Chapter 1 To7 With Course Outline

Thermodynamics - I

ARBAMINCH UNIVERSITY, ARBAMINCH

FACULTY OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

SUBJECT NAME: Thermodynamics - I (ME 321)PRE REQUISTIE: Senior Standing CONTACT HOUR: 2 Hrs Lect, 3 Hrs TutorialDURATION: 2007INSTRUCTOR: Mr.R.KAMATCHI, Asst. Prof. / Mechanical Engineering.

Course out line

Thermodynamics is the science of energy transfer and its effect on physical

properties of substances. It is based upon observations of common experience which have

been formulated into thermodynamics laws. These laws govern the principles of energy

conversion. Thermodynamics applications are found in the fields of technology, notably

internal combustion engines, steam turbines, steam and nuclear power plants, air

conditioning, refrigeration, jet propulsion compressor etc., so this is important for

mechanical engineering to know the basic laws which governs energy conversion.

Course content

CHAPTER – I - BASIC CONCEPTS OF THERMODYNAMICS

Introduction – macroscopic and microscopic approach – system – control volume

– properties – processes and cycles – homogeneous and heterogeneous system

– thermodynamic equilibrium – quasi static process.

CHAPTER – II - TEMPERATURE SCALE AND ENERGY INTERACTIONS

Zeroth law of thermodynamics – comparison of thermometers – work transfer:

PdV work in various quasi static processes – other type of work transfer. Heat

transfer.

CHAPTER – III - FIRST LAW OF TD FOR CLOSED AND OPEN SYSTEM

First law for a closed system undergoing a cycle – under going a change of state

– PMM1. First law for a open system – mass and energy balance.

Prepared By R.kamatchi, Asst.Prof. / Mech.1

Thermodynamics - I

CHAPTER – IV - SECOND LAW OF THERMODYNAMICS

Kelvin – Planck statement, Clausius statement of second law – reversibility and

irreversibility – entropy – Clausius theorem – property of entropy.

CHAPTER – V - PROPERTIES OF PURE SUBSTANCES

P-V, P-T, PVT surface – T-S and H-S diagram( Mollier Diagram) – dryness

fraction – measurement of steam quality

CHAPTER – VI - PROPERTIES OF GASES AND GAS MIXTURES

Avogadro’s law – internal energy, enthalpy and specific heats of gas mixtures –

gibbs function.

CHAPTER – VII - PSYCHROMETRY

Introduction – properties – psychrometric chart – processes.

REFERENCES:1. Y.A. CENGEL, M.A. BOLE, - THERMODYNAMICS – AN ENGINEERING

APPROACH.

2. ROGERS & MAYTHEW – ENGINEERING THERMODYNAMICS –

Longman Publishers.

3. EASTOP & MEEONKEY – APPLIED THERMODYNAMICS FOR

ENGINEERING TECHNOLOGISTS

4. R. JOEL – ENGINEERING THERMODYNAMICS - Longman Publishers.

5. P.K. NAG – ENGINEERING THERMODYNAMICS - Tata McGraw –Hill

Publishing Company Limited, New Delhi.

MARK DISTRIBUTION:

ATTENDANCE : 5 MARKS

MID TERM EXAM : 30 MARKS

ASSIGNMENT : 5 MARKS

FINAL EXAM : 60 MARKS --------

TOTAL MARKS : 100 MARKS


Thermodynamics - I

CHAPTER – I

BASIC CONCEPTS OF THERMODYNAMICS

1.1. Introduction:

Thermodynamics is the branch of science which deals with the transfer of energy

and its effect on physical properties of substances. It is based upon observations of

common experience which have been formulated into thermodynamics laws. These laws

govern the principles of energy conversion. Thermodynamics applications are found in

the fields of technology, notably internal combustion engines, steam turbines, steam and

nuclear power plants, air conditioning, refrigeration, jet propulsion compressor etc.

1.2. Macroscopic Vs microscopic approach:

There are two points of view from which the behavior of matter can be studied:

the macroscopic and microscopic. In the case of macroscopic approach, a certain quantity

of matter is considered, with out the events occurring at the molecular level being taken

into account. From the microscopic point of vie, matter is composed of myriads of

molecules. The behavior of the quantity of matter is described by summing up the

behavior of each molecule, is called microscopic thermodynamics. Macroscopic

thermodynamics is only concerned with the effects of the action of many molecules, and

these effects can be perceived by human senses.

1.3. System:

A thermodynamic system is defined as a quantity of matter or a region in space

upon which attention is concentrated in the analysis of a problem. Everything external to

the system is called as surroundings or the environment. The system is separated from the

surrounding by the system boundary. The boundary may fixed or moving. A system and

its surroundings together comprise a universe.

1.4. Types of system:

1.4.1. Closed system:

It is a type of system of fixed mass. There is no mass transfer across the system

boundary. There may be energy transfer into or out of the system. Ex: a certain quantity

of fluid in a cylinder bounded by a piston constitutes a closed system.


Thermodynamics - I

Boundary energy out

No mass transfer

Energy in Surroundings

1.4.2. Open system:

It is one in which matter across the boundary of the system. There may be energy

transfer also. Most of the engineering devices are generally open systems, eg., an air

compressor in which air enters at low pressure and leaves at high pressure and there are

energy transfers across the system boundary.

Mass in

Boundary energy out

Surroundings

Energy in

Mass out

1.4.3. Isolated system:

Isolated system is one in which there is no interaction between the system and

surroundings. It is of fixed mass and energy, and there is no mass or energy transfer

across the system boundary.

No mass and

Energy transfer

1.5. Control volume and control surface:

The attention is focused on a certain volume in space surrounding the system

known as control volume, bounded by a surface called the control surface. Matter as well

as energy can cross the control surface.


System

System

System

Thermodynamics - I

1.6. Thermodynamic properties, processes and cycles:

Every system has certain characteristics by which its physical condition may be

described, e.g., volume, temperature, pressure etc. such characteristics are called

properties of the system. These are all macroscopic in nature. When all the properties of a

system have definite values, the system is said to exist at a definite state. Properties are

the co ordinates to describe the state of a system. Properties are of two types. Intensive

properties and extensive properties.

Intensive properties: These are independent of the mass in the system. Eg., pressure,

temperature.

Extensive properties: These are related to mass. Eg., volume, energy etc. if mass is

increased, the values of the extensive properties also increase.

Specific properties: extensive properties per unit mass, eg., specific volume, specific

energy, density etc.

A A – B -- Process

1

P B 1- 2- 1 - Cycle

2

V

Change of state and process: Any operation in which one or more of the properties of a

system changes is called a change of state. The succession of states passed through

during a change of state is called the path of the change of state. When the path is


Thermodynamics - I

completely specified, the change of state is called a process. Eg. Constant pressure

process.

Cycle: A thermodynamic cycle is defined as a series of state changes such that the final

state is identical with the initial state.

1.7. Homogeneous system and Heterogeneous system:

A quantity of matter homogeneous throughout in chemical composition and

physical structure is called a phase. Every substance can exist in any one of the three

phases, viz., solid, liquid and gas. A system consisting of a single phase is called a

homogeneous system, while a consisting of more than one phase is known as

heterogeneous system.

1.8. Thermodynamic equilibrium:

A system is said to exist in a state of thermodynamic equilibrium when no change

in any macroscopic property is registered, if the system is isolated from its surroundings.

A system is said to be in a state of thermodynamic equilibrium, if the conditions for the

following three types of equilibrium are satisfied.

1.8.1. Mechanical equilibrium:

In the absence of any unbalanced force within the system itself and also between

the system and surroundings, the system is said to be in a state of mechanical

equilibrium.

1.8.2. Chemical equilibrium:

If there is no chemical reaction or transfer of matter from one part of the system to

another, such as diffusion or solution, the system is said to exist in a state of chemical

equilibrium.

1.8.3. Thermal equilibrium:

When a system existing in mechanical equilibrium and chemical equilibrium is

separated from its surroundings by a diathermic wall (diathermic means ‘which allows

heat to flow’) and if there is no spontaneous change in any property of the system, the

system is said to exist in a state of thermal equilibrium. When this is not satisfied, the

system will undergo a change of state till thermal equilibrium is restored.


Thermodynamics - I

When the conditions for any one of the three types of equilibrium are not

satisfied, a system is said to be in a non equilibrium state.

1.9. Quasi – static process:

Let us consider a system of a gas contained in a cylinder as shown in figure.1. The

system initially is in equilibrium state, represented by the properties p1, v1, t1. The weight

on the piston just balances the upward force exerted by the gas. If the weight is removed,

there will be an unbalanced force between the system and the surroundings, and under

gas pressure, the piston will move up till hits the stops. The system again comes to an

equilibrium state, being described by the system are non equilibrium states which cannot

be described by the thermodynamic coordinates. The figure 2 shows points 1 and 2 as the

initial and final equilibrium states joined by a dotted line, which has got no meaning

otherwise.

Now if the single weight on the piston is made up of several very small pieces of

weights (figure.3) and these weights are removed one by one very slowly from the top of

the piston, at any instant of the upward travel of the piston, if the gas system is isolated,

the departure of the state of the system from the thermodynamic equilibrium state will be

infinitesimally small.

So every state passed through by the system will be an equilibrium state. Such a

process, which is but a locus of all the equilibrium points passed through by the system,

is known as a quasi – static process.


Thermodynamics - I

‘Quasi’ means ‘almost’. Infinite slowness is the characteristic feature of a quasi –

static process. A quasi – static process is thus a succession of equilibrium states. A quasi

– static process is also called ‘reversible process’.

CHAPTER – II

TEMPERATURE SCALE AND ENERGY INTERACTIONS

2.1. Introduction:

The property which distinguishes thermodynamics from other sciences is

temperature. One might say that temperature bears as important a relation to

thermodynamics as force does to statistics or velocity does to dynamics. Temperature is

associated with the ability to distinguish hot from cold. When two bodies at temperatures

are brought into contact, after some time they attain a common temperature and are then

said to exist in thermal equilibrium.

2.2. Zeroth law of thermodynamics:

When a body A is in thermal equilibrium with a body B, and also separated with

a body C, then B and C will be in thermal equilibrium with each other. It is the basis of

temperature measurement.


Thermodynamics - I

2.3. Comparison of thermometers:

Constant volume gas thermometers

Constant pressure gas thermometers

Electric resistance thermometer

Thermocouple

Liquid in glass thermometer.

2.3.1. Gas thermometers:

A schematic diagram of a constant volume gas thermometer is given in figure. A

small amount of gas is enclosed in bulb B which is communication via the capillary tube

C with one limb of the mercury manometer M. The other limb of the mercury manometer

is open to the atmosphere and can be moved vertically to adjust the mercury levels so that

the mercury just touches lip L of the capillary. The pressure in the bulb is used as a

thermometric property and is given by

P = P0 + ρ g z

Where ‘P0’ the atmospheric pressure and ‘ρ’ is the density of the Mercury.

In a constant pressure gas thermometer, the mercury levels have to be adjusted

to keep Z constant, and the volume of gas V, which would vary with the temperature of

the system, becomes the thermodynamic property. The constant volume gas thermometric

is, how ever, mostly in use, since it is simpler in construction and easier to operate.


Thermodynamics - I

2.3.2. Electric resistance thermometer:

In the resistance thermometer, the change in resistance of a metal wire due to its

change in temperature is the thermometric property. The wire, frequently platinum, may

be incorporated in a wheat stone bridge circuit. The platinum resistance thermometer

measures temperature to a high degree of accuracy and sensitivity, which makes it

suitable as a standard for the calibration of other thermometers.

In a restricted range, the following quadratic equation is often used

R = R0 (1 + At + Bt2)

Where R0 is the resistance of the platinum wire when it is surrounded by melting ice and

A and B are constants.

2.3.3. Thermocouple:

A thermocouple circuit made up from joining wires A and B made of dissimilar

metals are shown in figure. Due to seeback effect, a net e.m.f. is generated in the circuit


Thermodynamics - I

which depends on the difference in temperature between the hot and cold junctions and

is, therefore, a thermodynamic property of the circuit. This e.m.f. can be measured by a

micro voltmeter to a high degree of accuracy. The choice of metals depends largely on

the temperature range to be investigated, and copper – constantan, chromel – alumel and

platinum – platinum – rhodium are typical combination in use.

A thermocouple is calibrated by measuring the thermal e.m.f. at various known

temperatures, the reference junction being kept at 00 c.

The results of such measurements on most thermocouples can usually be

represented by a cubic equation of the form.

ε = a + bt + ct2 + dt3

Where ‘ε’ the thermal e.m.f. The constants a, b, c and d are different for each

thermocouple.

The advantage of thermocouple is that it comes to thermal equilibrium with the

system whose temperature is to be measured quite rapidly, because its mass is small.

2.4. Energy interactions:

A closed system and its surroundings can interact in two ways: a) by work

transfer b) by heat transfer, these are called energy interactions and these bring about

changes in the properties of the system. Thermodynamics mainly studies these energy

interactions and the associated property changes of the system.

2.5. Work transfer:

Work is one of the basic modes of energy transfer. In mechanics the action of a

force on a moving body is called work. The force is a means of transmitting an effect

from one body to another. In mechanics the work can also be defined as, The work is

done by a force as it acts upon a body moving in the direction of the force.

In thermodynamics, work transfer is considered as occurring between the system

and the surroundings. Work is said to be done by a system if the sole effect on things

external to the system can be reduced to the raising of a weight. The weight may not

actually be raised, but the net effect to the system would be the raising of a weight.


Thermodynamics - I

When work is done by a system, it is arbitrarily taken to be positive, and when

work is done on a system, it is taken to be negative. The symbol ‘W’ is used for work

transfer.

The unit of work is N.m or joule [1 N.m = 1 joule]. In MKS units, it is kgf.m. The

rate of work is done by or upon, the system is known as power. The unit of power is

watts. (Or) J/s.

The action of a force through a distance is called mechanical work since other

forms of work can be discussed below.

2.5.1. pdV work or displacement work:

Let the gas in the cylinder be a system having initially the pressure p 1 and volume

V1 as shown in figure. The system is in thermodynamic equilibrium, the state of which is

described by the coordinates p1 and V1. The piston is only boundary which moves due to

gas pressure. P2, v2

Gas system

p1, v1

Let the piston move out to a final position 2, which is also a thermodynamic

equilibrium state specified by pressure p2 and volume V2. At any intermediate point in the

travel of the piston, let the pressure be p and V. This must be an equilibrium state, since

macroscopic properties p and V are significant only for equilibrium states. When the

piston moves an infinitesimal distance dl, and if ‘a’ be the area of the piston, the force

F = p.a

And the infinitesimal amount of work done by the gas on the piston.

dW = F.dl = p.a.dl = p.dV

Where,

dV = a.dl = infinitesimal displacement volume.

The differential sign in dW is work in infinitesimal volume.

When the piston moves out from position 1 to position 2 with the volume

changing from V1 and V2, the amount of work W done by the system will be

W1-2 = integral of pdV


Thermodynamics - I

The magnitude of the work is given by the area under the path 1-2 as shown in

below figure. Since p is at all times a thermodynamic co-ordinate, all the states passed

through by the system as the volume changes from V1 to V2 must be equilibrium states,

and path 1-2 must be quasi – static. The piston moves infinitely slowly so that every state

passed through is an equilibrium state. The integration pdV can be performed only on a

quasi – static path.

p

p1 ----

p2 ------------------

v

v1 v2

Work transfer

2.5.2. pdV – work in various quasi – static processes:

a) Constant pressure process:

It is also called as isobaric or isopiestic process.

W1-2 = pdV = p (V2 – V1)

1 2

p

v1 v2 v

b) Constant volume process:

It is also called as isochoric process.

W1-2 = pdV = 0.

p ------------ 1

------------ 2

V


W1-2

Thermodynamics - I

c) Constant temperature process:

It is also called as isothermal process.

W1-2 = p1V1 ln (p1 / p2) = p1V1 ln (V2 / V1)

p

p1 ----

p2 ------------------

V

v1 v2

d) Process in which pVn = C, where n is a constant.

It is also called as polytrophic process.

W1-2 = [p1V1 / n-1] [1- (p2 / p1)n -1 / n]

p

n = 0

n = 1

n = 2

n = 3

n = α

V

2.6. Other types of work transfer:

2.6.1. Electrical work:

When a current flows through a resistor, taken as a system, there is work transfer

into the system. This is because the current can drive a motor, the motor can drive a

pulley and the pulley can raise a weight.

The rate of work transfer = I.E, where ‘E’ is the potential difference across the wire and

‘I’ the current flowing.

I ---------------------------- I System boundary -----------------------------


Thermodynamics - I

2.6.2. Shaft work:

When a shaft taken as the system, is rotated, there is work transfer into the

system. This is because the shaft can rotate a pulley which can raise a weight. If ‘T’ is the

torque applied to the shaft rotating at ‘N’ r.p.m. The rate of work done would be 2 π T.N

(N.m / min).

------------------------------- System boundary

------------------------------- Shaft

2.6.3. Paddle – wheel work or stirring work:

As the weight is lowered, and the paddle wheel turns, there is work transfer into

the fluid system which gets stirred. Since the volume of the system remains constant,

pdV = 0 although dW # 0.

System

Weight

2.6.4. Flow work:

The flow work represents the amount of work that must be done on a system to

introduce a unit mass of material into it. The fluid crossing section 1 exerts a normal

pressure p1 against the area A1, giving a total force p1A1. in time dτ, this force moves in

its own direction a v1 dτ. Where v1 is the velocity of flow. The work in time dτ,is p1A1v1

dτ or the work per unit time is p1A1v1.

Flow area A1


motor

Thermodynamics - I

2.6.5. Work done in stretching a wire:

If the length of a wire in which there is a tension (F) is changed from L to L + dL,

the infinitesimal amount of work that is done is equal to

dW = - F . dL.

The minus sign is used because a positive value of dL means as expansion of the

wire, for which work must be done on the wire, i.e. negative work.

For a finite change of length from L1 to L2.

W1-2 = - integral of (F .dL)

2.6.6. Work done in changing the area of a surface film:

The work done on a homogeneous liquid film in changing its surface area by an

infinitesimal amount dA is

dW = σ dA

W1-2 = integral of σ dA

Where ‘σ’ the interfacial tension per unit length.

2.6.7. Magnetization of a paramagnetic solid:

The work done per unit volume on a magnetic material through which the

magnetic and magnetization fields are uniform is

dW = - H dl.

W1-2 = - integral of H dl.

Where ‘H’ is the field strength,

‘I’ is the component of the magnetization field in the direction of the field. The minus

sign provides that an increase in magnetization (positive dI) involves negative work.

2.7. Net work done by a system:

The total or net work done by the system would be equal to the algebric sum of

these as given below

W total = W displace + W shear + W electrical + W string.

2.8. Path function:

It depends on the path the system follows in going from state 1 to state 2. It does

not a function of the end states of the process. These are called inexact or imperfect

deferential. Ex: Work done or heat transfer.


Thermodynamics - I

The amount of work involved in each process is not the function of the end states of the

process. It depends on the path of the system follows.

2.9. Point function:

Thermodynamics properties are point functions, since for a given state, there is a

definite value for each property. The change in thermodynamic property of a system in

a change of state is independent of the path the system follows during the change of

state, and depends on the initial and final states of the system. The differentials of point

functions are exact or perfect differentials.

Ex: volume, pressure, temperature, etc..,

2.10. Heat transfer:

Heat is defined as the form of energy that is transferred across a boundary by

virtue of a temperature difference. The temperature difference is the ‘potential’ and heat

transfer is the ‘flux’. The transfer of heat between two bodies in direct contact is called

conduction. Heat may be transferred between two bodies separated by empty space or

gases by the mechanism of radiation through electromagnetic waves. The transfer of heat

between a wall and a fluid system in motion is called as convection. The symbol used for

heat transfer is ‘Q’. Q (+ ve)

Boundary

Surroundings

Q (- ve)

Heat flow into the system is taken as positive, and heat flow out of the system is

taken as negative.

A process, in which no heat crosses the boundary of the system, is called an

adiabatic process. A wall which is impermeable to the flow of heat is an adiabatic wall,

where as a wall which permits the flow of heat is a diathermic wall. The unit of heat

transfer is Joule in SI unit and calorie in MKS unit.


System

Thermodynamics - I

One calorie is the energy required to raise the temperature of 1gram of water by

1degree Celsius. [1 cal = 4.187 J]

2.10.1. Specific heat:

The amount of heat required to raise a unit mass of the substance through a

unit rise in temperature is called specific heat. It is denoted by the symbol ‘c’.

c = [Q / m.∆t] J / Kg K.

Where ‘Q’ is the amount of heat transfer in Joule

‘m’ is the mass of the substance in Kg.

‘∆t’ the rise in temperature in K

Since heat is not a property, the specific heat is qualified with the process through which

exchange of heat is made. For gases, if the process is at constant pressure, it is denoted by

‘cp’. if the process is at constant volume, it is denoted by ‘cv’. For solids and liquids, the

specific heat does not depend on the process.

2.10.2. Latent heat:

The amount of heat transfer required to cause a phase change in unit mass of a

substance at a constant pressure and temperature. It is denoted by ‘l’.


Thermodynamics - I

CHAPTER – III

FIRST LAW OF TD FOR CLOSED AND OPEN SYSTEM

3.1. Introduction:

According to conservation of energy, “Energy can be neither created nor

destroyed but it can be transferred from one form to other form”. The transfer of heat and

the performance of work may both cause the same effect in the system. Heat and work

are different forms of the same entity, called energy, which is conserved. Energy which

enters the system as heat may leave the system as work, or energy which enters the

system as work may leave as heat.

This is applied for a closed system undergoing a cycle and undergoing a change

of state.

3.2. First law for a closed system undergoing a cycle:

Let us consider a closed system which consists of a known mass of water

contained in an adiabatic vessel having a thermometer and a paddle wheel as shown in

figure.1. Let a certain amount of work W1-2 be done upon the system by the paddle wheel.

The quantity of work can be measured by the fall of weight which drives the paddle

wheel through a pulley.

Figure 1

The system was initially at temperature t1, the same as that of atmosphere, and

after work transfer let the temperature rise to t2. The pressure is always 1 atm. The

process 1-2 undergone by the system is shown in figure 2 in an generalized

thermodynamic coordinates X and Y. let the insulation now be removed. The system and


Thermodynamics - I

surroundings interact by heat transfer till the system returns to the original temperature t1,

attaining the condition of equilibrium with the atmosphere. The amount of eat transfer Q2-

1 from the system during the process, 2-1 as shown in figure.2.

1 Q1-2

Y Figure 2

W1-2 2

X

The system thus executes the cycle, which consists of a definite amount of work

input W1-2 to the system followed by the heat transfer of an amount of heat Q 2-1 from the

system.

If the cycle involves many more heat and work quantities, the same result will be

found. It is expressed algebraically,

(∆W) cycle = J (∆Q) cycle

Where ‘J’ - The joule’s equivalent. This is expressed in the form

∫dW = ∫dQ

Where the symbol ∫ denotes the cyclic integral for the closed path.

This is called first law for a closed system undergoing a cycle.

3.3. First law for a closed system undergoing a change of state:

The expression (∆W) cycle = J (∆Q) cycle, applies only to systems undergoing

cycles, and the algebraic summation of all energy transfer across system boundaries are

zero.

But if a system undergoes a change of state during which both heat and work

transfer are involved, the net energy transfer will be stored or accumulated within the

system. If Q is the amount of heat transferred to the system and W is the amount of work

transferred from the system during the process as shown in figure, the net energy transfer

(Q-W) will be stored in the system. Energy in storage is neither heat nor work, and is

given the name internal energy of the system.


Thermodynamics - I

W

Q

System

Therefore

Q – W = ∆E

Where ‘∆E’ - increase in the energy of the system.

Or

Q = ∆E + W

Here Q, W and ∆E are all expressed in the same units (in Joules). Energy may be

stored by a system in different modes.

If there is more energy transfer quantities involved in the process as shown in

figure, the first law gives

Q2

Q3

W3

Q1

W1 System

W2 W4

(Q2 + Q3 – Q1) = ∆E + (W2 + W3 – W1 – W4)

Energy thus conserved in this operation. The first law is a particular formulation

of the principle of the conservation of energy.

This equation does not give an absolute value of energy, E but only the change of

energy ∆E for the process. It can however, be shown that the energy has a definite value

at every state of a system and is therefore, a property of the system.


Thermodynamics - I

3.4. Energy – a property of a system:

Consider a system which changes its state from state 1 to state 2 by the following

the path A, and returns from state 2 to state 1by the following the path B, as shown in

figure.

1 C where A, B and C are path of the system

P A B

2

V

Write the first law of thermodynamics for path A

QA = ∆EA + WA

And for path B

QB = ∆EB + WB

The processes A and B together constitute a cycle, for which

(∑W)cycle = (∑Q)cycle

or

WA + WB = QA + QB

QA - WA = QB - WB

From the above equations, we yields

∆EA = - ∆EB -----------------1

Similarly, the system returned from state 2 to state 1 by the following the path C instead

of path B

∆EA = - ∆EC ------------------2

From equations 1 and 2

∆EB = ∆EC

Therefore the change in energy between two states of a system is the same, what

ever path the system may follow in undergoing that change of state. Hence, energy has a

definite value for every state of the system. Therefore, it is a point function and a

property of a system.


Thermodynamics - I

The energy is an extensive property of a system. The specific energy is an

intensive property. (e = E / m)

3.5. Different forms of energy:

The symbol E refers to the total energy of the system. Basically there are three

forms in which energy may be stored in a system, which are

Kinetic energy: It refers to the energy of a system in motion.

Potential energy: It is associated with external conservative forces, such as the force of

gravity or internal forces like elastic force.

The kinetic and potential energy of a system are sometimes referred as the bulk energy.

Molecular internal energy or internal energy: The part of the total energy which is

stored in the molecular and atomic structure of the system is known as the molecular

internal energy or simply internal energy (U).

The total energy E, is given by

E = EK + EP + U

In the absence of motion and gravity

EK = 0; EP = 0

And

E = U

The first law of thermodynamics becomes,

Q = ∆U + W

In differential forms,

dQ = dE + dW

dQ = dU + dW

In the absence of other type of work,

dQ = dE + pdV

dQ = dU + pdV

Or, in the integral form

Q = ∆U + ∫pdV

Q = ∆E + ∫pdV


Thermodynamics - I

3.6. Specific heat at constant volume:

The specific heat of a substance at constant volume (cv) is defined as the rate of

change of specific internal energy with respect to temperature when the volume is held

constant.

3.7. Enthalpy:

The enthalpy of a substance h, is defined as

h = u + pv.

It is an intensive property of a system.

Total enthalpy

H = U + pV.

3.8. Specific heat at constant pressure:

The specific heat at constant pressure (cp) is defined as the rate of change of

enthalpy with respect to temperature when the pressure is held at constant.

3.9. Energy of an isolated system:

An isolated system is one in which there is no interaction of the system with the

surroundings. For an isolated system, dQ = 0, dW = 0.

The first law gives,

dE = 0

Or

E = constant. Therefore the energy of an isolated system is always constant.

3.10. Perpetual motion machine of the first kind – PMM1

The first law states that the general principle of the conservation of energy. There

can be no machine which would continuously supply mechanical work without some

other form of energy disappearing simultaneously. Such a fictitious machine is called a

perpetual motion machine of the first kind, or PMM1. A PMM1 is thus impossible.

The converse of the above statement is also true. i.e. there can be no machine which

would continuously consumes work without some other form of energy appearing

simultaneously.


Thermodynamics - I

Q Q

W W

3.11. First law applied to Flow processes or First law applied to open system:

3.11.1. Steady flow processes:

As a fluid flows through a certain control volume, its thermodynamic properties

may vary along the space coordinates as well as with time. If the rates of flow of mass

and energy through the control surface change with time, the mass and energy with in the

control volume also would change with time.

At the steady state of a system, any thermodynamic property will have a fixed value at a

particular location, and will not alter with time. Thermodynamic properties vary along

with the space coordinates, not with the time. ‘Steady state’ means that the state is steady

or invariant with time.

3.11.2. Mass balance and energy balance in a simple steady flow process:

REFER CLASS NOTES FOR DERIVATION

3.11.3. Some examples of steady flow processes:

Nozzle and diffuser

Throttling device

Turbine and compressor

Heat exchanger

3.11.4. Variable flow processes:

Filling up and evacuating gas cylinders.


Engine Engine

Thermodynamics - I

CHAPTER – IV

SECOND LAW OF THERMODYNAMICS

4.1. Introduction:

The first law of thermodynamics states that a certain energy balance will hold

when a system undergoes a change of state or a thermodynamic process. But it does not

give any information on whether that change of state or the process is at all feasible or

not. The first law cannot indicate whether a metallic bar of uniform temperature can

spontaneously become warmer at one end and cooler at the other. All that the law can

state is that if this process did occur, the energy gained by one end would be exactly

equal to that lost by the other. It is the second law of thermodynamics which provides the

criterion as to the probability of various processes.

Joule’s experiment amply demonstrates that energy, when supplied to a system in

the form of work, can be completely converted into heat. But the complete conversion of

heat into work in a cycle is not possible. So heat and work are not completely

interchangeable forms of energy. Work is said to be high grade energy and heat is low

grade energy. The complete conversion of low grade energy into high grade energy in a

cycle is impossible.

4.2. Cyclic heat engine:

A heat engine cycle is a thermodynamic cycle in which there is a net heat transfer

to the system and a net work transfer from the system. The system executes a heat engine

cycle is called a heat engine.

4.3. 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.

4.4. Kelvin – Planck statement of second law:

It is impossible for a heat engine to produce net work in a complete cycle if it

exchanges heat only with bodies at a single fixed temperature.


Thermodynamics - I

If Q2 = 0 (i.e. W = Q1, or eff. = 100 % ) the heat engine will produce net work in a

complete cycle by exchanging heat with only one reservoir, thus violating the Kelvin –

Planck statement. Such a heat engine is called a perpetual motion machine of the second

kind, abbreviated to PMM2. a PMM2 is impossible.

4.5. Clausius’ statement of the second law:

It is impossible to construct a device which, operating in a cycle, will produce

no effect other than the transfer of heat from a cooler to a hotter body.

Heat can’t flow from a body at a lower temperature to a body at a higher

temperature. Some work must be expended to achieve this.

4.6. Refrigerator:

A refrigerator is a device which, operating in a cycle, maintain a body at a

temperature lower than the temperature of the surroundings. There is a performance

parameter in a refrigerator cycle, called the co efficient of performance, abbreviated to

COP, which is defined as the ratio of desired effect produced to the work input. The COP

value always less than one for refrigerator.

4.7. Heat pump:

It is a device which, operating in a cycle, maintain a body at a temperature higher

than the temperature of the surroundings. The performance of the heat pump can be

defined as the heat supplied to the body to the work input. The COP value of the heat

pump is always greater than one.

ie COP of Hear Pump = COP of refrigerator + 1

4.8. Reversibility and irreversibility:

The second law of thermodynamics enables us to divide all the processes in two

classes:

4.8.1. Reversible or ideal process:

A reversible process is one which is performed in such a way that at the

conclusion of the process, both the system and surroundings may be restored to their


Thermodynamics - I

initial states, without producing any changes in the rest of the universe. Let the state of a

system be represented by A and let the system be taken to state B by following the path

A-B. If the system and also the surroundings are restored to their initial states and no

change in the universe is produced, then the process A-B will be a reversible process. In

the reverse process, the system has to be taken from state B to A by following the same

path B-A. A reversible process should not have any trace to show that the process had

ever occurred. A reversible process is an idealized hypothetical process, approached only

as a limit. It is said to be an asymptote to reality.

4.8.2. Irreversible or natural process:

Any natural process carried out with a finite gradient is an irreversible process.

All spontaneous processes are irreversible. The causes of irreversibility are mentioned

below:

1. Lack of equilibrium during the process

2. Involvement of dissipative effects

1. Lack of equilibrium during the process:

The lack of equilibrium (mechanical, thermal, chemical) between the system and

its surroundings or between two systems, or two parts of the same system, causes a

spontaneous change which is reversible. The following are specific examples in this

regard.

Heat transfer through a finite temperature difference

Lack of pressure equilibrium within the interior of the system or between the

system and the surroundings.

Free expansion

2. Irreversibility due to dissipative effects:

The irreversibility of a process may due to the dissipative effects in which work is

done without producing an equivalent increase in the kinetic or potential energy of any

system. The transformation of work into molecular internal energy either of the system or

of the reservoir takes place through the agency of such phenomena as friction, viscosity,

inelasticity, electrical resistance, and magnetic hysteresis. These effects are known as

dissipative effects, and work is said to be dissipated.


Thermodynamics - I

4.9. Condition of irreversibility:

A natural process is reversible because the condition for mechanical, thermal and

chemical equilibrium are not satisfied, and the dissipative effects, in which work is

transformed into an increase in internal energy, are present. For a process to be

reversible, it must not posses these features. If a process is performed quasi – statically,

the system passes through states of thermodynamic equilibrium, which may be traversed

as well in one direction as in the opposite direction. If there are no dissipative effects, all

the work done by the system during the performance of a process in one direction can be

returned to the system during the reversible process.

A process will be reversible when it is performed in such away that the system is

at all times infinitesimally near a state of thermodynamic equilibrium and in the absence

of dissipative effect of any form. Reversible processes are, therefore, purely ideal,

limiting cases of actual processes.

4.10. Carnot’s theorem:

It states that of all heat engines operating between a given constant temperature

source and a given constant temperature sink, none has a higher efficiency than a

reversible engine.

4.11. Entropy:

When the first law of thermodynamics was applied for thermodynamic processes,

the existence of a property, the internal energy, was found. Similarly, the second law of

thermodynamics was applied for thermodynamic processes, it leads to the definition of a

new property, known as entropy. In fact, thermodynamics is the study of three E’s,

namely energy, equilibrium and entropy. It is a function of quantity of heat which

shows the possibility of conversion of heat into work.

It may be stated roughly that the entropy of a system is a measure of degree of

molecular disorder existing in the system.

4.12. Clausius’ theorem:

Let a system be taken from an equilibrium state i to another equilibrium state f by

following the reversible path i-f, as shown in figure. Let a reversible adiabatic i-a be


Thermodynamics - I

drawn through i and another reversible adiabatic b-f be drawn through f. then a reversible

isotherm a-b is drawn in such a way that the area under i-a-b-f is equal to the area under

i-f. Applying the first law for

Process i-f

Qi-f = Uf – Ui + Wif

Process i-a-b-f

Qiabf = Uf – Ui + Wiabf

Since

Wif = Wiabf

Therefore

Qi-f = Qiabf = Qia + Qab + Qbf

Since

Qia= 0 and Qbf = 0

Qif = Qab

Heat transferred in the process i-f is equal to the heat transferred in the isothermal

process a-b.

Thus any reversible path may be substituted by a reversible zigzag path, between

the same end states, consisting of a reversible adiabatic followed by a reversible isotherm

and then by a reversible adiabatic, such that the heat transferred during the isothermal

process is the same as that transferred during the original process.

Let a smooth closed curve representing a reversible cycle be considered (Refer

figure). Let the closed cycle be divided into a larger number of strips by means of

reversible adiabatics. Each strip may be closed at the top and bottom by reversible

isotherms. The original closed cycle is thus replaced by a zigzag closed path consisting of

alternate adiabatic and isothermal processes, such that the heat transferred during all the

isothermal processes is equal to the heat transferred in the original cycle. Thus the

original cycle is replaced by a number of Carnot cycles. If the adiabatics are close to one

another and the number of Carnot cycles is large, the saw-toothed zigzag line will

coincide with the original cycle.

For the elemental cycle abcd, dQ1 heat is absorbed reversibility at T1, and dQ2

heat is rejected reversibility at T2


Thermodynamics - I

(dQ1 / T1) = (dQ2 / T2)

If heat supplied is taken as positive and heat rejected as negative

(dQ1 / T1) + (dQ2 / T2) = 0

Similarly, for the elemental cycle efgh,

(dQ3 / T3) + (dQ4 / T4) = 0

If similar equations are written for all the elemental carnot cycles, then for the whole

original cycle.

(dQ1 / T1) + (dQ2 / T2) + (dQ3 / T3) + (dQ4 / T4) + ……..= 0

Or

The cyclic integral of (dQ / T) for a reversible cycle is equal to zero. This is known as

clausius’ theorem.

4.13. Property of entropy:

Let a system be taken from an initial equilibrium state ‘i’ to a final equilibrium

state ‘f’ by following the reversible path R1 as shown in figure. The system is brought

back from ‘f’ to ‘i’ by following another reversible path R2. Then the two paths R1 and

R2 together constitute a reversible cycle. From clausius’ theorem

(dQ / T) = 0

The above integral may be replaced as the sum of two integrals, one for path R1

and the other for path R2

1 R2

P R1

2

V


Thermodynamics - I

Since R1 and R2 represent any two reversible paths, ∫ (dQ / T) is independent of

the reversible path connecting ‘i’ and ‘f’.

Therefore, there exists a property of a system whose value at the final state ‘f’

minus its value at the initial state ‘i’ is equal to ∫ (dQ / T). This property is called entropy,

and is denoted by ‘S’. If ‘Si’ is the entropy at the initial state ‘i’ and ‘Sf’ is the property at

the final state ‘f’, then

∫ (dQ / T) = Sf – Si

When two equilibrium states are infinitesimally near

(dQR / T) = dS

Where ‘dS’ - an exact differential

Because ‘S’ is a point function and a property. The subscript R in dQ indicates that heat

dQ is transferred reversibly.

The word ‘entropy’ was first introduced by clausius, taken from the Greek word

‘tropee’ meaning ‘transformation’. It is an extensive property, and has the unit J/K. the

specific entropy

s = S / m; unit J / Kg K

4.14. The inequality of clausius:

Let us consider a cycle ABCD as shown in figure. Let AB be a general process, either

reversible or irreversible, while the other processes in the cycle are reversible. Let the

cycle be divided into a number of elementary cycles, as shown. For one of these

elementary cycles

REFER CLASS NOTES FOR DERIVATION


Thermodynamics - I

CHAPTER – VII

PSYCHROMETRY

7.1. Introduction:

The name ‘psychrometrics’ is given to the study of the properties of air – water

vapour mixtures. It also includes the study of behavior of dry air and water vapour

mixing under various sets of conditions. Atmospheric air is considered to be a mixture of

dry air and water vapour. The control of moisture content in the atmosphere is essential

for the satisfactory operation of many processes involving hygroscopic materials like

paper and textiles, and its important in comfort air conditioning.

7.2. Psychrometry terms or properties:

Dry air: The pure dry air is a mixture of number of gases such as nitrogen, oxygen, CO2,

H2, He, etc. But the nitrogen and oxygen is a major portion of the combination. The

oxygen has 21% and nitrogen has 79% by volume. Similarly, oxygen has 23% and

nitrogen has 77% by mass.

Moist air: It is the mixture of dry air and water vapour. The amount of water vapour

present in the air depends upon the absolute pressure and temperature of the mixture.

Saturated air: It is the mixture of air and water vapour, when the air has diffused the

maximum amount of water vapour into it.

Humidity: The amount of water vapour present in the air is called as Humidity.

Relative humidity: It is ratio of partial pressure of water vapour in a mixture (pw) to the

saturation pressure ps of pure water, at the same temperature of mixture.

R.H. = φ = (pw) / ps

It can be defined in the following way,

Mass of water vapour in a given volume of air at temperature ‘T’ to the mass of water

vapour when the same volume of air is saturated at temperature ‘T’.


Thermodynamics - I

Specific humidity: It is defined as the mass of water vapour per unit mass of dry air in a

mixture of air and water vapour.

W = m / G

Specific humidity is the maximum, when air is saturated at temperature ‘T’

Wmax = ms / G

Finally,

W = 0.622 (pw / p - pw)

Ws = 0.622 (ps / p - ps)

Degree of saturation: It is the ratio of actual specific humidity and the saturated specific

humidity. It is denoted by the symbol ‘μ’.

μ = (pw /ps) (p - ps / p - pw)

Dry bulb temperature (DBT): It is the temperature measured with the help of an

ordinary thermometer. It is measured in degree Celsius.

Wet bulb temperature: It is the temperature measured with the help of thermometer,

when the bulb is enveloped by a cotton wick saturated with water.

Dew point temperature: It is the temperature at which the water vapour begins to

condense.

Wet bulb depression: It is the temperature difference between DBT and WBT.

Dalton’s law of partial pressures: It states, “The total pressure exerted by the mixture

of air and water vapour is equal to the sum of the pressures, which each constituent

would exert, if it occupied the same space by itself”.

P = Pa + Pw


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