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ME1201-ENGINEERING THERMODYNAMICS

S.K.AYYAPPAN, Lecturer, Department of mechanical engineering

UNIT I

BASIC CONCEPTS AND FIRST LAW

Concept of continuum – macroscopic approach – Thermodynamic systems –

closed –open – isolated –Thermodynamic Property – state – path and process –

quasi-static process – work –modes of work –Zeroth law of thermodynamics –

concept of temperature and heat – Concept of ideal and real gases –First law of

thermodynamics – application to closed and open systems – internal energy –

specific heat capacities – enthalpy – steady flow process with reference to

various thermal equipments



Introduction:

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

substances.

Therme means heat and dynamics means power.

Thermodynamics is a field of science which deals with

a) Energies possessed by gases and vapours,

b) Conversion of energies in terms of heat and mechanical work, and

c) The relationship with properties of system.

But, thermal engineering deals with the applications of thermodynamics and its laws

relative to the work absorbing and producing devices, and improving their performance.

Principles of energy conversion

Application of thermodynamics laws and principles are found in all field of energy

technology

Steam and nuclear power plants

Internal combustion engines

Gas turbines

Air conditioning

Refrigeration

Gas dynamics

Jet propulsion

Compressors

Chemical process plants,

Direct energy conversion devices.

Basic concepts:

Density (ρ)

Density, ρ= mass/volume=m/v kg/m3

Specific weight (w)

Sp.weight, w= weight/volume= W/V N/m3

Specific volume (v)

Specific volume, v= volume/mass= V/m m3/kg

Specific gravity (s)

Specific gravity’s= Density (or) sp.weight of the given substance

Density (or) specific weight of the standard substance

Pressure (p)

P= force/area=F/A N/m3

1 Pascal- 1 N/m3

1 bar= 105

N/m3= 100 kN/m2

1 Torr= 1mm of mercury (Hg) =133.3 N/m2

1mm of water (H2O) =9.80665 N/m2



Atmospheric pressure (patm)

Atmospheric pressure= 1.01325 bar

= 101.325 kN/m2 or kpa

= 101325 N/m2 or pa

= 760 mm of Hg

= 10.34 m of water

=14.69 psi

Gauge pressure (pg)

It is the pressure recorded by the pressure gauge. All pressure gauges read ‘zero’ pressure at

atmospheric level. Hence, they actually measure the difference of fluid pressure and

atmospheric pressure.

Vacuum pressure (pvac)

The pressure below the atmospheric pressure is called as vacuum pressure. It is also called as

negative pressure.

The pressure gauge which is used to measure vacuum pressure is called vacuum gauge.

Absolute pressure (p abs)

The pressure measured from absolute zero pressure

Absolute pressure= atmospheric pressure+gauge pressure

Absolute pressure= atmospheric pressure-vacuum pressure

Pabs=patm+pg

Pabs=patm-pvac

Temperature (T)

Measure of velocity of fluid particles. Degree of hotness or coldness or level of heat intensity

of a body

Absolute temperature:

The temperature measured from the absolute zero temperature

Standard temperature and pressure (STP)

The standard atmospheric condition is

Standard temperature=15ºc

Standard pressure= 760 mm of hg

= 101.325 kN/m2

Normal temperature and pressure (NTP)

The condition of temperature at 0ºc and 760 mm of Hg

Unit:

The primary quantities are measured in terms of the basic or fundamental units and the

secondary Quantities are measured in terms of derived units.

Fundamental Units

Fundamentals units are the basic unit normally which are unit of mass (M), unit of length (L)

and unit of time(T), but in the International System of units, there are seven fundamental

units and two supplementary units, which cover the entire field of science and engineering.

Fundamental and Supplementary Units

Fundamental Unit:

Physical Quantity-Unit-Symbol

1. Mass (M) -kilogram -kg



2. Length (L) -metre -m

3. Time (t) –second-s

4. Temperature (T)- kelvin -K

5. Electric current (I) -ampere -A

6. Luminous intensity (Iv) -candela -Cd

7. Amount of substance (n) –mole- mole

Supplementary Unit:

1. Plane angle (α, β, θ, φ)- radian-rad

2. Solid angle (Ω) -steradian -Sr

Derived Units

Some units expressed in terms of other basic units, which are derived from fundamental units

are

known as derived units. The derived units, which will be commonly used in this book,

Derived Units

Physical Quantity-Unit-Symbol

1. Area- m2 -A

2. Angular velocity -rad/s- ω

3. Angular acceleration -rad/s2 -α

4. Linear velocity- m/s- V

5. Linear acceleration -m/s2- a

6. Mass density- kg/m3- ρ

7. Force, weight- N –F,W

8. Work, energy, enthalpy-J-W, E, H

9. Pressure -N/m2-p

10. Power -Watt -P

11. Absolute or dynamic viscosity- N-s/m2-μ

12. Kinematic viscosity-m2/s-υ

13. Characteristic gas constant-J/kg.K-R

14. Universal gas constant-J/kgmol.K-Rm

15. Frequency-Hz, 1Hz = 1cps-f

16. Thermal conductivity-W/mK-k

17. Specific heat-J/kg.K-C

18. Molar mass or molecular mass-kg/mol-M

19. Sp. weight or wt. density-kgf/m3-wS

20. Sp. Volume-m3/kg-vS

21. Volume-m3-

Systems Of Units

There are only four systems of units, which are commonly used and universally recognized.

These are known as:



(1) C.G.S systems (2) F.P.S systems (3) M.K.S systems (4) S.I (System Internationale or

International system of units).The internationally accepted prefixes in S.I to express large and

small quantities.

Prefix Factors

Factor of Multiplication-Prefix-Symbol

1012-tera-T

109-giga-G

106-mega-M

103-kilo-k

122-hecto-h

101-deca-da

10–1-deci-d

10–2-centi-c

10–3-milli-m

10–6-micro-m

10–9-nano-n

10–12-pico-p

Mass (M)

Mass is the amount of matter contained in a given body and it does not vary with the change

in its position on the earth’s surface.

Weight (W)

The weight is the amount of force of attraction, which the earth exerts on a given body. The

weight of the body will vary with its position on the earth’s surface, because force of

attraction vary with variation of distance between the two bodies.

Force (F)

Force may be defined as an agent which produces or tends to produce, destroy or tends to

destroy the motion. According to Newton’s Second Law of Motion, the applied force or

impressed force is directly proportional to the rate of change of momentum

F α mv-mu/t

F α m (v-u/t)

F α ma

F=k.m.a

Where k is the constant of proportionality. If the unit of force adopted so that it produces unit

acceleration to a body of unit mass, then

1 = k.1.1

k=1

F=m.a

Force=mass*acceleration

In S.I the unit is newton (N) and 1N = 1 kg m/s2.



There are two types of units of force, absolute and gravitational. When a body of mass 1 kg is

moving with an acceleration of 1 m/s2, the force acting on the body is 1 newton(N). This is

the absolute unit of force.

When a body of mass 1 kg is attracted towards the earth with an acceleration of 9.81m/s2, the

force acting on the body is 1 kilogram-force, briefly written as ‘kgf’ or kg-wt. The unit of

force in kgf is called gravitational or engineers, unit of force or metric unit of force. From the

Newton’s Second

Law of Motion

F=k.m.a=m.g/gc=weight

a=g (acceleration due to gravity), and

k=1/gc, while

gc=9.80665 kg m/s2 =9.81 kg.m/s

2.1/kgf

kgf = 1 kg*9.81 m/s2 /gc = weight, 1 kgf = 1 kg* 9.81 m/s

2=9.81 m/s

2=9.81 N

If, local value of g is numerically the same as gC then the weight of 1 kg becomes equal to 1

kgf.

The gravitational unit of force is ‘g’ times greater than the absolute unit of force or S.I unit of

force, as

1 kgf = 1 kg × 9.81 m/s2 = 9.81 m/s2 = 9.81 N

Specific Weight (wS)

It is the weight per unit volume. It is also known as the weight density. It may be expressed in

kgf/m3, in MKS system of unit and newton/m3 in S.I.

Specific weight (wS) =

Specific Volume (vS)

It is defined as the volume per unit mass. It may be expressed in m3/kg.

Pressure

Pressure is the normal force exerted by a system against unit area of the boundary surface.

The unit of pressure depends on the units of force and area. In S.I, the practical units of

pressure are N/mm2,

N/m2, kN/m2, MN/m2 etc.

A bigger unit of pressure known as bar, such that

1 bar = 1 × 105 N/m2 = 0.1 × 106 N/m2 = 0.1 MN/m2

Other practical units of pressure are Pascal (Pa), kilopascal (kPa) & mega Pascal (MPa), such

that

1 Pa = 1N/m2

1 kPa = 1 kN/m2 = 103 N/m2

1 MPa = 1 × 106 N/m2 = 103 kPa = 1 N/ mm2



Absolute, Gauge and Vacuum Pressure

The pressure is measured in two different systems. In one system, it is measured

above the absolute zero or complete vacuum, and is defined as absolute pressure. In other

system, pressure is measured above the atmospheric pressure, and is defined as gauge

pressure. So

(a) Absolute pressure:

It is defined as the pressure which is measured with reference to absolute zero

pressure.

(b) Gauge pressure: It is defined as the pressure which is measured with reference to

Atmospheric pressure. It is measured with the help of a pressure measuring

instrument. It is a pressure above the atmospheric pressure.

(b) Vacuum pressure:

It is the pressure below the atmospheric pressure. Sometimes it is called as

negative gauge pressure. The relationship between the absolute pressure, gauge

pressure and vacuum pressure are shown in figure

Mathematically

Pressure Measurement by Manometer

A manometer is normally used to measure pressure. In manometer the pressure is determined

according to the hydrostatic formula. The manometric liquid may be mercury, water, alcohol,

etc. A U-tube manometer is shown in figure 1.12. Since manometric fluid is in equilibrium,

the pressure along a horizontal line AB is the same for either limb of manometer, then



Where p is the absolute pressure in the bulb, patm is the atmospheric pressure exerted on the

free surface of liquid and ρ1 and ρ2 are the densities of the liquid in the bulb and manometer

respectively.

Conversion Factor for Pressure

Normal Temperature and Pressure (N.T.P)



Normal temperature is at 0°C or 273 K temperature and normal pressure is 760 mm of Hg.

Normal temperature and pressure are briefly written as N.T.P.

Standard Temperature and Pressure (S.T.P)

The temperature and pressure of any gas, under standard atmospheric condition, is taken as

15°C (288K) and 760 mm of Hg respectively.

Energy

The simplest definition of energy is the capacity for doing work. In other words, a system is

said to posses energy when it is capable of doing work. The energy can be classified as (i)

Stored energy and (ii) Transit energy.

The stored energy is a thermodynamic property as it depends on the point, not upon the path.

The stored energy is the energy which is contained within the system boundaries. Examples

of stored energy are (i) potential energy (ii) kinetic energy (iii) internal energy etc. The transit

energy is in transition and crosses the system boundaries. Examples of transit energy

are (i) heat (ii) work (iii) electrical energy etc. The transit energy is not a thermodynamic

property as it depends upon the path.

Types of Stored Energy

The potential energy, kinetic energy or an internal energy are the different types of stored

energy and are discussed in detail, as follows:

Potential Energy

The energy possessed by a body, or a system for doing work, by virtue of its location or

configuration is called potential energy. If a body of mass m is at an elevation of z above the

datum plane, the potential energy (P.E) possessed by the body is given by

PE = mgz = W.z

Where g is the acceleration due to gravity.

Kinetic Energy

The energy possessed by a body, or a system for doing work, by virtue of its motion is called

kinetic energy. If a body of mass of m moves with a velocity v the kinetic energy(KE)

possessed by the body is given by

KE =1/2 mv2

The sum of the potential energy and kinetic energy of a body is called the Mechanical energy

of the body.

Internal Energy

This energy is possessed by a body, or a system due to its molecular arrangement and motion

of the molecules. It is usually represented by U and the change in internal energy (dU). It

depends upon the change in temperature of the system. Change of internal energy dU = Cv

(T2 − T1)

Where Cv is specific heat at constant volume &

T1 and T2 are the temperature at state points

The total energy of the system (E) is equal to the sum of the P.E, K.E and internal energy.

E = P.E + K.E + U

[Any other form of the energy such as chemical, electrical energy etc. are neglected]

Again E = mgz +1/2 mv2 + U = ME + U



While Mechanical energy (M.E) = P.E. + K.E = mgz +1/2 mv2

For unit mass, total energy

e = gz +1/2 v2 + u

When the system is stationary and the effect of gravity is neglected, then,

E = U and e = u

Law of Conservation Of Energy

The law of Conservation of Energy states that the energy can neither be created nor

destroyed, though it can be transformed from one form to any other form, in which the energy

can exist.

Power

Power may be defined as the rate of doing work or work done per unit time or rate of energy

transfer or storage. Mathematically,

Power = work done/ time taken=energy storage or transfer /time taken

The unit of power in S.I is watt (W)

1 W = 1 N.m/s = 1 J/s

A bigger unit of power called kilowatt (kW) or megawatt (MW)

1 kW = 1000 W and 1 MW = 106 W = 1000 kW

If T is the torque transmitted expressed in N.m or J and the angular speed is ω in rad/s, then

Power (P) = T × ω= T ×2πN/60

Watt, ω = 2πN/60

N is speed in r.p.m

Hence, Efficiency (η) =power output/power input

Specific heat capacity (C)

The quantity of heat transfer required for raising or lowering the temperature of unit mass of

the substance through one degree when the volume remains constant.j/kg K or kJ/kg K

Specific heat capacity at constant volume (Cv)

The quantity of heat transfer required for raising or lowering the temperature of unit mass of

the substance through one degree when the volume remains constant.

When the gas is heated or cooled by constant volume process, the heat transfer, Q=m Cv (T2-

T1) kJ.

Specific heat capacity of constant pressure (Cp)

The quantity of heat transfer required to raise or lower the temperature of unit mass of the

substance through one degree when the pressure is kept constant.

When the gas is heated or cooled at constant pressure process, the heat transfer, Q=m Cp (T2-

T1) Kj

For any gas, Cp is always greater than Cv.

γ=Cp/Cv

For air, Cp=1.005 kj/kg K, Cv=0.718 kj/kg K, γ=1.4

Macroscopic Vs microscopic viewpoint

Two points of view from which the behavior of matter can be studied The macroscopic and

the microscopic.

Classical thermodynamics or macroscopic approach:



A certain quantity of matter is considered, without the events occurring at the molecular level

being taken into account.

Statistical thermodynamics or Microscopic approach:

Matter is composed of myriads of molecules.

The behavior of the gas is described by summing up the behavior of each molecule

Microscopic or statistical thermodynamics

Macroscopic thermodynamics is only concerned with the effects of the action of many

molecules, and these effects can be perceived by human senses.

Thermodynamics system and control volume:

Thermodynamic 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.

Surroundings

Everything external to the system is called the surroundings or the environment.

Boundary

The system is separated from the surroundings by the system boundary

The boundary may be either fixed or moving.

Universe:

A system and its surroundings together comprise a universe.

Three classes of systems,

a) Closed system

b) Open system

c) Isolated system

Closed system:

System of fixed mass. There is no mass transfer across the system boundary. There may be

energy transfer into or out of the system. A certain quantity of fluid in a cylinder bounded by

a piston constitutes a closed system.

Open system:

One in which matter crosses the boundary of the system. There may be energy transfer also.

Most of the engineering devices are generally open systems.

Example:

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

energy transfers across the system boundary.

Isolated system:

One in which there is no interaction between the system and the surroundings. It is of fixed

mass and energy, and there is no mass or energy transfer across the system boundary.

If a system is defined as a certain quantity of matter, then the system contains the same matter

and there can be no transfer of mass across its boundary.

However, if a system is defined as a region of space within a prescribed boundary, then

matter can cross the system boundary. While the former is called a closed system, the latter is

an open system.

Control volume:



For thermodynamic analysis of an open system, such as an air compressor, attention is

focused on a certain volume in space surrounding the compressor.

Control surface:

Bounded by a surface called the control surface. Matter as well as energy crosses the control

surface.

A closed system is a system closed to matter flow, through its volume can change against a

flexible boundary. When there is matter flow, then the system is considered to be a volume of

fixed identity, the control volume.

There is thus no difference between an open system and a control volume.

Thermodynamics properties, processes and cycles:

Properties of the system:

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

E.g., volume, temperature, pressure. Such characteristics are called properties of the system.

These are all macroscopic in nature.

State:

When all the properties of a system have definite values, the system is said to exist at a

definite state. Properties are the coordinates to describe the state of a system. They are the

state variables of the system.

Change of state:

Any operation in which one or more of the properties of a system changes

Path of change of state:

The succession of states passed through during a change of state is called the path of the

change of state.

Process:

When path is completely specified, the change of state is called a process, e.g., control

pressure process.

Thermodynamic cycle:

Series of state changes such that the final state is identical with the initial state.

Types of properties:

Intensive properties:

Independent of the mass in the system, e.g., pressure, temperature, etc.

Extensive properties:



Related to mass, e.g., volume, energy,

If mass is increased, the values of the extensive properties also increase.

Specific extensive properties:

Extensive properties per unit mass, are intensive properties, e.g., specific volume,specific

energy, density.

Homogeneous and heterogeneous systems:

Phase:

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 spaces. Solid, liquid, and gas.

Homogeneous system:

A system consisting of a single phase

Heterogeneous system:

A system consisting of more than one phase.

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.

An isolated system always reaches in course of time a state of thermodynamics equilibrium

and can never depart from it spontaneously.

Therefore, there can be no spontaneous change in any macroscopic property if the system

exists in an equilibrium state.

Thermodynamic studies mainly the properties of physical systems that are found in

equilibrium states.

A system will be in a state of thermodynamic equilibrium, if the conditions for the following

three types of equilibrium are satisfied.

a) Mechanical equilibrium

b) Chemical equilibrium

c) Thermal equilibrium

Mechanical equilibrium:

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

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

If an unbalanced force exist, either the system alone or both the system and the

surroundings will undergo a change of state till mechanical equilibrium is attained.

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.

Thermal equilibrium:

When a system existing in mechanical 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 not satisfied, the system undergoes a change of state till thermal equilibrium is

restored.

Nonequilibrium state:

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

system is said to be in a nonequilibrium state.

Unbalanced force in the interior of a system or between the system and the

surroundings, pressure varies from one part of the system to another.

Quasi-static process:

Let us consider a system of gas contained in a cylinder. The system initially is in

equilibrium state, represented by the properties p1, v1, and 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 it hits the stops. The system again comes to an equilibrium

state, being described by the properties p2, v2, t2. But the intermediate states passed

through by the system are nonequilibrium states which cannot be described by

thermodynamic coordinates.

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 many very small pieces of weights,

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.

Quasi meaning almost. Infinite slowness is the characteristics feature of quasi-static

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

A quasi-static process is also called a reversible process.



Path

Properties are the thermodynamic co-ordinates of the state of a system. So the properties

are state variable of the system. When any one or more of the properties of a system

change, it is called a change of state. When a system passes through a series of states

during a change of state from the initial state to the final state, it is called the path of the

change of state.

Process

When a system passes through a successive states during a change of state from the initial

state to the final state, with a completely specified path for each successive change in

states, the change of state is defined as a process, e.g., a constant volume process,

constant pressure process.It is shown in figure 1.5, where 1-2 is a constant volume

process and 2-3 is a constant pressure process.

A process is designated by the path followed by the system in reaching the final

equilibrium state from the given initial state.

Cyclic Process or Thermodynamic Cycle

When a process or processes are performed on a system in such a way that the initial and

the final states will be same, then the process is called thermodynamic cycle or cyclic

process. In figure 1-A-2 and 2-B-1 are two simple processes whereas 1-A-2-B-1 is a cyclic

process, whose final and initial states are the same.



Non-equilibrium Process

Non-equilibrium process is a process carried out in such a way that the initial state-point

and the final state-point are in equilibrium but the intermediate state-points, through which

the system is passing, are in non-equilibrium state. Figure 1.8 shows the non equilibrium

process whose initial and final equilibrium states are joined by a dotted line which has got no-

meaning otherwise

Reversible Process

Reversible process is a process carried out in such a way that at every instant, the system

deviation is only infinitesimal from the thermodynamic state, and also which can be reversed

in direction and the system retraces the same equilibrium states. Thus in reversible process,

the interactions between the system and the surroundings are equal and opposite in direction.

The Quasi-static or Quasiequilibrium process is also known as reversible process. In

reversible process the work done could be written in the form when there is a

change in system boundaries.

Irreversible Process

A process is said to be irreversible, while initial and final states both being in equilibrium,

when reversed, the system and the surroundings do not come to the original initial state and a

trace of history of the forward process is left. In actual practice, most of the processes are

irreversible, to turbulence in the system, temperature gradients in the system and due to

friction. In irreversible processes, the network output is less than and is given by



Flow Process

The process occurring in the control volume of open system which permits the transfer of

mass to and from the system is known as flow process. The working substance, in flow

processes, enters the system and leaves after doing the work. The flow processes may be

classified as (1) steady flow processes and (2) unsteady flow processes. The conditions which

must be satisfied for a steady flow process are as following:

(i) The mass flow rate through the system remains constant.

(ii) The rate of heat transfer is constant.

(iii) The rate of work transfer is constant.

(iv) The characteristics of the working substance, like velocity, pressure, density etc., at

Any points do not change with time. If any one of these conditions are not satisfied,

then the flow process is said to be an unsteady flow process.

Non-flow Process

The process in which mass of working substance is not permitted to cross the boundary of the

control volume of the system is called non-flow process. Generally non-flow processes occur

in the closed system.

Concept of continuum:

A continuous homogenous medium is called as continuum. Based on macroscopic

approach.

Continuum is based on macroscopic approach. Here, the matter is treated as continuous

instead of disregarding the behavior of individual molecules.

For example, let us consider the mass δm with a volume of δv at a particular point ‘P’

The density of the system is δm / δv.

The graph is plotted between δm / δv and δv. if δm / δv becomes very small, relatively

few molecules pass into and out of the control volume in random motion. Therefore, the

average density varies with time. It is very difficult to determine a definite value of δm /

δv. When the smallest volume of δv1 is continuous, the density ρ of the system at any

particular point is defined as

Ρ = Lt δm

Sv δv δv

At the same time, the fluid velocity at P is instantaneous velocity of the center of gravity

of the smallest corresponding continuous volume δv1

Characteristic gas equation:



General gas equation for ideal gas is

Pv / T = constant

Where

p- Pressure in N/m2

V- Volume in m3

T- Temperature in ºC

Taking R as constant

Pv / T = R

Pv = RT

If we consider mass ‘m’, then the equation becomes

pV=mRT

This equation is known as characteristic gas equation.

Cycle

A series of state changes such that the final state is identical with the initial state is known

as cycle.

If a thermodynamic system undergoes a series of processes and returns to its initial

position, then the process is called cyclic process.

There are two types of cyclic processes

a) Closed cycle

b) Open cycle

1. Closed cycle

In a closed system, the working substance is recirculated again and again within the

system itself without taking any mass transfer. It is shown in fig.

2. Open cycle

In an open cycle, the working substance is exhausted to atmosphere after completing

the process. Sp, here both the mass and energy transfer take place.

A closed system and its surroundings can interact in two ways. a) by work transfer,

and b) by heat transfer. These may called energy interactions.

Work transfer (W)

Work is one of the basic modes of energy transfer.

A force is a means of transmitting an effect from one body to another.

In mechanics work is defined as the work is done by a force as it acts upon a body

moving in the direction of the force.

The action of a force through a distance (or of a torque through an angle) is called

mechanical work.

Work transfer is considered as occurring between the system and 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 be raised with the pulley driven by the motor. The sole effect on

things external to the system is then the raising of a weight.

Positive work

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



Negative work

When work is done on a system, it is taken to be negative.

The symbol W is used for work transfer.

a) W is positive

System W

Surroundings

W b) W is negative

System

Surroundings

Work interaction between a system and the surroundings.

The unit of work is N.m or Joule ( 1 Nm = 1 Joule).

Power

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

of power is J/s or watt.

Work is one of the forms in which a system and its surroundings can interact with

each other. There are various types of work transfers which can get involved between

them.

PdV-Work OR Displacement work

Let the gas in the cylinder be a system having initially the pressure p1 and volume v1.

The system is in thermodynamic equilibrium, the state of which is described by the

coordinate’s p1, v1. The piston is the only boundary which moves due to gas pressure.

Let the piston move out to a new final position 2, equilibrium state pressure p2 and

volume v2. At any intermediate point in the travel of the piston, pressure p and the

volume V.

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

piston, the force F acting on the piston F=p.a. and the infinitesimal amount of work

done by the gas on the piston

aW=F.dl=padl=pdV

where dV=adl=infinitesimal displacement volume. When the piston moves out from

position 1 to position 2 with the volume changing fro, V1 to V2, the amount of work

W done by the dydtem will be

W1-2= V2

∫v1 pdV

The magnitude of the work done is given by the area under the path 1-2, since p is at

all times a thermodynamic coordinate.

All the state passed through by the system as the volume changes from V1 to V2 must

be equilibrium states, and the 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.

Example of Work



Paddle Wheel Work

This is also known as Stirring Work where ∫ pd = 0, but work is done.

The paddle wheel work is an illustration of shaft-work. Paddle wheel work process is

a process involving friction in which the volume of the system does not change at all,

and still work is done on the system. Representation of the process is provided by a

system in which a paddle wheel turns a fixed mass of fluid as shown in Fig. Consider

that in the system weight is lowered, paddle wheel runs. The work is transferred

across the system boundary in the fluid system. The volume of the system remains

constant and the work, pd

If m is the mass of the weight lowered through a distance dz and T is the torque

transmitted by the shaft in rotating through an angle dθ, the differential work transfer

to the fluid is given by δW = mgdz = Tdθ

Thus, ∫ pd does not represent work for this case, although work has been done on

the system. So work may be done on a closed system even though there is no volume

change.

Path function and point function:

It is possible to take a system from state 1 to state 2 along many quasi-static paths,

such as A,B or C. area under each curve represents the work for each process,

Path function

The area under each curve represents the work for each process, amount of work

involved in each case is not a function of the end states of the process, and it depends

on the path the system follows in going from state 1 to state 2. For this reason, work is

called a path function, and dW is an inexact or imperfect differential.

Point functions

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

definite value for each property. The change in a 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 only on the initial and final states of the system. The differentials

of point functions are exact or perfect differentials, and the integration is simply

V2∫v1 dV= V2-V1

The change in volume thus depends only on the end states of the system irrespective

of the path of the system follows.

On the other hand, work done in a quasi-static process between two given states

depends on the path followed.

2∫1 dW≠ W2-W1

2∫1 Dw=W1-2 or 1W2

dv=1/p dw

1/p is called the integrating factor.

The initial and final states of the system are the same,the change in any property is

zero

dv=0, dp=0, dT=0

Where the symbol denotes the cyclic integral for the closed path. Therefore,the

cyclic integral of a property is always zero.

PdV-work in various quasi-static processes:

a) Constant pressure process (isobaric or isopiestic process)

W1-2= 2∫1 pdV

= p [v]1

2

= p [V2-V1]

W1-2= V2∫v1 pdV=p (V2-V1)

b) Constant volume process (isochoric process) (P=C)

W1-2= 2∫1pdV=0

V1=V2=V=0

There is no work transfer in this process

c) Process in which pV=C

W1-2= V2∫v1 pdV Pv=p1V1=C

P=(p1V1)/V

W1-2= p1v1

V2∫v1 dV/V=p1V1 ln V2/V1

=P1V1 ln p1/p2

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

pVn=p1V1

n=p2V2

n=C

p= (p1V1n)/V

n



W1-2= V2∫v1 pdV

= V2∫v1 p1V1

n/V

n.dV

= (p1V1n)[V

-n+1/-n+1]

v2

V1

= p1V1n/1-n (V2

1-n-V1

1-n)

=p1V1n*V2

1-n - p1V1

n*V1

1-n / 1-n

= p1V1-p2V2 / n-1=p1V1 / n-1[1- (p2/p1) n-1/n

]

Free expansion with zero work transfer

Let us consider a gas separated from the vacuum by a partition. Let the partition

be removed. The gas rushes to fill the entire volume. The expansion of a gas

against vacuum is called free expansion. if we neglect the work associated with

the removal of partition

2∫1 dw=0, although 2∫1 pdV≠0

Heat transfer:

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

virtue of a temperature difference.

Conduction

Transfer of heat between two bodies in direct contact

Radiation

Heat transferred between two bodies separated by empty space or gases by the

mechanism of radiation through electromagnetic waves.

Convection:

Refers to the transfer of heat between a wall and a fluid system in motion.

Heat flow in to a system is taken to be positive

Heat flow out of a system is taken as negative

Energy transfer by virtue of temperature difference is called heat transfer

Adiabatic process:

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.

A wall which permits the flow of heat is a diathermic wall.

Unit of heat is joule in S.I units.

Heat transfer- a path function

Heat transfer is a path function,that is , the amount of heat transferred when a

system changes from a state 1 to a state 2 depends on the intermediate states

through which the system passes, its path. Therefore dQ is an inexact differential.

2∫1 dQ=Q1-2 or Q2



The displacement work is given by

W1-2=2∫1dW=

2∫1pdV

Work transfer- area under the path on p-v diagram

Q1-2=2∫1 dQ=

2∫1TdX

dQ=TdX

dX=1/T dQ

Specific heat:

The specific heat of a substance is defined as the amount of heat required to raise

a unit mass of the substance through a unit rise in temperature. The symbol c will

be used for specific heat.

C=Q/m.∆t j/kg k

Latent heat:

The latent heat is the amount of heat transfer required to cause a phase change in

unit mass of a substance at a constant pressure and temperature.

First law of thermodynamics: First law for a closed system undergoing a cycle

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

which enters the system as work may leave as heat.

(∑W) cycle=J (∑Q) cycle

dw=J dQ

Denotes the cyclic integral for the closed path.

This is the first law for a closed system undergoing a cycle

First law for a closed system undergoing a change of state

(∑W) cycle= (∑Q) cycle

Q-W=∆E

∆E is the increase in the energy of the system

Q=∆E+W

(Q2+Q3-Q1)= ∆E+ (W2+W3-W1-W4)

Energy- a property of the system:

QA=∆EA+WA

And for path B

QB=∆EB+WB

The process A and B together constitute a cycle

(∑W) cycle= (∑Q) cycle

WA+WB=QA+QB

QA-WA=WB-QB



∆EA=-∆EB

∆EA=-∆EC

∆EB=∆EC

Specific energy e= E/m (J/kg)

dE=0, dV=0

Different forms of stored energy:

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.

Cv= (əu/əT)v

For a constant volume process

(∆u)v=T2∫T1Cv dT

Q=∆u+W

dQ=du+dW

Q=∆u+W

dQ=du+dw

for a process in the absence of work order than PdV work

dw=pdV

dQ=du+pdV

when the volume is held constant

(Q)v=(∆u)v

(Q)v=T2∫T1 Cv dT

Specific heat of a substance is defined interms of heat transfer

Cv=(əQ/əT)v

(dQ)v=du

The product mCv=Cv is called the heat capacity at constant volume (J/K).

Enthalpy

The enthalpy of a substance, h is defined as

h=u+pv

it is an intensive property of a system (Kj/kg)

dQ=du+pdV

At constant pressure

PdV=d(pv)

(dQ)p=du+d(pv)

(dQ)p=d(u+pv)



(dQ)p=dh

h=u+pv is the specific enthalpy, a property of the system.

h=u+RT

h=f(T)

total enthalpy H=mh

H=U+Pv

h=H/m (J/kg)

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 constant.

Cp=(əh/əT)p

(dQ)p=dh

(∆h)p=T2∫T1 Cp dT

The first law for a closed stationary system of unit mass

dQ=du+pdV

h=u+pv

dh=du+pdV+Vdp

=dQ+vdp

dQ=dh-vdp

(dQ)p=dh

(Q) p=(∆h)p

(Q)p=T2∫T1 Cp Dt

The heat capacity at constant pressure Cp is equal to mCp (J/K).

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

E= Constant

The energy of an isolated system is always constant.

Perpetual motion machine of the first kind-PMM1

The first law states the general principle of the conservation of energy. Energy is

neither created nor destroyed, but only gets transformed from one form to another.

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 in brief, PPM1.

A PMM1 is thus impossible.

The converse of the above statement is also true, there can be no machine which

continuously consume work without some other form of energy appearing

simultaneously.

Temperature



The temperature is an intensive thermodynamic property of the system, whose

value for the entire system is not equal to the sum of the temperature of its

individual parts. It determines the degree of hotness or the level of heat intensity

of a body or a system. A body is said to be at a high temperature or hot, if it shows

high level of heat intensity in it and a body is said to be at a low temperature or

cold, if it shows a low level of heat intensity.

Zeroth Law of Thermodynamics

This law states,” When each of two systems are in thermal equilibrium with a

third system, then the two systems are also in thermal equilibrium with one

another.”

Let a body X is in thermal equilibrium with a body Y, and also separately with a

body Z, then following above law, Y and Z will be mutually in thermal equilibrium

with each other. A system is said to be in thermal equilibrium, when there is no

temperature difference between the parts of the system or between the system and

the surroundings. Zeroth law provides the basis of temperature measurement.

Problems:

1. A stationary mass of gas is compressed without friction from an initial

state of 0.3 m3 and 0.105 Mpa to a final state of 0.15 m3 and 0.105 Mpa, the

pressure remaining constant during the process. There is a transfer of 37.6

Kj of heat from the gas during the process. How much does the internal

energy of the gas change?

First law for a stationary system in a process gives

Q=∆U+W

Q1-2=U2-U1+W1-2

W1-2=v2∫v1 pdV=p (V2-V1)

= 0.105 (0.15-0.30) Mj

=-15.75kJ

Q1-2=-37.6 Kj

Substituting in equation

-37.5 kj=U2-U1-15.75 kj

U2-U1=-21.85 kj

The internal energy of the gas decreases by 21.85 kj in the process.

2. When a system is taken from state a to state b,along path acb, 84 kj of heat

flow into the system, and the system does 32 kj of work.a) how much will the

heat that flows into the systems along path adb be, if the work done is 10.5 kj?

b) when the system is returned from b to a along the curved path, the work

done on the system is 21 kj. Does the system absorb or liberate heat, and how

much of the heat is absorbed or liberated? C) if Ua=0 and Ud=42kj, find the

heat absorbed in the processes ad and db.

Qacb=84 kj

Wacb=32kj



Qacb=Ub-Ua+Wacb

Ub-Ua=84-32=52kj

Qadb=Ub-Ua+Wadb

=52+10.5

=62.5kj

Qb-a=Ua-Ub+Wb-a

=-52-21

=-73

The system liberates 73 kj of heat

Wadb=Wad+Wdb=Wad=10.5 kj

Qad=Ud-Ua+Wad

=42-0+10.5=52.5 kj

Qadb=62.5 kj=Qad+Qdb

Qdb=62.5-52.5=10 kj

3. A piston and cylinder machine contains a fluid system which passes through a

complete cycle of four processes. During a cycle, the sum of all heat transfers is -

170 kj. The system completes 100 cycles per min. complete the following table

showing the method for each item, and compute the net rate of work output in

KW.

Process Q (kj/min) W (kj/min) ∆E (kj/min)

a-b 0 2170 -

b-c 21000 0 -

c-d -2100 - -36600

d-a - - -

Solution:

Process a-b:

Q=∆E+W

0=∆E+2170

∆E=-2170 Kj/min

Process b-c:

Q=∆E+W

21000=∆E+0

∆E=21000 Kj/min

Process c-d:

Q=∆E+W

-2100=-36600+W

W=34500 Kj/min

Process d-a:

∑cycle Q=-170 kj

The system completes 100 cycles/min.



Qab+Qbc+Qcd+Qda=-17000 kj/min

0+21000-2100+Qda=-17000

Qda=-35900 kj/min

Now ∫dE=0, since cyclic integral of any property is zero.

∆Ea-b+∆Eb-c+∆Ec-d+∆Ed-a=0

-2170+21000-36600+∆Ed-a=0

∆Ed-a=17770 kj/min

Wd-a=Qd-a-∆Ed-a

=-35900-17770

=-53670 kj/min

The table becomes

Process Q (kj/min) W (kj/min) ∆E (kj/min)

a-b 0 2170 -2170

b-c 21000 0 21000

c-d -2100 34500 -36600

d-a -35900 -53670 17770

Since rate of work output

= -17000 kj/min

=-283.3 Kw

Example 5

The internal energy of a certain substance is given by the following equation

u=3.56 pv+ 84

Where u is given in kj/kg, p is in kpa, and v is in m3/kg.

a system composed of 3 kg of this substance expands from an initial pressure of

500 kpa and a volume of 0.22 m3

to a final pressure 100 kpa in a process in which

pressure and volume are related by pv1.2

=constant.

a) If the expansion is quasi-static, find Q, ∆U, and W for the process.

b) In another process the same system expands according to the same pressure-

volume relationship as in part a) and from the same initial state to the same final

state as in part b) but the heat transfer in this case is 30 kj. Find the work

transfer for this process. C) Explain the difference in work transfer in parts a)

and b).

Solution;

u=3.56 PV+84

∆u=u2-u1=3.56 (p2v2-p1v1)

∆U=3.56 (p2v2-p1v1)

P1v11.2

=p2v21.2

∆U=3.56 (p2v2-p1v1)

P1v11.2

=p2v21.2



V2=V1 (p1/p2) 1/1.2

= 0.22 (5/1) 1/1.2

=0.22*3.83=0.845 m3

∆U=356 ( 1×0.845-5×0.22) KJ

=-356×0.255=-91 KJ

For a quasi-static process

W=∫ pdv= p2v2-p1v1/1-n

=( 1×0.845-5×0.22) 100/ 1-1.2

=127.5 kj

Q=∆U+W

=-91+127.5=36.5 kj

b) here Q=30 kj

Since the end states are the same, ∆u would remain the same as in a)

W=Q-∆U

=30-(91)

=121 kj

c) The work in b) is not equal to ∫ pdv since the process is not quasi-static.

Example 6

A fluid contained in a cylinder by a spring loaded, frictionless piston so that the

pressure in the fluid is a linear function of the volume (p= a+ bv). The internal

energy of the fluid is given by the following equation.

U= 34+3.15 pv

Where U is in kj, pin kpa, and V in cubic meter. If the fluid changes from an

initial state of 170 kpa, 0.03 m3 to a final state of 400 kpa, 0.06 m3, with no work

other than that done on the piston, find the direction and magnitude of the work

and heat transfer.

Solution:

The change in the internal energy of the fluid during the process.

U2-U1=3.15 (p2v2-p1v1)

=315 ( 4×0.06-1.7×0.03)

=315×0.189=59.5 kj

Now p= a+bV

170=a+b×0.03

400=a+b×0.06

From these two equations

a=-60 KN/m2

b=7667 KN/m2

work transfer involved during the process

W1-2= v1∫v2

pdV=V1∫V2

(a+bV) dV

=a (V2-V1) +b V22-V1

2/2

= (V2-V1)[a+b/2(V1+V2)]



=0.03 m3 [-60 KN/m

2+7667/2 KN/m

2×0.09 m

3]

= 8.55 kj

Work is done by the system, the magnitude being 10.35 kj.

Heat transfer involved is given by

Q1-2=U2-U1+W1-2

=59.5+8.55

=68.05 Kj

68.05 Kj of heat flow in to the system during the process.

First law applied to flow processes:

Introduction:

Any system, the rate of flow of working fluid is constant with respect to time, and

then the system is known as steady flow system.

The mass of working fluid enters the system and leaves the system after doing the

work. Therefore, this system is known as open system.

From first law of thermodynamics, the total energy entering the system is equal to

total energy leaving the system. This law is applicable to the steady state flow

systems.

Energy

It is defined as the capacity of the substance to do work. we can’t see it but can be

felt it.

i) stored energy

This is the energy which is contained within the system boundaries.

Ex: potential energy, kinetic energy, internal energy

Iii) Transit energy

This is the energy which crosses the boundary of a system.

Ex: heat energy, work energy, electrical energy

1. potential energy

It is the energy possessed by a system because of its height.

Potential energy, P.E=m.g.z joules

Where m- mass of the system in kg

g- Acceleration due to gravity in m/s2

z- Height of the system above from datum in m

2. Kinetic energy

It is defined as the energy possessed by the system by virtue of its motion.

Where K.E=mC2/2 joules

C- Velocity of the system (m/s)

3. Flow energy

It is the energy associated with the flow of mass across the boundaries of a

system. The displacing mass must do work on the mass being displaced. This

work is known as flow work.



Flow energy= force×distance moved

=p×A×x

[Pressure=force/area=F/A]

= p×V N-m [A×x= volume, V]

Where V=volume of the fluid flowing (m3/s)

For unit mass, flow energy is given by F.E=pV Nm/sec or J.

4.Total energy

Total energy Is the sum of all energies

Total energy= K.E+P.E+F.E+Internal energy+……..

For steady flow process, the following assumptions are to be made.

1. The rate of mass flow through the control volume is constant.

2. the rate of heat transfer is constant

3. The rate of work transfer is constant.

4. The state of working fluid at any point remains constant.

5. Only potential, kinetic, flow and internal energies are considered. There are no

other forms of energy such as electrical, chemical, magnetic etc.

6. Control volume:

Q=∆E+V

E represents all form of energy stored in the system.

For a pure substance

E=EK+EP+U

EK –kinetic energy

Ep - potential energy

U – Residual energy stored

Steady flow energy equation:

Consider an open system through in which the working substance flows as a

steady rate. The working substance entering the system at 1) and leaves the system

at 2)

SFEE SYSTEM

DATUM LEVEL

INLET 1

OUT LET 2

Z 2

Z1



Let, p1- pressure of the working substance entering the system (N/m2)

V1- specific volume of the working substance entering the system in m3/kg

C1- velocity of the working substance entering the system

u1- specific internal energy of the working substance entering the system in J/kg

z1- height above the datum level for inlet in m

p2,v2,C2,u2 and z2- corresponding values for the working substance leaving the system.

Q- heat supplied to the system in J/kg

W-work delivered by the system in J/kg

Total energy entering the system=P.E+K.E+I.E+F.E+Heat energy

=gz1+C12/2+u1+p1v1+Q

Total energy leaving the system=P.E+K.E+I.E+ F.E+work

=g.z2+C22/2+u2+p2v2+W

By first law of thermodynamics

Total energy entering the system=total energy leaving the system

gz1+C12/2+u1+p1v1+Q= gz2+C2

2/2+u2+p2v2+W

[h=u+pv]

gz1+C12/2+h1+Q= gz2+C2

2/2 +h2+W

the above equation is known as steady flow energy equation.

The above equation represents the energy flow per unit mass of the working substance (j/kg)

When the equation us multiplied by mass of the working substance through out, then all the

terms will represent the energy flow per unit time (J/S)

Then the above equation becomes’

m (gz1+C12/2+h1+Q) =m(gz2+C22/2+h2+W)

If the values of Q and W in kj/kg, and h1 and h2 are substituted in kj then the above equation

becomes.

m (gz1/1000+C12/2000+h1+Q) =m(gz2/1000+C22/2000+h2+W)

If Q and W are already in kW, and h1 and h2 are substituted in kj, then the above equation

becomes,

m (gz1/1000+C12/2000+h1) +Q =m(gz2/1000+C22/2000+h2) +W

The mass rate of the working substance is given by

m=A1C1/v1=A2V2/v2=kg/s

Where A1&A2-area of cross section at entry and exit in m2

Application of steady flow energy equation to various engineering systems:

1. Boiler or steam generator



A boiler is a device which is used to generate high pressure steam by supplying heat

to the water. In this system, heat energy is stored in the steam. Internal energy U

exists and flow energy PV exits due to movement of water. But, there is no work is

done by the system.

Potential energy (gz) and kinetic energy (C2/2) are very small. So we can neglect it.

Therefore z1=z2; C1=C2;W=0

Applying the above conditions in SFEE, we get

Q=h2-h1 kj

2. condenser

Device used to condense a hot steam in to water by using coolant. The main function of

the condenser is to transfer heat from steam to coolant.

In this system, there is no work done, change in kinetic and potential energies (W=0,

z1=z2, C1=C2)

Applying Steady Flow Energy Equation to This System

h1+Q=h2

Q=h2-h1 kj

3. Nozzle

Nozzle is a device which increases the velocity or kinetic energy of the working

substance at the constant pressure drop

In this system,

1) there is no work done by the system (w=0)

2) there is no heat transfer taking place (Q=0)

3) there is no potential energy (z1=z2)

Applying steady flow energy equation to this system, it may be written as

C12/2+h1=C2

2/2+h2

C22/2- C1

2/2=h1-h2

This equation shows that increase in kinetic energy will result decrease in enthalpy

From above equation, it may be written by

C22- C1

2=2(h1-h2)

Final velocity, C2=√2 (h1-h2) +C12 m/s

Since, the initial velocity C1 is very small, we can neglect it. Then, the above

equation becomes.

C2=√2×Cp (T1-T2) +C12 [h=Cp∆T]

C2=√2×Cp× [T1-T1 (p2/p1) γ-1/ γ

] +C12

[For isentropic process T2= (p2/p1) γ-1/ γ

×T1]

Final velocity

C2=√2×Cp×T1 (1-(p2/p1) γ-1/ γ

] +C12 m/s

3. Turbine

Turbine is a device which converts potential energy of working fluid into mechanical

work. The turbine is fully insulated. Therefore, there is no heat transfer



(Q=0)

Steam in 1

Turbine steam out 2

In the turbine, the expansion of working fluid is treated as reversible adiabatic or

isentropic. Change in potential and kinetic energy is negligible. Therefore,z1=z2

and C1=C2.

Applying steady flow energy equation to the above system, it may be written as

h1=h2+W

Work output, W=h1-h2 j/kg

4. Air compressor

Air compressor is a device which is used to compress air at high pressure. The

input for this compressor is atmospheric pressure. It is classified in to types.

i) Rotary compressor

It is one type of compressor which compresses air at high pressure by

using rotors. It supplies large of quantity air at moderate pressure.

In this compressor

i) There is no heat transfer (Q=0)

ii) There is no changes in potential and kinetic energies (z1-z2; C1=C2)

SFEE

h1=h2-W

h2-h1=W j/kg

The work done increases due to increase in enthalpy. A negative sign

shows that work is done on the system

ii) Reciprocating compressor

In this system, potential and kinetic energies are negligible (z1=z2)

And (C1=C2)

SFEE

h1-Q=h2-W ( W is work done on the system)

W=Q+(h2-h1) j/kg

-Q indicates the heat rejection to the surroundings

Formula:

1. SFEE per unit mass

gz1+C12/2+h1+Q=gz2+C2

2/2+h2+W

2) SFEE to boiler, Q=h2-h1

3) SFEE to condenser, Q= h2-h1

4) For nozzle SFEE, C22-C1

2/2=h1-h2

Final velocity, C2= √2 (h1-h2)+C12 m/s



If the initial velocity is neglected

C2=√2 (h1-h2)

5) For turbine, SFEE is

W=h1-h2

6) For rotary compressor, SFEE is

W=h2-h1

7) For reciprocating compressor, SFEE

W=Q+ (h2-h1)

Free Expansion Process

The free expansion, or unresisted expansion, process is an irreversible non-flow adiabatic process in

which the volume of a closed system increases, and still no work at all is done. So, here pd

but work done is zero. Representation of this unresisted expansion process is shown in Fig.

A free expansion occurs when a fluid is allowed to expand suddenly into a vacuum chamber through

an orifice of large dimensions.

Consider two chambers A and B separated by a membrane. The chamber A contains fluid

having volume 1 pressure p1 and temperature T1 and the chamber B is completely

evacuated, pressure i.e,p ext = 0. The fluid is in state 1 in chamber A. Let the membrane gets

ruptured. The fluid then fills both the chambers and reaches state 2. Initial pressure p1 of the

fluid dropped to p2 in the final state and volume 1 reaches to volume ∀ 2 in the final state.

Both the chambers are completely insulated so that heat transfer is zero.

Let us first consider the fluid and vacuum together as the system shown in Fig.2.11(a), so as

no work crosses the system boundary. Next we consider only the fluid as the system as in the

figure. We observe that the system boundary moves and volume of the system change from

1 to 2.But it is not quasi-equilibrium process and pext = 0 . Hence, ∫pext.d is also zero

and therefore, no work is done in the process. Free expansion process is thus an example of

an expansion process in which ∫pd is finite, but still W1-2 = 0. Hence, it is adiabatic process

where Q1-2 = 0 and U1-2 = 0



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