thermi fluid part2

8/16/2019 thermi fluid part2

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1

Chapter 8

Energy, Energy Transfer,

And General Energy Analysis



• Energy can exist in numerous forms such as thermal, mechanical,

kinetic, potential, electric, magnetic, chemical, and nuclear, and theirsum constitutes the total energy, E (kJ) of a system.

• Thermodynamics deals only with the change of the total energy.

•

Two groups of energy: macroscopic and microscopic.

• Macroscopic forms of energy: Those a system possesses as a wholewith respect to some outside reference frame (forms you can see), suchas kinetic and potential energies. t is related to motion and theinfluence of some external effects such as gra!ity, electricity andsurface tension.

• Microscopic forms of energy: Those related to the molecularstructure of a system and the degree of the molecular activity (formsthat are hidden).

• Internal energy, U (kJ): The sum of all the microscopic forms of energy(sensi"le, latent, chemical and nuclear).

FORMS OF EER!"



#

Sensi#le Energy $ nternal

energies associated with kinetic

energies of the molecules.

$atent Energy % internal energy

associated with phase change

%hemical Energy % nternal energy

associated with atomic "onds in a

molecule (chemical "ond aredestroyed during reaction resulted in

the change of the internal energy).

uclear Energy % nternal energy

associated with the strong "ond

within the nucleus of the atomsitself.

The !arious forms of

microscopic

energies that make

up sensible energy.

The internal energy of a

system is the sum of all formsof the microscopic energies.

Internal & Sensi#le ' $atent ' %hemical ' uclear

hermal & Sensi#le ' $atent



• inetic energy, E: The energy that a system possesses as a

result of its motion relati!e to some reference frame.

&inetic energy

&inetic energy

per unit mass

V %denotes the magnitude of the !elocity of the system relati!e to

some fixed reference frame.



kJ*kg+,-.=

==

22

22

/sm1000

kJ/kg1

2

)m/s30(

2ke

V

E/0M1$E

'etermine the specific kinetic energy of a mass whose !elocity is # ms, ink*kg

•1otential energy, 1E2 The energy that a system possesses as a result of its

ele!ation in a gra!itational field.

+otential energy

per unit mass

+otential energy



Energy of a systemper unit mass

Total energy of

a system

Total energy of a system consists of the kinetic, potential, and internal

energies.

kJ*kg+,-3=

==

22

2

/sm1000

kJ/kg1m)50)(m/s8.9( pe gz

E/0M1$E'etermine the specific potential energy, in k*kg, of an o"ect - m a"o!e a

datum in a location where g /.0 ms



2

3ass flow rate

Energy flow rate

3ost %losed System remain stationary during a process and thus

experience no change in their IEI% and 1OEI0$ energies.

Stationary Systems :4losed systems whose !elocity and ele!ation of the

center of gra!ity remain constant during a process.

The change in the total energy 5E of a stationary system is identical to the

change in its internal energy 56.

%ontrol 4olumes (7pen systems) typically in!ol!e fluid flow for long periods of

the time, and it is con!enient to express the energy flow associated with a fluid

stream in the rate form.

Mass flo5 rate, which is the amount of mass flowing through a cross section

per unit time. t related to the 4olume flo5 rate, which is the !olume of a fluid

flowing through a cross section per unit time



Energy can cross the

"oundaries of a closed system

in the form of heat and work.

Temperature difference is the dri!ing

force for heat transfer. The larger the

temperature difference, the higher is the

rate of heat transfer.

EER!" R0SFER 6" 7E07eat2 The form of energy that is

transferred "etween two

systems (or a system and itssurroundings) "y !irtue of a

temperature difference.



/

8eat is energy transition.

Energy is

recogni9ed as

heat transferonly as it

crosses the

system

"oundary.

process during, which there is no heat transfer is called an adia#atic

process. There two ways a process can "e adia"atic which are:

a);ystem is well insulated

");ystem and surroundings are at same temperature

'uring an adia"atic process, a systemexchanges no heat with its surroundings.



mount of heat transfer

when heat transfer rate

changes with time

mount of heat transfer

when heat transfer rate

is constant (5t t $ t1)

s a form of energy, heat has energy units, k*. The amount of heat

transferred during the process "etween two states (states 1 and ) is

denoted "y <1, or ust <.

8eat transfer

per unit mass

=elationship among >, <, and . Q



;ince heat transfer is energy in transition across the system "oundary due to a

temperature difference, there are three modes of heat transfer at the "oundary that

depend on the temperature difference "etween the "oundary surface and the

surroundings. These are conduction, con4ection, and radiation.

%onduction

s the transfer of energy from the more

energetic particles of a su"stance to the

adacent less energetic ones as a result of

interaction "etween particles.

%on4ection

s the transfer of energy "etween solid

surface and the adacent fluid that is in

motion, and in!ol!es the com"ined effects

of conduction and fluid motion.

Radiation

s the transfer of energy due to the

emission of electromagnetic wa!es.



EER!" R0SFER 6" 8OR• f energy crosses "oundary is not heat (due to temperature difference) then

it is work ?k* or @tuA

• 3ore specifically, work is the energy transfer associated with a force acting

through a distance

• 6nits are B.m or *C usually k* in ;.

• Examples include a rising piston, rotating shaft, current carrying wire, etc.

• Rate of doing is work is called power with units of k*s or kD



Energy ransport #y 7eat and 8ork and the %lassical Sign %on4ention

Energy may cross the "oundary of a closed system only "y heat or 5ork.

Energy transfer across a system "oundary due solely to the temperature difference

"etween a system and its surroundings is called heat.

Energy transferred across a system "oundary that can "e thought of as the energy

e9pended to lift a 5eight is called 5ork.

8eat and work are energy transport mechanisms "etween a system and its

surroundings. The similarities "etween heat and work are as follows:

1.@oth are recogni9ed at the "oundaries of a system as they cross the

"oundaries. They are "oth "oundary phenomena.

.;ystems possess energy, "ut no heat or work.

#.@oth are associated with a process, not a state. 6nlike properties, heat or

work has no meaning at a state.

.@oth are path functions (i.e., their magnitudes depends on the path

followed during a process as well as the end states.)



;ince heat and work are path dependent functions, they ha!e ine9act differentials

designated "y the sym"ol δ. The differentials of heat and work are expressed as δ<

and δD. The integral of the differentials of heat and work o!er the process path gi!es

the amount of heat or work transfer that occurred at the system "oundary during a

process.

2

12

1,

2

12

1,

(not Q)

(not )

along path

along path

Q Q

W W W

δ

δ

= ∆

= ∆

∫

∫ That is, the total heat transfer or work is o"tained "y following the process path and

adding the differential amounts of heat (δ<) or work (δD) along the way. The

integrals of δ< and δD are not < $ <1 and D $ D1, respecti!ely, which are

meaningless since "oth heat and work are not properties and systems do notpossess heat or work at a state.



+roperties are point functions

ha!e exact differentials (d ).

8owe!er, heat and work are path functions, that is, their magnitudes depend on the

path followed.

The following figure illustrates that properties (+, T, !, u, etc.) are point functions,

that is, they depend only on the states, and not on ho5 a system reaches that

state), and they ha!e exact differentials designated "y the sym"ol d .



1F

8eat and work are directional quantities, and thus the complete description of a heat

or work interaction re>uires the specification of "oth the magnitude and direction.

ccording to the classical sign con!ention, heat transfer to a system and work done

by a system are positi4eC heat transfer from a system and work done on a system

are negati4e.

The system shown "elow has heat supplied to it and work done "y it.

n this study guide we will use the concept of net

heat and net work.

Dhen the direction of a heat or work interaction is

not known, we can simply assume a direction for

the interaction.

http://4.bp.blogspot.com/_QYwcFosl4t0/SOJ7vkmFMOI/AAAAAAAAAIk/WItYBCuyVZE/s1600-h/hw4-p7.png



Electrical 8ork

The rate of electrical work done "y electrons crossing a system "oundary is called

electrical power and is gi!en "y the product of the !oltage drop in !olts and thecurrent in amps.

(W)eW V I =&

The amount of electrical work done in a time period is found "y integrating the rate of

electrical work o!er the time period.

2

1(kJ)eW V I dt = ∫

Electrical power in terms of resistanceR , current I , and potential difference :.



Mechanical Forms of 8ork

Dork is energy expended "y a force acting through a distance. Thermodynamic work

is defined as energy in transition across the system "oundary and is done "y a

system if the sole effect external to the "oundaries could ha!e "een the raising of aweight.

The work done "y a constant force G on a "ody displaced a distance s in the

direction of the force is gi!en "y

f the force G is not constant, the work done is o"tained "y adding (i.e., integrating)the differential amount of work( it is function of distance, s)

Dork Gorce × 'istance

Dhen force is not constant



There are two re>uirements for a work interaction "etween a system and its

surrounding to exist:

•There must "e a force acting on the "oundary

•The "oundary must mo!e

%ommon ypes of Mechanical 8ork Energy

•;haft Dork•;pring Dork•Dork done of Elastic ;olid @ars•Dork ssociated with the ;tretching of a Hi>uid Gilm•Dork 'one to =aise or to ccelerate a @ody



Energy transmission through rotating shafts

is commonly encountered in practice.

;haft work is proportional to the

tor>ue applied and the num"er

of re!olutions of the shaft.

The power transmitted through the shaft

is the shaft work done per unit time

;haft

work

This force acts through a distance s

force F acting through

a moment arm r

generates a tor>ue T

Shaft

Work



E/0M1$E'etermine the power transmitted through the shaft of a car when the

tor>ue applied is B.m and the shaft rotates at a rate of

re!olutions per minute (rpm)

Solution

( ) ( ) kW m N

kJ

sm N T nW sh 8.83.1000

1

60

min1

.200min

1

400022 =

== π π



Spring Work

Elongation

of a spring

under the

influence of

a force.

k: spring constant (kBm)

;u"stituting and integrating yield

x 1 and x : the initial and the final

displacements

The

displacement

of a linear

spring dou"les

when the force

is dou"led.

Dhen the length of the spring changes "y

a differential amount dx under the influence

of a force F , the work done is

Gor linear elastic springs, the displacement

x is proportional to the force applied



E/0M1$E8ow much work, in k*, can a spring whose spring constant is # kBcm

produce after it has "een compresses # cm from its unloaded lengthI

Solution

[ ]

kJ+,;<.=

⋅⋅=

⋅=

−=

−==== ∫ ∫ ∫

mkN1

kJ1m)kN135.0(

mkN0.135

0)m03.0(2

kN/m300

)(2

22

2

1

2

2

2

1

2

1

2

1

x xk

xdxk kxdx FdsW F

x



he First $a5 of hermodynamicsThe first law of thermodynamics is known as the conser4ation of energy principle.

t states that energy can #e neither

created nor destroyed=only change

forms

*ouleJs experiments lead to the conclusion: For all adiabatic processes between two

specified states of a closed system, the net work done is the same regardless of the

nature of the closed system and the details of the process.

maor conse>uence of the first la5 is the existence and definition of the property

total energy .

Energy

cannot "e

created or

destroyedC

it can only

change

forms.

The increase in the energy of a



-

n the a"sence of any work

interactions, the energy

change of a system is e>ualto the net heat transfer.

The work

(electrical) done

on an adia"atic

system is e>ual

to the increase

in the energy ofthe system.

The work (shaft)done on an

adia"atic system

is e>ual to the

increase in the

energy of the

system.

The increase in the energy of a

potato in an o!en is e>ual to the

amount of heat transferred to it.



F

The first law of thermodynamics is an expression of the conser4ation of energy

principle.

Energy can cross the "oundaries of a closed system in the form of heat or 5ork.

Energy may cross a system #oundary (control surface) of an open system "y heat,

5ork and mass transfer .

system mo!ing relati!e to a reference plane is shown "elow where 9 is the ele!ation

of the center of mass a"o!e the reference plane and is the !elocity of the center ofmass.

he First $a5 and the %onser4ation of Energy

The work ("oundary) done on an adia"atic system ise>ual to the increase in the energy of the system.

The energy change

of a system during

a process is e>ual

to the net work and

heat transfer

"etween the system

and its

surroundings.

V



Energy i

n Energyout!

System

=eference +lane, !

43 V

Gor the system shown a"o!e, the conser4ation of energy principle or the first la5of thermodynamics is expressed as

=

−

systemtheo ene!gy

in tot"#$h"ngenet%he

systemthe#e"&ing

ene!gy

systemtheente!ing

ene!gy Total Total

or

E E E in out system− = ∆This relation is often referred to as the energy #alance and applica"le to any kind of

system undergoing any kind of process.



∆ ∆ ∆ ∆ E U KE PE = + +

Energy %hange of a System, >Esystem

'etermination of the energy of a system during a process in!ol!es the e!aluation of

the energy of the system at the #eginning and at the end of the process, and taking

their difference.

Bote that energy is a property, and the !alue of property does not change unless

the state of the system changes.

Bormally the stored energy, or total energy, of a system is expressed as the

sum of three separate energies. The total energy of the system, E system

, is gi!en as



/

=ecall that U is the sum of the energy contained 5ithin the molecules of the

system (sensi"le, latent, chemical and nuclear) other than the kinetic and potential

energies of the system as a whole and is called the internal energy.

The internal energy " is dependent on the state of the system and the mass of the

system.

f the system does not move with a velocity and has no change in elevation, it iscalled a stationary system, and the conser!ation of energy e>uation reduces to

in out E E U − = ∆

Bow the conser4ation of energy principle, or the first la5 of thermodynamics forclosed systems, is written as

in out E E U KE PE − = ∆ + ∆ + ∆

Mechanisms of Energy ransfer E and E



#

Mechanisms of Energy ransfer, Ein and Eout

The mechanisms of energy transfer at a system "oundary are: 8eat, Dork, mass flow.

8eat and work energy transfers across at the "oundary of a closed (fixed mass) system.

7pen systems or control !olumes ha!e energy transfer across the control surfaces "y

mass flow as well as heat and work.

; 7eat ransfer, ?2 8eat is energy transfer caused "y a temperature difference

"etween the system and its surroundings. Dhen added to a system heat transfer

causes the energy of a system to increase and heat transfer from a system

causes the energy to decrease. < is 9ero for adia"atic systems.

@ 8ork, 82 Dork is energy transfer at a system "oundary could ha!e caused a

weight to "e raised. Dhen added to a system, the energy of the system increaseC

and when done "y a system, the energy of the system decreases. D is 9ero forsystems ha!ing no work interactions at its "oundaries.

< Mass flo5, m2 s mass flows into a system, the energy of the system increases

"y the amount of energy carried with the mass into the system. 3ass lea!ing the

system carries energy with it, and the energy of the system decreases. ;ince no

mass transfer occurs at the "oundary of a closed system, energy transfer "y massis 9ero for closed systems.



The energy "alance for a general system is

( ) ( )

( ), ,

in out in out in out

mass in mass out system

E E Q Q W W

E E E

− = − + −

+ − = ∆

where the su"script KinL and KoutL denote >uantities that enter and lea!e the

system, respecti!ely. ll six >uantities on the right side of the e>uation represent

KamountL, and thus they are positi!e >uantities. The direction of any energy

transfer is descri"ed "y the su"script KinL and KoutL.



Expressed more compactly, the energy "alance is

Net ene!gy t!"nse! 'h"nge in inte!n"#, kineti$, y he"t, o!k, "n* m"ss potenti"#, et$., ene!gies

( )in out system E E E kJ − = ∆1 4 2 43 14 2 43

or on a rate form, as

E E E kW in out system− =+"te o net ene!gy t!"nse! y he"t, o!k, "n* m"ss

+"te $h"nge in inte!n"#, kineti$, potenti"#, et$., ene!gies

( )

∆

Gor constant rates, the total >uantities during the time inter!al ∆t are related to the>uantities per unit time as

, , "n* ( )Q Q t W W t E E t kJ = ∆ = ∆ ∆ = ∆ ∆& & &

The energy "alance may "e expressed on a per unit mass "asis as

( / )in out systeme e e kJ kg − = ∆

and in the differential forms as

( )

( / )

in out system

in out system

E E E kJ

e e e kJ kg

δ δ δ

δ δ δ

− =

− =



E/0M1$E rigid tank contains a hot fluid that is cooled while "eing stirred "y a paddle wheel.

nitially, the internal energy of the fluid is 0 k*. 'uring the cooling process, the fluid

loses - k* of heat, and the paddle wheel does 1 k* of work on the fluid.

'etermine the final internal energy of the fluid. Beglect the energy stored in thepaddle wheel

;ystem sketch:



( )( ) ( )

kJ U

kJ U kJ kJ

U U U QW

U W W QQ

U W QW Q

E E E

out in sh

out inout in

out out inin

systemout in

400

800500100

)(

2

2

12,

=−=−

−=∆=−∆=−+−∆=+−+

∆=−



#-

E/0M1$E1ositi4e and egati4e 8ork

n part a of figure, the system gains 1-* of heat

and * of work is done "y the system on its

surroundings.

n part b, the system also gains 1-* of heat, "ut

* of work is done on the system.

n each case, determine the change in internal energy

of the system.

(a)

(")

W QU +=∆

W QU +=∆

( ) ( )J2200J1500 −++=∆U J00−=

( ) ( )J2200J1500 +++=∆U J300+=



#F

# total of $%& ' of work is done on a gaseous refrigerant

as it undergoes compression( If the internal energy of the

gas increases by $$) ' during the process, what is thetotal amount of energy transferred as heat* +as energy

been added to or removed from the refrigerant as heat*

E/0M1$E

< M D 56

< M 1#- * 11 *

< $1 *

he sign for the value of - is negative( his indicates that energy is

transferred as heat from the refrigerant (



E/0M1$E ir flows into an open system and carries energy at the rate of # kD. s the air

flows through the system it recei!es F kD of work and loses 1 kD of energy "y

heat transfer to the surroundings. f the system experiences no energy change as the

air flows through it, how much energy does the air carry as it lea!es the system, inkDI

;ystem sketch:

7pen;ystem

%onser4ation of Energy:

( )

, ,

, ,

,

0

300 600 100 800

in out system

mass in in mass out out system

mass out mass in in out

mass out

E E E

E W E Q E

E E W Q

E kW kW

− = ∆+ − − = ∆ =

= + −

= + − =

& & &

&& & & &

&& & &

&

,mass in E &

inW &

out Q&

,mass out E &

First $a5 for a %ycle



thermodynamic cycle is composed of processes that cause the working fluid to

undergo a series of state changes through a process or a series of processes.

These processes occur such that the final and initial states are identical and thechange in internal energy (5Ecycle) of the working fluid is zero for whole num"ers of

cycles.

;ince thermodynamic cycles can "e !iewed as ha!ing heat and work (#ut not mass)

crossing the cycle system "oundary, the first law for a closed system operating in a

thermodynamic cycle "ecomes

net net yle

net net

Q W E

Q W

− = ∆

=

First $a5 for a %ycle



E/0M1$E steam power plant operates on a thermodynamic cycle in which water circulates

through a "oiler, tur"ine, condenser, pump, and "ack to the "oiler. Gor each

kilogram of steam (water) flowing through the cycle, the cycle recei!es k* of

heat in the "oiler, reects 1- k* of heat to the en!ironment in the condenser, andrecei!es - k* of work in the cycle pump. 'etermine the work done "y the steam in

the tur"ine, in k*kg.

The first law re>uires for a thermodynamic cycle

( )

-et "n*

2000 1500 5

505

net net yle

net net

in out out in

out in out in

out in out in

out

Q W E

Q W

Q Q W W

W Q Q W

W Q! "

m m! " " !

kJ !

kg

kJ

− = ∆

=− = −

= − −

= =

= − +

= − +

thermi fluid part2

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