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1.0 INTRODUCTION AND APPLICATIONS OF THERMODYNAMICS

INTRODUCTION

Thermodynamics is the study of the flow of heat into or out of a system, as the system

undergoes a physiacal or chemical transformation. (dynamics). It deals thus with the energyinteractions in physical systems. Classical thermodynamics can be stated in four laws

called the zeroth, first, second, and third laws respectively. The laws of thermodynamics

are empirical, i.e., they are deduced from experience, and supported by a large body ofexperimental evidence.

Metallurgical Thermodynamics is thermodynamics applied to Metallurgy.

1.1 APPLICATIONS OF THERMODYNAMICS

a) It tells whether a particular physical or chemical change can occur under a

given set of conditions of temperature, pressure and concentration.

b) It also helps how far a physical or chemical change can proceed untilequilibrium conditions are established

APPLICATIONS IN METALLURGY

a) In the construction of phase diagramsb) To understand various chemical reactions and to predict the correct reducing agent

in ferrous and non ferrous extractive metallurgy

c) To understand various phase transformations in the heat treatment process

d) To understand interactions of various alloying elements in alloys.

1.2 GAS LAWS

The laws which describe the behavior of a gas are known as gas laws. Which are as

follows:

1) Boyles Law : Boyles Law states that , if the temperature remains constant , thevolume of a given mass of a gas varies inversely as the pressure to which it issubjectedthat is

V 1

P

Or P V = K (constant)2) Charles Law : It states that, if the pressure remains constant , the volume of agiven mass of a gas varies directly as its absolute temperature.

That is V T, when P is constant

1.3 Daltons law of partial pressures

Dalton's law of partial pressures states that the totalpressure exerted by a gaseous

mixture is equal to the sum of thepartial pressures of each individual component in agas mixtureMathematically, P total = P1 + P2 +..+Pn

1.4 STATEMENT AND DERIVATION OF IDEAL GAS EQUATION

The statement of Ideal gas equation is P V = n R TWhere P---pressureV---Volume

n---no.of moles of ideal gas

R--- Universal gas constant

T--- Absolute Temperature of ideal gas.

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Derivation of Ideal gas equationAccording to Boyles Law

V 1

P

At Constant T and m

According to Charles Law is V T at constant P and m

Combining the above two laws we can write

V T

P

Or

PV = KT

Where Kis a constant whose value can be found as follows

P0V0= K

T0

Where P0 is 1 atm pressure

V0is 22.4 lit

T0is 2730K

If the above values are substituted in the above equation we get

K =0 .0821 lit-atm

Now K is known as universal gas constant and is represented by R

Therefore now the ideal gas law takes the following form

PV = RT

For n moles of ideal gas the equation then becomes

PV = nRT

1.5 PERFECT AND REAL GAS

An ideal gas orperfect gas is a hypothetical gas consisting of identical particles of zerovolume, with no intermolecular forces. Additionally, the constituent atomsormoleculesundergo perfectly elastic collisionswith the walls of the container. Ideal gases follow the

Boyles Law and Charles Law at all temperatures and pressures

Real gases do not exhibit these exact properties, although the approximation is often goodenough to describe real gases. Real gases behave as ideal gases only at at high temperaturesand low pressure.

1.6 SYSTEM SURROUNDING & BOUNDARY WITH EXAMPLES

System: A System is that part of the universe which is under thermodynamic study.

Surroundings: Everything external to the system is called surroundings.Boundary: The real or imaginary surface separating the system from the surroundings iscalled the boundary.

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In experimental work, a specific amount of one or more substances constitutes the

system. Thus 1 mole of oxygen confined in a cylinder fitted with a piston is athermodynamic system. The cylinder and the piston and all other objects outside the

cylinder form the surroundings. Here the boundary between thy system (oxygen) and the

surroundings (cylinder and piston) is clearly defined.

TYPES OF SYSTEMS

1.7 Homogeneous and heterogeneous systems

When a system is uniform throughout, it is called a Homogeneous system. Examplesare: a pure single solid, liquid or gas, mixture of gases and true solution of a solid ion aliquid. In metallurgy, Austenite (FCC solid solution of carbon in iron), ferrite (BCC solid

solution of carbon in iron), Cu-Ni alloys, etc are some of the examples of homogeneous

systems. A Homogeneous system is made of one phase only.

A heterogeneous, system is one, which consists of two or more phases. In other words itis not uniform through out. Examples of heterogeneous, systems are: Ice in contact withwater, ice in contact with vapour, etc. Here ice water and vapour constitute separate phases.

In metallurgy, Fe-0.4%C, Al-12%Si, Grey cast iron etc. are some of the examples of

heterogeneous, systems.

Differences between Homogeneous and Heterogeneous Systems

Homogeneous System Heterogeneous System

1) Composition is Uniform 1) Composition is not Uniform

2) Consists of Single Phase 2) Consists of more than one Phases

3) Example: Solutions, Cu-Ni Alloys 3) Example: Mixtures, Grey Cast Iron

1.8 Isolated system, Closed system, Open system and Adiabatic system

Basing on the criterion that whether or not the energy or mass transfer takes place through

the boundary of the system systems are of three types they are

1) Isolated system: An Isolated system is one that can transfer neither matter norenergy to and from its surroundings

Let us consider a system 100 ml of water in contact with its vapour in a closed vessel,

which is insulated. Since the vessel is sealed, no water vapour (matter) can escape from it.

Also because the vessel is insulated no heat (energy) can be exchanged with thesurroundings.

A substance say hot coffee contained in a thermos flaskis another example of an isolated

system.

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2) Closed system: A closed system is one which cannot transfer matter but cantransfer energy in the form of heat, work and radiation to and from its surroundings.Here the boundary is sealed but not insulated.

A specific quantity of hot water contained in a sealed tube is an example of a closed

system. While no water vapour can escape from this system, it can transfer heat through the

walls of the tube to the surroundings.A gas contained in a cylinder fitted with a piston constitutes a closed system. As the

piston is raised the gas expands and transfers heat (energy) in the form of work to the

surroundings.

3) Open System: An Open System is one, which can transfer both energy and matterto and from its surroundings.

Hot water contained in a beaker placed on laboratory table is an open system. The

water vapour (matter) and also heat (energy) is transferred to the surroundings through theimaginary boundary.

4) Adiabatic System: The system, in which no thermal energy passes into or out of the

system, is said to be Adiabatic System.

THERMODYNAMIC PROPERTIES

Thermodynamic properties are the thermodynamic coordinates, which fixes up the state of

the system. Examples are: Pressure, Volume, Temperature and Mass.

TYPES OF PROPERTIES

1.9 Intensive, Extensive, State and Path Properties

The macroscopic or bulk properties of a system (volume, pressure, mass etc) basing onwhether or not they can depend on mass can be divided into two classes

a) Intensive Properties

b) Extensive Properties

A property, which does not depend on the quantity of matter present in the system, is

known as Intensive property.Examples: Pressure, Temperature, density and Concentration etc.

A property that does depend on the quantity of matter present in the system is known as

Extensive property.Examples: Volume, No. Of moles, free energy, entropy etc.

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Basing on the criterion whether or not the properties depend on the path followed by the

system they are two types

a) State propertiesb) Path properties

State properties are those, which do not depend on the path followed by the system but

depend only on the initial and final states of the system.

Examples: Internal energy, Free energy, Entropy, Pressure, Volume, Temperature,Enthalpy etc.

Path properties are those, which do depend on the path followed by the system.Examples: Work done, Heat etc.

By definition the Extensive Properties are additive while intensive properties are not.

1.10 STATE OF A SYSTEM AND EQUATION OF STATE

State: A Thermodynamic system is said to be in certain state when all its propertiesare fixed.The fundamental properties, which determine the state of a system, are pressure (P),

temperature (T), volume (V) and composition. Since a change in the magnitude of such

properties alters the state of the system, these are referred to as state variables orthermodynamic parameters.

State Equation: An algebraic relation ship between state variables is called theequation of State.Example: For one mole of an Ideal gas the state equation is given as

P V = n R T

Where P is pressure, V is Volume, n is No. of moles, R is Universal gas constant and T is

Temperature

1.11 EQUILIBRIUM STATE AND THE CRITERIA FOR EQUILIBRIUM

Equilibrium StateA System in which the state variables have constant values through out the system issaid to be in a state of thermodynamic equilibrium.

Example: Suppose we have a gas confined in a cylinder that has a friction less

piston. If the piston is stationary, giving the values of pressure and volume can specify thestate of the gas. The system is then in a state of equilibrium.

Non-Equilibrium State

A System in which the state variables have different values in different parts of thesystem is said to be in a non-equilibrium state.

If the gas contained in a cylinder is compressed very rapidly by moving down the piston, it

pass through states in which pressure and temperature cannot be specified, since these

properties change through out the gas. The gas near the piston is compressed and heatedand that at the far end of the cylinder is not. The gas then would be said to be in non-

equilibrium state.

Thermodynamics is concerned only with equilibrium states.

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The Criteria for Equilibrium:For the establishment of thermodynamic equilibrium the system should be in the following

equilibria.

1) The temperature of the system must be uniform through out the system

(Thermal equilibrium).2) The mechanical properties must be uniform through out the system

(Mechanical Equilibrium).3) The Chemical composition of the system must be uniform through out the

system (Chemical equilibrium).

THERMODYNAMIC PROCESSES

When a thermodynamic system changes from one state to another, the operation iscalled a process. These processes involve the change of properties such as changes intemperature, pressure and volume etc.

1.12 Types of thermodynamic processes

1) Isothermal Process: Those Processes in which the temperature remains constant aretermed Isothermal Processes.

For an Isothermal Process dT = 0 (dT means difference or change in T)

2) Adiabatic Process: Those Processes in which no heat can flow into or out of thesystem, are called Adiabatic Processes.

For an Adiabatic Process Q = 0 (Qmeans difference or change in Q)

3) Isobaric Process: Those Processes in which the pressure remains constant are termed

Isobaric Processes.

For an Isobaric Process dP = 0 (dP means difference or change in P)

4) Isochoric Process: Those Processes in which the volume remains constant are termedIsochoric Processes.

For an Isochoric Process dV = 0 (dV means difference or change in V)

1.13 REVERSIBLE AND IRREVERSIBLE PROCESSES

Reversible Process: A Thermodynamic reversible Process is one that takes placeinfintesimally slowly and its direction at any point can be reversed by an infintesimalchange in the state of the system.

In fact, a reversible process is considered to proceed from the initial state to the

final state through an infinite series of infinitesimally small stages. At the initial, final andall intermediate stages, the system is in equilibrium state. This is so because an infintesimal

change in the state of the system at each intermediate step is negligible.

Irreversible Process: When a process goes from the initial to final state in a single stepand cannot be carried in the reverse order, it is said to be an irreversible process. Here the

system is in equilibrium state in the beginning and at the end, but not at points in between.Example:

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Consider a certain quantity of gas contained in a cylinder having a weightless and friction

less piston. The expansion of the gas can be carried by two methods illustrated below.

Let the pressure applied to the piston be P and this is equal to the internal pressureof the gas. Since the external and internal pressures are exactly counter balanced, the piston

remains stationary and there is no change in volume of the gas. Now suppose the pressure

on the piston is decreased by an infintesimal amount dP. Thus the external pressure on thepiston is being P-dP, the piston moves up and the gas will expand by an infintesimallysmall amount. The gas will therefore, be expanded infinitely slowly that is by a

thermodynamically reversible process. At all stages in the expansion of the gas, dP beingnegligibly small, the gas is maintained in a state of equilibrium through out, If at any pointof the process, the pressure is increased by dP, the gas would contract reversibly (fig. a).

On the other hand, the expansion is irreversible (fig. b) if the pressure on the piston

is decreased suddenly. It moves upward rapidly in a single operation. The gas is inequilibrium state in the initial and final stages only. The expansion of the gas, in this case

takes place in an irreversible manner.

Differences between Reversible and Irreversible Processes

Reversible Process Irreversible Process

1) Takes place infintesimally slowly 1) Takes place with finite speed

2) These are idealized and true in principle

only

2) All actual processes which occur are

Irreversible

3) System is at equilibrium at all stages of

the process

3) System is at equilibrium only at the initial

and final stages of the process

4) Work done is maximum 4) Work done is less than that of reversibleprocess

5) Efficiency of reversible process is

maximum

5) Efficiency is less

1.14 HEAT AND WORK

When a change in the state of a system occurs, energy is transferred to or from the

surroundings. This energy may be transferred as heat or mechanical work.

Heat: Heat is defined as the energy in transitWork: Mechanical work is defined as forceXdistance.Units of Heat: In S.I units heat is measured in joules.Units of Work: In S.I units Work is measured in joules.

Sign Convention of Heat: The symbol of Heat is Q. If the heat flows from thesurroundings into the system to raise the energy of the system; it is taken to be positive,

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+Q. If heat flows from the system into the surroundings, lowering the energy of the system,

it is taken to be negative, -Q.

Sign Convention of Work: The symbol of Work is W. If the Work is done by the systemthen work is taken as positive +W. On the other hand if work is done on the system it is

taken as negative, -W.

1.15 PRESSURE-VOLUME WORK

In physics mechanical work is defined as force multiplied by the distance through which

the force acts. In thermodynamics the only type of work generally considered is the work

done in expansion (or compression) of a gas. This is known as Pressure Volume WorkorPV workorExpansion work.

Derivation of equation for work of expansion

Consider a gas contained in a cylinder fitted with a friction less piston. The constantpressure acting is P. If the gas expands at constant pressure, the piston moves through a

distance let this distance is l.

Then work = forceXdistance

W = fxl But f = PxA (here A=area of cross section of the piston)

There fore W = PxAxl

= Px l (here l = change in volume)

1.16 COMPLETE / EXACT DIFFERENTIAL OF THERMODYNAMICPROPERTIES

If value of a thermodynamic property is independent of the path followed by the system

then that property is called exact differential

Mathematically, if Z is a thermodynamic property and is a function of two other

thermodynamic properties x and y then Z is said to be a complete differential if the

following changes in Z are equal

dZI =Z

dx +Z

dyx y

dZII =Z

dy +Z

dxy x

Then dZI = dZII

Or the condition for Complete or Exact differential is

2Z=

2Z

xy yx

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There fore Work = Pressure X change in Volume

l

Gas at constant pressure

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