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1 Document Name Your Company Name (C) Copyright (Print Date) All Rights Reserved ن مراجع تخصصی برتری برازش و فناورین حوزه آمویان و فعا ی دانشجو کلبه دانش کتاب و جسوهونه نو سوالم افسار نر پروشه وقاله ه فیلن آهوزشی[email protected]

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Page 1: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

1

Document Name

Your Company Name (C) Copyright (Print Date) All Rights Reserved

ی دانشجویان و فعاالن حوزه آموزش و فناوریبرابرترین مراجع تخصصی

کلبه

دانش

کتاب و

جسوه

نوونه

سوال

نرم افسارپروشه و

هقاله

فیلن

آهوزشی

[email protected]

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Center of Excellence in Energy Conversion (CEEC)

Sharif University of Technology, Tehran, Iran

Winter 2006

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=

→=

���4 P��=�2 �lS ,K2< ����<���/ ���/$ R�C+�`� P�< 1��+ n!�

D���� ��H:oo pv CوC��J D � ���j� �� �I .

)�~��(

−=

−=

=−

=

1

1

k

kRC

k

RC

RCC

C

Ck

ooo P

vo

vP

vo

Po

)�~�*( 0=+=+= PdvdTCPdvduTds vo

)�~��( )(

1vdPpdv

RdT +=

)�~*�( 0)( =++ PdvvdPPdvR

Cvo

)�~*(( 0)(

1

1=++

−PdvvdPPdv

k

)�~*�( 00 =+→=+v

dvk

P

dPkPdvvdP

)�~*)(

1

2

1

1

1

2

1

2

2

1

1

2

)()(

)(

==

=

=

=

kk

k

k

k

P

P

T

T

v

v

P

P

mRTPv

constPv

υ

υ

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Page 69: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

gz

! ���4 =�2 P�< ����<���/ ���/$ �� ��4 BC+�`�vopo cc ,,<�G )�~*+(

k

vPvPTT

k

mRw

TTmCuumW

WuumQ

v

−=−

−=

−−=−−=

+−=

−−

1)(

1

)()(

)(

11221221

121221

211221

0

�I�' %� � �U3�� �I'�# ��# d) ∫=− Pdvw 21(!�'� :

)�~*�( k

vPvPwconstPv

k

−=⇒= −

1

112221

�S ���/$ ��S!�),K2< �lS(���4 =�2 P�<

�'D E f99. '� . � P-v��5�H ��`��� ��` ��M

)�~*�( constPvn =

)�~*�( n

v

v

P

P)()(

2

1

1

2 =

)�~**( 1

2

1

1

2

1

2 )()( −

== nn

ln

v

v

P

P

T

T

)�~*�( 1,

1

)(

1

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2

1

21 ≠−

−=

−−== ∫− n

n

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n

vPvPPdvw

���4 =�2 P����� �lS ,K2< ���/$

e4� :�# d��m�'��5�H )�~��( 2211 vPvPCP =⇒=υ

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1 2

1

1

2

2

11121 lnlnln

P

PmRT

v

vmRT

P

PvPPdvw

P=cte

Isobaric

Pv1=cte

Isothermal

Pvk=cte

Isentropic

Pvn=cte, n= ∞

Isochoric

P

v

Pvn=cte,

Polytropic

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Page 70: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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� :i'��$ F�Y3�� <��m�: )�~��( dTCdu v=

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)�~�+( PdvduTds +=

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1

PdvTds

)�~��( ∫ ∫ ===−

2

1 1

2

2

1

1121 lnv

vvPPdvTdsq

��������� �!� ���� (����T�< )�4 (HI

�'D E f9e. dbm4 ' �4�3�# !V$ t

<bm4 ' !30�� T�&t =+ mitm δ <bm4 ' !30�� D`��3��t=+ iit msS δ

�gD E f9E. dbm4 ' �4�3�# !V$t+δt

<bm4 ' !30�� T�&tt δ+ =++ etm mm δδ <bm4 ' !30�� D`��3��tt δ+=++ eett msS δδ

mt= t mN`5 �� ?5)�A (HI �>

st= t mN`5 �� ()*�+ ?S!)�/

Pi

Ti

vi

ei

si

T, δQ, dA

mt+δt= t+δtmN`5 �� ?5)�A (HI �>

st+δt= t+δtmN`5 �� ()*�+ ?S!)�/

Pe

Te

ve

ee

se

T, δQ, dA

δme

∆wcv

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)�~��( ∑∑∑ ≥−+cv

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cv

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dt

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iit

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msSS

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VC

T

Qsmsm

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..∑≥−VC

VC

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∑ ∑ ∫+

=−+− dtT

WLQsmsmsmsm

t

o

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..1122

&&&&

P�< S!)�� Z��3$� ��� )�4 (HI

�'D E f9�. N�m� � !30�� R�I �`��3�5 � ���� F ��

)�~(�+(

∑ ∑ ∑≥−+ )( ....

T

Qsmsm

dt

ds VC

iiee

VC&

&&

N�m�

dtم1�2

dS

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∑ eesm&

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QC.V.

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Page 72: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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o

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TT

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T

Q

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surrVCNet

o

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o

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o

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≥+=

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<

>

>

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..

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......

0 &&

&&

k�@ ;�M K4�$

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dt

dS VC P` o

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dSNet K=� <=I �'

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vhzg

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ii +++=+++

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22

( )T

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ie

..&

& ≥−

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ei ss =

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i

ei vdPhhvdPdhvdPdhTds

( )ei

ei

ei zzgVV

hhw −+−

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( )eiei

e

izzg

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−+−= ∫ 2

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J (�!3�� ���/$�lS ,K2< ! ��

)�~((�( ( ) qm

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ie ==−&

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Page 73: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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Page 75: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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Page 76: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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Tg

Tg

TTTTTTQ

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TTQ

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===⇒=⇒⇒

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=

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=

ε

εεε

ε

ε

ε

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Page 77: کلبه دانشdl.kolbedanesh.com/kolbe/97/3/jalal/Thermodynamic-[… · ,, DW =3I K =4˘$

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1

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2

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4321

ln

ln.ln

ln0

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VV

VV

T

T

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QQ

V

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QV

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PdVdTCQ

TTTT

L

HL

H

V

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+=

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V

VR

T

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RTdVdTCPdVdTCQ

VV

VV

−=⇒−=

⇒+=⇒+=⇒ δ

��5�H4-1

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zg

)�~(�+(

L

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L

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V

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T

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Q

Q

V

V

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43

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zz

89�: ;$���� <�: =>��

1. R.E. Sonntag, C. Borgnakke and G.J. Van Wylen, Fundamentals

of Thermodynamics, John Wiley & Sons, New York, 1997

2. M.W. Zemansky and R. H. Dittman, Heat and Thermodynamics,

McGraw-Hill, 1997

3. Y.A. Cengel and M.A. Boles, Thermodynamics: An Engineering

Approach, McGraw-Hill, New York, 2002

4. J.S. Hsieh, Engineering Thermodynamics, Prentice Hall, 1993

5. A. Bejan, Advanced Engineering Thermodynamics, John Wiley

& Sons, New York, 1988

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