamic system contains some matter with energy in its various forms# the system can becompletely described by specifying the following variables.

The composition of the matter in terms of mole numbers of each constituent.The energy of the system.The volume of the system# andThe measurable properties# such as pressure and temperature.


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@y specifying these !uantities# the state of the system is defined. 2nce the system is in a given state# it possessesa uni!ue state of properties li-e pressure# ' # temperature# T # density# etc. All the properties of a system cannot bevaried independently since they are interrelated through e$pressions of the following type

or e$ample# the pressure# temperature and molar volume / 0 of an ideal gas are related by the e$pression ' *T . %ere * is a constant. 2nly two of the three variables ' # and T can be varied independently. Cuestion is thatfor a given thermodynamics system# how many variables can be varied independently.

The State Postulate

As noted earlier# the state of a system is described by its properties. @ut we -now from e$perience that we do notneed to specify all the properties in order to fi$ a state. 2nce a sufficient number of properties are specified# the restof the properties assume certain values automatically. The number of properties re!uired to fi$ the state of a systemis given by the state postulate:

The state of a simple compressible system is completely specified by two independent properties.

A system is called a simple compressible system in the absence of electrical# magnetic# gravitational# motion# andsurface tension effects. These effects are due to e$ternal force fields and are negligible for most engineeringproblems. 2therwise# an additional property needs to be specified for each effect which is significant. If thegravitational effects are to be considered# for e$ample# the elevation , needs to be specified in addition to the twoproperties necessary to fi$ the state.

The state postulate is also -nown as the two+property rule.The state postulate re!uires that the two properties specified be independent to fi$ the state. Two properties areindependent if one property can be varied while the other one is held constant. Temperature and specific volume#for e$ample# are always independent properties# and together they can fi$ the state of a simple compressiblesystem /ig. ;.30.

igure /"#

or a simple compressible substance /gas0# we need the following properties to fi$ the state of a system:

or 'T or T or u' or u . hy not u and TH They are closely related. orideal gas uu/t0

Temperature and pressure are dependent properties for multi+phase systems. At sea level / ' 3 atm0# water boilsat 355o but on a mountain+top where the pressure is lower# water boils at a lower temperature. That is# T f/'0 during a phase+change process# thus temperature and pressure are not sufficient to fi$ the state of a two+phasesystem. Therefore# by specifying any two properties we can specify all other state properties. )et us choose '

and

Then


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T T/'# 0 u u/'# 0 etc.

&an we say /p# 0

(o. or- is not a state property# nor is the heat added /C0 to the system.

2eroth +aw of Thermodynamics

Statement: If a body 3 is in thermal e!uilibrium with body 6 and body 4# then the body 6 and body 4 are also inthermal e!uilibrium with each other

igure /"!

Two systems 3 and 6 with independent variables / U3# 13# (30 and /U6# 16# (60 are brought into contact with

each other through a diathermal wall /figure ;.60. )et the system 3 be hot and system 6 be cold. @ecause ofinteraction# the energies of both the systems# as well as their independent properties undergo a change. The hotbody becomes cold and the cold body becomes hot. After sometime# the states of the two systems do not undergo

any further change and they assume fi$ed values of all thermodynamic properties. These two systems are thensaid to be in a state of thermal e!uilibrium with each other. The two bodies which are in thermal e!uilibrium witheach other have a common characteristic called temperature. Therefore temperature is a property which has thesame value for all the bodies in thermal e!uilibrium.

Suppose we have three systems 3# 6 and 4 placed in an adiabatic enclosure as shown in figure ;.4.

igure /"%


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The systems 3 and 6 do not interact with each other but they interact separately with systems 4 through adiathermal wall. Then system 3 is in thermal e!uilibrium with system 4 and system 6 is also in thermal e!uilibriumwith system 4. @y intuition we can say that though system 3 and 6 are not interacting# they are in thermale!uilibrium with each other.

Suppose system 3 and 6 are brought into contact with each other by replacing the adiabatic wall by a diathermalwall as shown in figure ;.4 /@0. urther they are isolated from system 4 by an adiabatic wall. Then one observes nochange in the state of the systems 3 and 6.

Temperature Scale

@ased on ,eroth law of thermodynamics# the temperature of a group of bodies can be compared bybringing a particular body /a thermometer0 into contact with each of them in turn. To !uantify themeasurement# the instrument should have thermometric properties. These properties include: Thelength of a mercury column in a capillary tube# the resistance /electrical0 of a wire# the pressure of agas in a closed vessel# the emf generated at the Gunction of two dissimilar metal wires etc. arecommonly used thermometric properties.

To assign numerical values to the thermal state of a system# it is necessary to establish a temperaturescale on which temperature of a system can be read. Therefore# the temperature scale is read byassigning numerical values to certain easily reproducible states. or this purpose# it is customary to use

a Ice 'oint: The e!uilibrium temperature of ice with air saturated water at standardatmospheric pressure which is assigned a value of 5o&.

b Steam 'oint: The e!uilibrium temperature of pure water with its own vapor at standardatmospheric pressure# which is assigned a value of 355o&.

This scale is called the &elsius Scale named after Anders &elsius.

Perfect 3as Scale

An ideal gas obeys the relation

' * T where * is the Universal Las &onstant / * >.43P FBmol =0. This e!uation is only an appro$imation to the actualbehavior of the gases. The behavior of all gases approaches the ideal gas limit at sufficiently low pressure /in the

limit ' 50. The perfect gas temperature scale is based on the observation that the temperature of a

gas at constant volume increases monotonically with pressure. If the gas pressure is made to approach ,ero# thegas behavior follows the relation

' * T

igure ;.P shows a constant volume gas thermometer.The bulb is placed in the system whose temperature is to be measured. The mercury column is so adGusted that thelevel of mercury stands at the reference mar- S . This ensures that the volume of the gas is held at a constantvalue. )et the pressure of the gas be read as '. )et a similar measurement be made when the gas bulb ismaintained at the triple point of water# ' tp. e can obtain triple point by putting water and ice in an insulated

chamber and evacuating air / which is then replaced by water vapour0.


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igure /"*

The temperature of the triple point of water has been assigned a value of 6


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the system can be obtained only when the gas behaves li-e an ideal gas# and hence the value is to be calculated in

limit 'tp 5. Therefore

# as

A constant pressure thermometer also can be used to measure the temperature. In that case#

when

%ere 1tp is the volume of the gas at the triple point of water and 1 is the volume of the gas at the system

temperature.


irst )aw of Thermodynamics

%eat is a 'ath unction

Energy is a 'roperty of the System

A 'erpetual "otion "achine of irst =ind

Analysis of &losed Systems

irst +aw of Thermodynamics

A series of E$perimants carried out by Foule between 3>P4 and 3>P> from the basis for the irst )aw ofThermodyanmics

The following are the observations during the 'addle heel e$periment shown in ig. .3.

igure 0"#

or- done on the system by lowering the mass m through change in 'E of m

Temperature of the system was found to increase

System was brought into contact with a water bath


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System was allowed to come bac- to initial state

Energy is transferred as heat from the system to the bath

The system thus e$ecutes a cycle which consists of wor- input to the system followed by the transfer of heat fromthe system.

/.30

henever a system undergoes a cyclic change# however comple$ the cycle may be# the algebraic sum of the wor-transfer is e!ual to the algebraic sum of the energy transfer as heat /I*ST )A 2 T%E*"2DM(A"I&S0.

Sign convention followed in this te$t:

or- done by a system on its surroundings is treated as a positive !uantity.

Energy transfer as heat to a system from its surroundings is treated as a positive !uantity

/.60

or#

,eat is Path unction

)ets us consider following two cycles: 3a6b3 and la6cl and apply the first law of thermodynamics E! /.60 to get

igure 0"!

/.40

or#

/.P0

Subtracting E!. /.P0 from E!. /.40

/.;0

Since# wor- depends on the path


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/.0

Therefore#

/.0

and depend on path function followed by the system. The !uantity is the same for both the

processes and connecting the states 6 and 3. The !uantity does not depend on path followedby the system# depends on the initial and final states. %ence is an e$act differential.

Differential of property of the system

This property is the internal energy of system# E

/.?0

Energy of an Isolated System

An isolated system is one in which there is no interaction of the system with the surroundings. or an isolatedsystem

/.350


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A Perpetual $otion $achine of irst 4ind

Thermodynamics originated as a result of man8s endeavour to convert the disorgani,ed form of energy/internal energy0 into organi,ed form of energy /wor-0.

/.33

0An imaginary device which would produce wor- continuously without absorbing any energy from itssurroundings is called a 'erpetual "otion "achine of the irst -ind# /'""=0. A '""= is a devicewhich violates the first law of thermodynamics. It is impossible to devise a '""= /igure .40

igure 0"%

The converse of the above statement is also true# i.e.# there can be no machine which wouldcontinuously consume wor- without some other form of energy appearing simultaneously.

Analysis of 5losed System

)et us consider a system that refers to a definite !uantity of matter which remains constant while thesystem undergoes a change of state. e shall discuss the following elementary processes involvingthe closed systems.

&onstant 1olume 'rocess

2ur system is a gas confined in a rigid container of volume 1 /*efer to igure .P0


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igure 0"*

)et the system be brought into contact with a heat source.

The energy is e$changed reversibly. The e$pansion wor- done /'d10 by the system is ,ero.

Applying the first law of thermodynamics# we get

/.360

or#

/.340

%ence the heat interaction is e!ual to the change in the internal energy of the system.

&onstant 1olume Adiabatic 'rocess

*efer to igure .; where a change in the state of the system is brought about by performing paddlewheel wor- on the system.


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igure 0"/

The process is irreversible. %owever# the first law gives

/.3P0

or

/.3P0

Interaction of heat and irreversible wor- with the system is same in nature. /+0 represents the wor-done on the system by the surroundings

Specific ,eat at 5onstant .olume

@y definition it is the amount of energy re!uired to change the temperature of a unit mass of the substance by onedegree.

/.30

hile the volume is held constant. or a constant volume process# first law of thermodynamics gives

/.3


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0

Therefore#

/.3>0

here is the specific internal energy of the system. If varies with temperature# one can use mean

specific heat at constant volume

/.3?0

The total !uantity of energy transferred during a constant volume process when the system temperature changesfrom

/.65

0

The unit for is -FB-g=. The unit of molar specific heat is -FB-mol=.


&onstant 'ressure 'rocess 3

&onstant 'ressure 'rocess 6

Specific %eat at &onstant 'ressure

&onstant Temperature 'rocess

Adiabatic 'rocess

5onstant Pressure Process6#

A gas in the piston+cylinder assembly is considered as the system of interest /figure


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igure 1"#

The pressure is maintained at a constant value by loading the system with a mass.

The cylinder is brought into contact with a heat source.

Energy transfer as heat ta-es place reversibly. The wor- is done by system when it changes from the initial state /30to the final state /60.

/


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igure 1"!

(ow the application of first law enables us to write

/


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There will be an accompanying change in temperature.

Specific heat at constant pressure is defined as the !uantity of energy re!uired to change thetemperature of a unit mass of the substance by one degree during a constant pressure process.

/


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Adia'atic Process

1Irreversible Adiabatic 'rocess

A process in which there is no energy transfer as heat across the boundaries of the system# is called an adiabaticprocess. or an adiabatic process# C5. 'addle wheel wor- is performed on the system /igure


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Therefore#

/


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The lecture contains

&haracterisation of *eversible Adiabatic 'rocess

'olytropic 'rocess

Ideal Las "odel

5haracterisation of 7eversi'le Adia'atic Process

)et us find out the path followed by the system in reaching the final sate starting from the initial state. e havealready seen that for an ideal gas

/>.30

or#

/>.60

or#

/>.40

or#

/>.P0

or

constant/>.;

0

Since#

/>.0

rom />.P0 and />.0 we get


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/>..>0

or#

constant />.?0

Polytropic Process

Ideal gas undergoes a reversible+adiabatic process the path followed by the system is given by

constant />.350

and the wor- done per -g of gas

/>.330

To generalise#

/>.360

n is polytropic inde$ / is the property of the system# also it indicates reversible+adiabatic process0

n 5# constant pressure process

n 3# constant temperature process

n # reversible adiabatic process

n #constant volume process

Ideal 3as $odel


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or many gases# the ideal gas assumption is valid and the relationship can be simplified by

using the ideal gas e!uation of state:

or an ideal gas# it has been mentioned that the specific internal energy is a function of

temperature only#

Accordingly# specific enthalpy is a function of temperature only# since

'hysically# a gas can be considered ideal only when the inter+molar forces are wea-.

This usually happens in low pressure and high temperature ranges.

/>.340

/>.3P0

$ Specific heat ratio

/>.3;0

/>.30

or#

/>.3.3>0

In some cases# the temperature dependence of the specific heat can be written in polynomial form.

2therwise# ideal gas tables are also available. They are easier to use compared to the thermodynamictables since temperature is the only parameter.


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Thermodynamic Properties of fluids

"ost useful properties:

'roperties li-e pressure# volume and temperature which can be measured directly. Also

viscosity# thermal conductivity# density etc can be measured.

'roperties li-e internal energy# enthalpy etc. which cannot be measured directly

Pure Su'stance

A pure substance is one which consists of a single chemical species.

5oncept of Phase

Substances can be found in different states of aggregation. Ice# water and steam are the three different

physical states of the same species . @ased on the physical states of aggregation the

substances are generally classified into three states as

a.Solidb.li!uidc.gas

The different states of aggregation in which a pure substance can e$ist# are called its phases. "i$turesalso e$ist in different phases. or e$ample# a mi$ture of alcohal and water can e$ist in both li!uid andvapour phases. The chemical composition of the vapour phase is generally different from that of the

li!uid phase.

Lenerali,ing the above observations# it can be said that a system which is uniform throughout both inchemical composition and physical state# is called a homogeneous substance or a phase.

All substances#+solids# li!uids and gases# change their specific volume depending on the range ofapplied pressure and temperature.

hen the changes in the specific volume is negligible as in the case of li!uids and solids# the substancemay be treated as incompressible.

The isothermal compressibility of a substance % is defined as

The coefficient of volume e$pansion of a substance is defined as


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E&uations of State

E!uations that relate the pressure# temperature and specific volume or molar volume of a substance.

They predict the relationship of a VgasW reasonably well within selected regions.

@oyle8s law:

at con&tant pre&&'re

or#

&onstant at constant temperature

&harles8 )aw:

At constant pressure

At constant volume

@oyle8s law and &harles8 law can be combined to yield

here * is the characteristic gas constant. If the specific volume is substituted by the

molar volume# then * is substituted by the universal gas constant# >.43P -F B -mol =. Again# it


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can be shown that for an ideal gas .

In summary# the Ideal gas e!uation:

where * is the specific constant

# where is the universal gas constant />.43P -F B - mole =0 " is the molar

mass# defined as the mass of one mole of a substance. e can also write

where is the molar volume.

E$ample: " 6> -g B -mol for nitrogen /since its molar mass is 6>0

" 46 -g B -mol for o$ygen / 26with a molar mass of 460

(ote: "any gases such as air# o$ygen can be treated as ideal gases. %owever# dense gases such aswater vapor and refrigerant vapor should not be treated as ideal gas. Use property table instead.

Ideal 3as

The -inetic theory of gases model a gas as a collection of elastic particles. The statistical analysis ofthese with some assumptions results as the ideal gas law

"ost gases deviate from ideal gas in the vicinity of the critical point and saturated vapour line.

"ost gases behaves li-e ideal gas at high temperature and low pressure regions.

8oules Experiment

*efer to figure ?.3

igure 9"#

2ne of the vessels was filled in with air at 66 atm pressure and the other vessel was evacuated. Theinitial temperature of the water bath was measured. The valve was opened allowing air to occupy boththe containers. The temperature of the water bath was measured again and it was found that thetemperature did not change. The gas contained in both the vessels is our system. 5 and C5. Sincethe number of moles of the gas also remains constant# it follows that . The pressure and thevolume of the gas changed and yet the internal energy did not change. %ence

So#


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(91)

(92)

Since#

(93)

(9*)

.an der (aals e&uation of state:

The gases at low pressure and high temperatures follow ideal gas law. Lases that do not follow idealgas law are re!uired to be represented by a similar set of mathematical relations. The first effort wasfrom clausius.

&lausius 'roposed

/?.;0

1an der aals# by applying the laws of mechanics to individual molecules# introduced two correctionterms in the e!uation of ideal gas. 1an der aals e!uation of state is given by.

/?.0

The term accounts for the intermolecular forces and b accounts for the volume occupied by

the gas molecules.


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Since 1an der aal8s e!uation ta-es into account the inter+molecular forces# it is e$pected to hold goodfor li!uid phase also. (ow a days# the 1an der aal8s e!uation is used to predict the phase e!uilibriumdata. The constants and b are determined from e$perimental data. %owever# rearrangingthe 1an der aal8s e!uation# we get

/?..;

h /-FB-g0 6>

s /-FB-g -0 >.36

The values for a given condition are to be evaluated through interpolation.


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&onservation of "ass applied to a control volume

&onservation of Energy applied to a &ontrol 1olume

5onservation of $ass applied to a control volume

)et us consider the law of conservation of mass as applied to the control volume.

igure #!"#

During a time interval # let the mass enter the control volume and the mass leave thecontrol volume. )et represent the mass inside the control volume at time t# andrepresent the mass inside the control volume at time /tNdt0. The law of conservation of mass gives:


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/36.30

/36.60

%ere the )%S gives the change in mass within the &1 during the time interval # while *%S gives the

net mass flow into the &1 during the time . Dividing both sides of the e!uation by # we get

/36.40

In the limiting case as # we obtain

/36.P0

The )%S gives rate of accumulation of mass inside the &1 and the *%S has respective terms givingrate of mass entering the &1 and rate of mass leaving the &1.

If the &1 has many inlet and e$it ports# the e!uation becomes

/36.;0


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)et total mass inside the &1 at time .

total mass inside the &1 at time .

specific energy of matter inside the control volume at time t.

specific energy of matter inside the control volume at time .

and 'ressure at the inlet and e$it ports# respectively.

and low velocity at the inlet and e$it ports# respectively.

and specific volumes at the inlet and e$it ports respectively

and specific energy of the material at the inlet and e$it ports respectively.

*ate of energy flow as heat into the control volume

*ate of shaft wor- done by the control volume

The mass contained in the region A which enters the control volume during the time interval

The mass contained in the region @ which leaves the control volume during the time interval


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rom the mass balance# we can write

/36.0

where is the mass entering the control volume during the differential time . To accommodate

this# the mass inside the control volume has to be compressed such that its volume decreases by theamount . This is accomplished by the pressure acting on the material entering the controlvolume. Therefore# the wor- done

Since the mass has to leave the control volume at the e$it port# the wor- done #

Energy of the system at time

Energy of the system at time

During the time interval e may account for the following

Energy transferred as heat to the system

Shaft wor- done by the system

Energy flow as heat into the control volume and the shaft wor- delivered by the control volume areta-en as positive. @y applying the first law of thermodynamics# we get

/36.0

or#


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/36.?0

In the limiting case#

/36.350

here#

and

elevation of the e$it and inlet ports above the datum level. The above e$pression can now be

rearranged as

/36.330

*ate of energy accumulation *ate of energy inflow + *ate of energy outflow


Steady State low 'rocesses

Application of Steady State low 'rocesses

Steady6state low Processes


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"any of the engineering devices li-e turbines# compressors# pumps# no,,les# condensers# heat e$changers etc.operate at steady state conditions. The general e$pression developed for the control volume in the earlier lecturecan be simplified if steady flow conditions are assumed.

These are:

The mass flows into the control volume at a constant rate and leaves the control volume at the same rate.

Therefore# there is no accumulation of mass inside the control volume. Thus# .or#

/34.30

The state of the matter at the inlet# e$it and at any given point inside the control volume does not changewith respect to time. Therefore#

/34.60

The rate of energy transfer as heat and wor- across the control surface is a constant. constantconstant

ith these# the first law for the control volume reduces to the form

/34.40

Application of Steady6state low Processes

/a0 Turbine:

Turbine converts enthalpy into useful wor-. Steam or gas at high temperature and pressure is allowed to e$pandthrough a system of rotors.

igure #%"#

The change in -inetic and potential energy of steam or gas as it passes through the turbine can be ignored withoutintroducing much error. urther# if the heat losses from the turbine are negligible# the first law for this steady stateflow reduces to

/34.P0

Therefore# in an adiabatic turbine# the wor- done per unit mass of the fluid is e!ual to the decrease in the enthalpyof the fluid. %ere# is positive


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/34.?0

e get#

/34.350


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igure #%"*

The figure 34.P e$plains the wor-ing of a simple heat e$changer. The governing e!uation may be

modified for multiple entry and multiple e$it of the system as

/34.360/34.340/34.3P0/34.3;0

urther# and

/34.30

is the mass flow rate of cold fluid and is the mass flow rate of hot fluid.


Throttling 'rocess

Application of Throttling 'rocess

Throttling Process:


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The porous plug e$periment was designed to measure temperature changes when a fluid flows steadily through aporous plug which is inserted in a thermally insulated# hori,ontal pipe. The apparatus used by Foule and Thomsonis shown in igure 3P.3.

igure #*"#

A gas at pressure and temperature flows continuously through a porous plug in a tube

and emerges into a space which is maintained at a constant pressure . The device is thermally

insulated and -ept hori,ontal. &onsider the dotted portion as control volume.

This results in

Therefore# whenever a fluid e$pands from a region of high pressure to a region of low pressure through a porousplug# partially opened valve or some obstruction# without e$changing any energy as heat and wor- with the

surrounding /neglecting# the changes in 'E and =E0# the enthalpy of the fluid remains constant# and the fluid is saidto have undergone a throttling process. If the downstream pressure is held at several different values successively

and at each of these is measured# we shall obtain a situation e$plained by igure 3P.6.

igure #*"!


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Each plotted point represents a state for which the enthalpy is e!ual to . If we Goin all these points we

shall be able to obtain a constant enthalpy line /figure 3P.40.

igure #*"%

Such a plot of ' versus yields may also be called isenthalpic curve. The slope of the isenthalpic curve

is called the Foule+Thomson coefficient and given by

The e$periments are conducted with different and in order to find out the isenthalpic

curves. A family of isenthalpic curves is shown in igure 3P.P which is typical of all real gases.

igure #*"*

The point at which is called the inversion point. The locus of all the inversion points is the inversion

curve.

In the region left of the inversion curve# . In the throttling process the down stream

pressure is always less than the upstream pressure . Therefore# whenever a real gas is


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subGected to throttling# the temperature of the gas decreases if the initial state lies in the region to the left of theisenthalpic curve. This is e$plained by a process from to in igure 3P.P.

To the right of the inversion curve# . If the initial state of gas lies in the region to the right of the inversion

curve# the temperature of the gas increase upon throttling. or almost all the gases# at ordinary range of pressures

and temperature# and the ma$imum inversion temperature is above the room temperature. The

e$ceptions are hydrogen# helium and neon. or hydrogen# the ma$imum inversion temperature is 655 = and forhelium the ma$imum inversion temperature is 6P =. If hydrogen is throttled at room temperature# the temperature ofthe gas increases. To produce low temperature by throttling# the initial temperature of hydrogen should be below655 =. This is usually accomplished by cooling with li!uid nitrogen. Similarly# in the production of li!uid helium bythrottling# the initial temperature of helium should be below 6P =. %ence it is cooled by li!uid hydrogen prior tothrottling.

Suppose an ideal gas is throttled. Since throttling process is isenthalpic# and for an ideal gas enthalpy is a function

of temperature only# the temperature of an ideal gas does not change during a throttling process. %ence

for an ideal gas.

Applications of Throttling

/a0 *efrigeration

The wor-ing fluid /called refrigerant0 leaving the evaporator as vapour at state 3 undergoes an adiabaticcompression in a compressor and leaves as saturated vapour at state 6. This compressed refrigerant enters acondenser where it reGects heat to the ambient atmosphere and leaves as a saturated li!uid at high pressure atstate 4. Then the li!uid refrigerant at high pressure undergoes throttling and leaves as a mi$ture of li!uid andvapour at low pressure at state P. During throttling# the li!uid vapori,es partially and its temperature decreases. Thecooled refrigerant then passes through an evaporator where it absorbs energy from the body to be cooled# andleaves as hot vapor at state 3. inally# the hot refrigerant vapour goes to the compressor# thus completing a cycle.

igure #*"/

Applying the first law of thermodynamics to each of the units /control volume0 the following relations are obtained:

&ompressor /adiabatic0

&ondenser /constant pressure cooling0

Throttling /isenthalpic0

Evaporator /constant pressure heat addition0

The coefficient of performance /&2'0 of the refrigerator is defined as the ratio of the energy absorbed at theevaporator to the energy re!uired to perform the tas-.


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hen a real gas which is initially at a temperature lower than the ma$imum inversion temperature is throttled# itstemperature decreases. This principle is used by )inde in the )i!uefaction of gases. *efer to figure 3P. forunderstanding the operating cycle.

igure #*"0

The gas is compressed to a high pressure and then cooled at constant pressure in a counter current heate$changer with the cold gas which comes from the separator. The cooled gas is throttled to a low pressure. Thussome amount of gas is converted into the li!uid phase. The two+phase mi$ture comes to the separator. The li!uid iswithdrawn and the cold gas is fed to the heat e$changer. Then the gas enters the compressor along with a freshstream of ma-e up gas for li!uefaction.


Transient low 'rocesses

&harging of a &ylinder / &ontrol 1olume Analysis0

Discharging of a cylinder /&ontrol 1olume Analysis0

Transient low Processes

During charging and discharging of cylindersBtan-s the condition of the fluid inside the cylindersBtan-s change withtime. The rates of inflow and outflow of mass are not identical and there is accumulation of mass and energy insidethe control volume.


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igure #/"#

These processes are transient flow processes. The first law e$pression for a control volume is given by

/3;.30

5harging of a 5ylinder


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Integration of the above e!uation over time gives the change of mass in the control volume during the chargingoperation

/3;.0

(ow in the e!uation /3;.P0# the last term on the *%S can be evaluated as

/3;.0

Substituting /3;.0# /3;.0 in /3;.P0 we get

/3;.?0

If the cylinder is initially empty and the filling operation is carried out under adiabatic conditions the abovee$pression reduces to

/3;.350

If the gas is treated as ideal and

Then#

/3;.330

here# is the final temperature of the gas in the cylinder and is the ratio of the specific heats. is the

temperature of the gas in supply mains.

Discharging of a cylinder


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)et# pressure of the gas inside the cylinder at

temperature of the gas inside the cylinder at

specific internal energy of the gas inside the cylinder at

and denote corresponding !uantities of the gas left in the cylinder after the dischargingoperation.

velocity of the escaping gas. rom the first law# we can write

/3;.360

(o material flows into the cylinder and the potential energy changes can be ignored.Then

/3;.340

or the discharging process# the conservation of mass gives

/3;.3P0

4ntegrating the aboe e'ation oer time gie&

/3;.3;0

Integration of the governing e!uation yields

/3;.30

(ow the term on the left hand side may be evaluated as


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/3;.30

and

/3;.3?0

inally invo-ing /3;.30 and /3;.3?0 in /3;.30 we get

/3;.650

It is assumed that the gas escapes with a uniform velocity 1 and specific enthalpy h.

5ase of an Ideal 3as

&onsider a small amount of gas in the cylinder /confined in an imaginary envelope0 in the cylinder as a system.

igure #/"%

Imagine a situation when gas escapes the cylinder.The boundary of the system changes continuously and eventually occupies the entire volume of the cylinder. Thegas which is left in the cylinder does not e$change energy in the form of heat with the surroundings. It undergoesan adiabatic e$pansion. e can prove that the gas undergoes a reversible adiabatic e$pansion.

The general e$pression is:


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/3;.630

e can change the basis of analysis from a control mass to a control volume based analysis. Under such asituation# )et us consider the cylinder volume as the volume of interest.

# and ignore the change in =E and 'E

/3;.660

rom the principle of conservation of mass

/3;.640

Therefore

/3;.6P0

or a perfect gas# and . Then e!uation /3;.6P0 can be rewritten as

/3;.6;0

or#

/3;.60

or#

/3;.60

@y integration between final state and initial state

/3;.6?0

As

/3;.450

or#


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/3;.430

here is the characteristics gas constant

So#

/3;.460

and

/3;.440

Invo-ing these relations# we get

/3;.4P0

or#

/3;.4;0

/3;.40

Therefore the gas that remains in the tan- can be considered to have undergone a reversible adiabatic e$pansionfrom the initial pressure to the final pressure .

Iit k Thermo Part 1 - Copy

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