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A. K. M. B. RashidProfessor, Department of MME

BUET, Dhaka

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Introduction to thermodynamics

Power and limitations of thermodynamics

The structure of thermodynamics

MME6701: Brief lecture format

The term “thermodynamics” is introduced by Lord Kelvin in 1849 by combining two Greek words therme (heat) and dynamis (force)

William Thompson, 1st Baron Kelvin (a.k.a. Lord Kelvin) (1824 – 1907)

British Mathematical Physicist and Engineer

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This special branch of science was born in the middle of 19th century mainly to describe the operation of steam engine and their limit of operation.

Sadi Carnot (1796-1832):

The "father" of thermodynamics

Sadi Carnot, “Reflections on the Motive Power of Fire”, 1824.

A discourse on heat, power, and engine efficiency, which marks the start of thermodynamics as a modern science.

The principal job of thermodynamics was to see the power of heat: the capacity of hot bodies to produce work.

A branch of physical science concerned with the transfer of heat and appearance/disappearance of work

Effect of environment (as determined by Temperature andPressure) on the state of rest

Study of changes in energy accompanying chemical and physical changes, which allows experimentally determined laws to be derived from certain basic principles, and helps to predict changes whose have not been observed

Deals generally with energy and with the relationships among the properties of matter

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The principles of thermodynamics is exceedingly simpleand general in its applicabilitycan be applied to any kind of natural process

Case Study :

Attempts to prepare diamond from graphite

Production of pig iron in a blast furnace according to the reaction

Fe3O4 + 4CO = 3Fe + 4CO2

2.1 The Power of Thermodynamics

1. Work produced in steam engine

2. The reaction kinetics

3. Metal extraction and refining processes

4. The phase equilibria

Some Applications :

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The simplicity and generality of thermodynamics render it incapable of answering many of the specific questions that arise in connection with those problems

Considers only the initial and final states of any system undergoing a change

Provide no information about the mechanism of the change between these states, or the rate at which such change takes place

Applicable only to macroscopic systems (i.e., system as a whole) and not to microscopic systems of individual atoms and molecules

2.2 The Limitations of Thermodynamics

Classical thermodynamics

macroscopic viewpoint towards mater assuming that the matter is continuous

requires no information about the detail structure of matter on the atomic scale, nor it is necessary to assume that molecules exist

conclusions are quite general

2.3 Classification of Thermodynamics

based on average behavior of large groups of individual microscopic particles, assuming that the matter is discontinuous

microscopic approach is more elaborate and is rather involved

Statistical thermodynamics

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The science of thermodynamics is rooted with logics and reasons.

At its foundation there are a very few, very general, and therefore very powerful principles: The Laws of Thermodynamics.

The structure of thermodynamics can be visualised as an inverted pyramid.

separates the problem using a

enclosure (known as the boundary)

from the rest of the universe (known

as the surroundings), close enough

to the system to have some

perceptible effect on the system.

Identify the part of universe that encompasses the problem (known as the system)

Surroundings

The subset of the universe in focus

for a particular application

System

Boundary

Temperature, TPressure, PVolume, VComposition, Xk

. . . . .

specify the conditions of the system

at the point of investigation in terms

of thermodynamic properties.

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TA , PA , VA

State A

Process

State B

TB , PB , VB

A process is a change in the condition or state of the system

If the system undergoes a process, use thermodynamic relations to compute the changes of these properties.

Thermodynamic systems

Thermodynamic properties

Thermodynamic processes

Thermodynamic relations

Strategy in Studying Thermodynamic

Structure

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Certain portion of the universe that encompasses the whole problem at hand; the boundary separates the system from its surroundings.

Be explicit about the nature of the contents of the system, and the specific location and character of its boundary

across the boundary of a system, heat flows, work appears or disappears, and sometimes even matter moves.

3.1 Thermodynamic Systems

The system and its surroundings are considered to be isolated.

Unary system (single component) Aluminium can

Quartz (SiO2)

Water (H2O) (when undecomposed)

Multi-component system (more than one component) Steel bar (containing Fe, C, Si, etc.)

Water (H, O)

Unary vs. multi-component

Classification of Thermodynamic Systems

Homogeneous vs. heterogeneous

Homogeneous system (single phase) Ice (solid phase)

Water (liquid phase)

Heterogeneous system (more than one phase) Steel (containing ferrite and cementite)

Ice water (solid and liquid phases)

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Closed vs. open

Closed system (energy but mass transfer across boundary)

A piece of paper

Open system (mass and energy transfer across boundary)

A cup of tea

Isolated system (neither mass nor energy transfer across boundary)

Hot milk in thermos flask

Non-reacting vs. reacting

Non-reacting system (no chemical reaction within) Sugar-water solution in a glass

A piece of copper rod

Reacting system (involving chemical reaction) Liquid steel in a crucible

A piece of aluminium in sodium hydroxide solution

Otherwise simple vs. complex

Otherwise simple system No force field other than mechanical force is acting upon the system

Complex system Force field other than mechanical such as magnetic, electrical,

rotational, etc. is acting upon the system.

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Self Assessment Question #2.1

Classify the following thermodynamic systems:

(a) a solid bar of copper

(b) a glass of ice water

(c) a yttria stabilised zirconia furnace tube

(d) a styrofoam coffee cup

(e) a eutectic alloy turbine blade rotating at 20000 rpm

Identifiable characteristics of matter whose are observableand can be measured either directly or indirectly are called variables, functions or, properties.

Examples: pressure, temperature, volume, mass, velocity, work, etc.

The physical properties of thermodynamics are distinct in two respects:

they can be expressed quantitatively in terms of dimensions and units

the measured value at any particular point of time is unique.

3.2 Thermodynamic Variables

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It is the internal condition of a system as defined by the values of all its properties. It gives a complete description of the system.

Properties describe and specify the state of the system in such a way that identical states have identical properties.

If in any operation, one or more properties of a system change, the system changes its state.

Thermodynamic State

Microscopic state and macroscopic state

In microscopic sense, any thermodynamic system is not continuous.

If the masses, velocities, positions and all modes of motions of all the particles in any particular instance is known, then this would describe the microscopic state or condition of the system and would, in turn, determine all the properties of the system.

In macroscopic sense, the system is continuous and we determine the properties of the system as a whole. Temperature, pressure, volume, etc. are some of the common macroscopic properties of a system.

The state of the system described this way is known as the macroscopic state of the system

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Independent properties and dependent properties

State functions and process variables

Intensive, extensive, and specific properties

Classifications of Thermodynamic

Variables

Independent and Dependent Properties

It is not necessary to quantify all of the properties to define completely the state of system.

It is found that when a very small number of properties have been measured at any instance of time, all other thermodynamic properties are fixed automatically.

Thus, only a few numbers of independent properties are measured experimentally and the remaining multitude of dependent properties is calculated using those independent properties. Temperature and pressure are two common independent properties.

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State Functions or Thermodynamic Variables

Depends on the current condition or state of the system, not on how the system is arrived at that condition.

Rafiq weighs 72 kg and is 1.75 m tall. We are not concerned how he got

to that stage. We are not interested what he ate!!.

The temperature today is 500 K. We do not indicate whether the day is

heated up to that temperature or cooled down to it.

Example of state functions:

Pressure, Temperature, Volume, Energy, etc.

For any given values (XA,YA) in state A, there is a corresponding value of ZA.

If a variable Z depends only on the current values of the variables X and Y, then all three variables are state functions.

The functional relationship among these variables, Z = Z (X, Y), is represented by a surface in (X, Y, Z) space.

(XA,YA)

ZA

Z

Y

X

Z = Z (X, Y)

A

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Any change in a state function depends only the initial and final state of the system, not on the path followed.

DZ = ZB - ZA

Processes

(XA, YA)

(XB, YB)

Z B

Z A

Z

Y

X

D Z

a

b

c

Z = Z (X, Y)

Process Variables

Only have meaning for changing systems

Examples: Heat (Q) and Work (W).

Change is inherent to the very concept of these quantities. The values of process variables at rest are zero.

Depends explicitly upon the path, that is, the specific sequence of states the system takes while moving from state A to state B.

A system can have some energy, but the system contain no work. Thus, energy is a property of system, work is not.

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Intensive, Extensive, and Specific Properties

Intensive properties

Values are independent of the size/extent of system

Vary from place to place within the system at any moment

The fundamental or derived properties of system are always intensive

Examples: Temperature, Pressure

Extensive properties

Values depends on the size/extent of system

Only have a value for the system as a whole

The total properties the system are always extensive

Examples: Volume, Mass, Energy

Specific properties

Extensive variables per unit mass or volume

All specific properties are intensive properties

Examples: Density, specific volume, specific energy

A process suggests

change in system from one state to another

some operations by which the change is achieved

3.3 Thermodynamic Processes

A path represents a sequence of situations a system passes through during a change in the state of the system.

B

A

ab

c

Three different paths

a, b, c for the process AB

Process A B

System changes from state A to state B;

But does not indicate any particular

operation or the path it followed

A process is often specified with certain constraints imposed on the system and/or its surroundings.

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Adiabatic Process

No heat transfer occurs across the boundary between the system and its surroundings

If the temperature gradient, DT = 0, no heat will transfer

If DT 0, heat will transfer (which is a rate process)so for a short period of time, the process can be assumed to be adiabatic (e.g., compression of air and gasoline in internal combustion engine)

How to recognise an adiabatic process?

Process is carried out quickly

Well insulated boundary

Isothermal Process

Temperature is uniform at every point throughout the system and remains constant during the entire process

If DT = 0, Transfer of heat = 0.

If DT 0, Transfer of heat/work will occur until DT = 0.

If the process produces heat Transfer of heat and/or work across the boundary is mandatory

Process should occur for a prolonged period of time to encourage heat

transfer

How to recognise an isothermal process? Process is carried out very slowly (close to infinity)

Permeable boundary

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Isobaric Process

Pressure remained constant throughout the system.

Volume remained constant throughout the system.

Impermeable and rigid container/boundary

Isochoric Process

The initial and final states of the system are the same.

The overall changes in all state variables are zero.

Cyclic Process

If the cyclic change in a state of a system results a ZERO change in a property, that property is a state function

0dZ

Table 2.1:

Characteristics of different thermodynamic processes

Process Constraints imposed Quantity exchanged

IsobaricPressure remains constant (DP=0)

Heat and work may be exchanged

IsothermalTemperature remains constant (DT=0)

Heat and work may be exchanged

Isochoric Volume remains constant (DV=0)

Only heat is exchanged

Adiabatic System remains insulated (Q=0)

Only work is exchanged

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1. Laws of Thermodynamics

These fundamental equations form the basis of all thermodynamic

relations.

Generally describes the connection between the different forms of

energy and state variables.

2. Definitions

There are quite a few number of thermodynamic properties

that are defined in terms of previously formulated quantities.

They describe a particular class of system or process.

In this category, there are some energy function and some

experimental variables.

3.4 Thermodynamic Relations

3. Coefficient Relations

These equations are known as the coefficient relations

),( YXZZ

dYY

ZdX

X

ZdZ

XY

NdYMdXdZ X

Y

Y

ZN

X

ZM

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4. Maxwell Relations

¶M

¶Y

æ

èç

ö

ø÷X

= ¶

¶Y

¶Z

¶X

æ

èç

ö

ø÷X

é

ëê

ù

ûúY

= ¶2Z

¶X. ¶Y

¶N

¶X

æ

èç

ö

ø÷Y

= ¶

¶X

¶Z

¶Y

æ

èç

ö

ø÷Y

é

ëê

ù

ûúX

= ¶2Z

¶Y. ¶X

dZ =MdX +NdY

M =¶Z

¶X

æ

èç

ö

ø÷Y

and N =¶Z

¶Y

æ

èç

ö

ø÷X

¶M

¶Y

æ

èç

ö

ø÷X

= ¶N

¶X

æ

èç

ö

ø÷Y

This equation is known as the Maxwell relation.

If a function Z = Z (X, Y) obeys the Maxwell relation,

the function Z will be a state variable.

5. Condition for Equilibrium

When an external force is acted upon a system, the system undergoes

changes until it has exhausted all of its capacity for change.

When the system attains this final resting place, we indicate that the

system is in equilibrium with its surroundings.

The conditions for equilibrium are a set of equations that describe the

relationships between state functions that must exist within the system

when it attains the equilibrium (or stable) state.

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Example 2.1

Is the function

z = 9x2y2 dx + 6x3y dy

an exact differential ?

x

y

z

zA

zB

A(1,1)

B(2,4)

C (1,4)

D (2,1)

Dz = DzCA + DzBC = 381

Dz = DzDA + DZBD = 381

Dz = DzBCA = DzBDA

Thus the function z is an exact differential

Problem 2.15:

Write total differential equation of the function

z = 17 x4y + 22 xy5

and then, using Maxwell relation, prove that z is a state function.

dZ = [ 17 (4x3) y + 22 y5 ] dx + [ 17 x4 + 22 x (5y4) ] dy

M = 68 x3y + 22 y5

N = 17 x4 + 110 xy4

(M/y)x = 68 x3 + 110 y4

(N/x)y = 68 x3 + 110 y4

So M/y)x = (N/x)y

Thus, z is a state function.

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1 Introduction; The Structure of Thermodynamics

2 The Laws of Thermodynamics

3 Thermodynamic Variables and Relations

4 Equilibrium in Thermodynamic Systems

5 Solution Thermodynamics

6 Thermodynamics of Reactive Systems

7-8 Surfaces and Interfaces

9-10 Defects in Crystals

11 Applications of Thermodynamics to Materials Systems

12 Statistical Thermodynamics

13-14 Kinetics of Materials

Course Website:http://teacher.buet.ac.bd/bazlurrashid

1. RT DeHoff, Thermodynamics in Materials Science

2. BS Bokstein, MI Mendelev, DJ Srolovitz, Thermodynamics

and Kinetics in Materials Science: A Short Course.

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