Thermodynamics Solution Manual(references) PDF

Preview

Summary

Preface This manual contains more or less complete solutions for every problem in the book. Should you find errors in any of the solutions, please bring them to my attention. Over the years, I have tried to enrich my lectures by including historical information on the significant developments in the...

Description

Preface This manual contains more or less complete solutions for every problem in the book. Should you find errors in any of the solutions, please bring them to my attention. Over the years, I have tried to enrich my lectures by including historical information on the significant developments in thermodynamics, and biographical sketches of the people involved. The multivolume Dictionary of Scientific Biography, edited by Charles C. Gillispie and published by C. Scribners, New York, has been especially useful for obtaining biographical and, to some extent, historical information. [For example, the entry on Anders Celsius points out that he chose the zero of his temperature scale to be the boiling point of water, and 100 to be the freezing point. Also, the intense rivalry between the English and German scientific communities for credit for developing thermodynamics is discussed in the biographies of J.R. Mayer, J. P. Joule, R. Clausius (who introduced the word entropy) and others.] Other sources of biographical information include various encyclopedias, Asimov’s Biographical Encyclopedia of Science and Technology by I. Asimov, published by Doubleday & Co., (N.Y., 1972), and, to a lesser extent, Nobel Prize Winners in Physics 1901-1951, by N.H. deV. Heathcote, published by H. Schuman, N.Y. Historical information is usually best gotten from reading the original literature. Many of the important papers have been reproduced, with some commentary, in a series of books entitled “Benchmark Papers on Energy” distributed by Halsted Press, a division of John Wiley and Sons, N.Y. Of particular interest are: Volume 1, Energy: Historical Development of the Concept, by R. Bruce Lindsay. Volume 2, Applications of Energy, 19th Century, by R. Bruce Lindsay. Volume 5, The Second Law of Thermodynamics, by J. Kestin and Volume 6, Irreversible Processes, also by J. Kestin. The first volume was published in 1975, the remainder in 1976.

v

vi Other useful sources of historical information are “The Early Development of the Concepts of Temperature and Heat: The Rise and Decline of the Caloric Theory” by D. Roller in Volume 1 of Harvard Case Histories in Experimental Science edited by J.B. Conant and published by Harvard University Press in 1957; articles in Physics Today, such as “A Sketch for a History of Early Thermodynamics” by E. Mendoza (February, 1961, p.32), “Carnot’s Contribution to Thermodynamics” by M.J. Klein (August, 1974, p. 23); articles in Scientific American; and various books on the history of science. Of special interest is the book The Second Law by P.W. Atkins published by Scientific American Books, W.H. Freeman and Company (New York, 1984) which contains a very extensive discussion of the entropy, the second law of thermodynamics, chaos and symmetry. I also use several simple classroom demonstrations in my thermodynamics courses. For example, we have used a simple constant-volume ideal gas thermometer, and an instrumented vapor compression refrigeration cycle (heat pump or air conditioner) that can brought into the classroom. To demonstrate the pressure dependence of the melting point of ice, I do a simple regelation experiment using a cylinder of ice (produced by freezing water in a test tube), and a 0.005 inch diameter wire, both ends of which are tied to the same 500 gram weight. (The wire, when placed across the supported cylinder of ice, will cut through it in about 5 minutes, though by refreezing or regelation, the ice cylinder remains intact.—This experiment also provides an opportunity to discuss the movement of glaciers.) Scientific toys, such as “Love Meters” and drinking “Happy Birds”, available at novelty shops, have been used to illustrate how one can make practical use of the temperature dependence of the vapor pressure. I also use some professionally prepared teaching aids, such as the three-dimensional phase diagrams for carbon dioxide and water, that are available from laboratory equipment distributors. Despite these diversions, the courses I teach are quite problem oriented. My objective has been to provide a clear exposition of the principles of thermodynamics, and then to reinforce these fundamentals by requiring the student to consider a great diversity of the applications. My approach to teaching thermodynamics is, perhaps, similar to the view of John Tyndall expressed in the quotation “It is thus that I should like to teach you all things; showing you the way to profitable exertion, but leaving the exertion to you—more anxious to bring out your manliness in the presence of difficulty than to make your way smooth by toning the difficulties down.” Which appeared in The Forms of Water, published by D. Appleton (New York, 1872).

Solutions to Chemical and Engineering Thermodynamics, 3e

vii

Finally, I usually conclude a course in thermodynamics with the following quotation by Albert Einstein: “A theory is more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability. Therefore, the deep impression classical thermodynamics made upon me. It is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never by overthrown.”

1 



D 7KHUPRVWDWLFEDWKLPSRVHVLWVWHPSHUDWXUH7RQWKHV\VWHP E &RQWDLQHULPSRVHVFRQVWUDLQWRIFRQVWDQWYROXPH 7KHUPDO LVRODWLRQ LPSOLHV WKDWKHDWIORZPXVWEH]HURZKLOHPHFKDQLFDOLVRODWLRQDQGFRQVWDQWYROXPH LPSOLHV WKHUH LV QR ZRUN IORZ  &RQVHTXHQWO\ WKHUH LV QR PHFKDQLVP IRU DGGLQJRUUHPRYLQJHQHUJ\IURPWKHV\VWHP7KXVV\VWHPYROXPHDQGHQHUJ\ DUHFRQVWDQW F 7KHUPDOO\LVRODWHGŸDGLDEDWLF )ULFWLRQOHVVSLVWRQŸSUHVVXUHRIV\VWHPHTXDOVDPELHQWSUHVVXUHRUDPELHQW SUHVVXUH  ZJ$ LI SLVWRQF\OLQGHU LQ YHUWLFDO SRVLWLRQ  +HUH w = weight of piston,  $ LWVDUHDDQGJLVWKHIRUFHRIJUDYLW\ G 7KHUPRVWDWLFEDWKŸFRQVWDQWWHPSHUDWXUH7 )ULFWLRQOHVVSLVWRQŸFRQVWDQWSUHVVXUHVHHSDUWFDERYH  H 6LQFH SUHVVXUH GLIIHUHQFH LQGXFHV D PDVV IORZ SUHVVXUH HTXLOLEUDWHV UDSLGO\ 7HPSHUDWXUHHTXLOLEUDWLRQZKLFKLVDUHVXOWRIKHDWFRQGXFWLRQRFFXUVPXFK PRUH VORZO\  7KHUHIRUH LI YDOYH EHWZHHQ WDQNV LV RSHQHG IRU RQO\ D VKRUW WLPHDQGWKHQVKXWWKHSUHVVXUHLQWKHWZRWDQNVZLOOEHWKHVDPHEXWQRWWKH WHPSHUDWXUHV D :DWHULVLQDSSURSULDWHDVDWKHUPRPHWULFIOXLGEHWZHHQq&DQGq&VLQFH WKH YROXPH LV QRW D XQLTXH IXQFWLRQ RI WHPSHUDWXUH LQ WKLV UDQJH LH WZR WHPSHUDWXUHVZLOOFRUUHVSRQGWRWKHVDPHVSHFLILFYROXPH 9 7 q & ~ 9 7 q &  9 7 q & ~ 9 7 q &  HWF 





9+2





  

 7

 

7LQ R &DQG9LQFF  J &RQVHTXHQWO\ ZKLOH 7 XQLTXHO\ GHWHUPLQHV 9  9  GRHV QRW XQLTXHO\ GHWHUPLQH7 E $VVXPLQJ WKDW D PHUFXU\ WKHUPRPHWHU LV FDOLEUDWHG DW q& DQG q& DQG WKDW WKH VSHFLILF YROXPH RI PHUFXU\ YDULHV OLQHDUO\ EHWZHHQ WKHVH WZR WHPSHUDWXUHV\LHOGV

Chapter 1

R &  9 7

 2 7 9 27

7 2

9 7 9 R & 

R

R &

7 27   &7 V

R

 &   &   7V

R



ZKHUH 7 LV WKH DFWXDO WHPSHUDWXUH DQG 7V  LV WKH WHPSHUDWXUH UHDG RQ WKH WKHUPRPHWHU VFDOH  $W q& 9 7 q &  FF J   +RZHYHU H[S

WKHVFDOHWHPSHUDWXUHIRUWKLVVSHFLILFYROXPHLVIURPHTQ DERYH

7V

9H[S 7     u 

     u 



q &

7KXV 7  7V  DW q& q &   5HSHDWLQJ FDOFXODWLRQ DW RWKHU WHPSHUDWXUHV\LHOGVILJXUHEHORZ 

'7 L







  





7



L

7KH WHPSHUDWXUH HUURU SORWWHG KHUH UHVXOWV IURP WKH QRQOLQHDU GHSHQGHQFH RI WKHYROXPHRIPHUFXU\RQWHPSHUDWXUH,QDUHDOWKHUPRPHWHUWKHUHZLOODOVR EHDQHUURUDVVRFLDWHGZLWKWKHLPSHUIHFWERUHRIWKHFDSLOODU\WXEH F

:KHQZHXVHDIOXLGILOOHGWKHUPRPHWHUWRPHDVXUH '7 ZHUHDOO\PHDVXUH '/  ZKHUH 0 w9 w7 '7

2

'9 $

'/

7

$

$VPDOODUHD$DQGDODUJHPDVVRIIOXLG0PDJQLILHV '/ REWDLQHGIRUDJLYHQ '7   7KXV ZH XVH D FDSLOODU\ WXEH VPDOO $  DQG EXOE ODUJH 0  WR JHW DQ DFFXUDWHWKHUPRPHWHUVLQFH w9 w7 LVVRVPDOO

2

7

 

D %\ DQ HQHUJ\ EDODQFH WKH ELF\FOH VWRSV ZKHQ ILQDO SRWHQWLDO HQHUJ\ HTXDOV LQLWLDONLQHWLFHQHUJ\7KHUHIRUH

  NP u  P u KU   KU NP VHF 



  PY 

PJK RUK

L

I

Y J L

I

 u 



P VHF

RUK P E 7KHHQHUJ\EDODQFHQRZLV     PY PY  PJK RUY  Y    JK    NP  P NP  VHF    u  u P u u  Y   KU KU P VHF Y  NPKU$Q\RQHZKRKDVELF\FOHGUHDOL]HVWKDWWKLVQXPEHULVPXFK I

I

L

 

 

L

I

L

L

 

 

I

WRRKLJKZKLFKGHPRQVWUDWHVWKHLPSRUWDQFHRIDLUDQGZLQGUHVLVWDQFH 

7KHYHORFLW\FKDQJHGXHWRWKHPIDOOLV P NP  VHF  u u u P  KU P VHF Y  NPKU1RZWKLVYHORFLW\FRPSRQHQWLVLQWKHYHUWLFDOGLUHFWLRQ7KH LQLWLDOYHORFLW\RINPKUZDVREYLRXVO\LQ WKH KRUL]RQWDO GLUHFWLRQ 6R WKH ILQDO YHORFLW\LV NP Y Y   Y    KU 

2'Y 7

 

 u 

 

I

[



\

D 6\VWHPFRQWHQWVRIWKHSLVWRQDQGF\OLQGHU FORVHGLVREDULF FRQVWDQWSUHVVXUH 0% 0  0 '0  Ÿ 0 0 0 0 0 (% 08   08 'M H 4  W s  3G9

I

3 8

7 4  I 3G9 4  3I G9 4  309  9 5  8 7 4  30 29  9 7 0 28  8 7  0 2 39  39 7 0 28  39 7  28  39 7 0 2 +  + 7

2 0 28

0 8   8

4

































Solutions to Chemical and Engineering Thermodynamics, 3e

3

Chapter 2

  EDU |   03D 9  

7  7  /LQHDULQWHUSRODWLRQ  7 q & )LQDOVWDWH 3   03D  9  7 q &  7 q & /LQHDULQWHUSRODWLRQ

8  

+  

    PNJ  

,QLWLDOVWDWH

  7      7 q &        +        +          4 NJ   N- NJ   N:

I

 3G9

0

EDU u 9  9

EDU u 

5

 P NJ EDU u     

3D NJ u u   u    P NJ  EDU P ˜ V ˜ 3D P ˜ V ˜ NJ

  N- NJ E 6\VWHPLVFORVHGDQGFRQVWDQWYROXPH 0% 0 0 0

3 80

(% 08   08 4

2

0 8   8

'M H

4  W s

0

I

0

– PdV

7

+HUH ILQDO VWDWH LV 3  u   EDU a  03D  9 VLQFHSLVWRQF\OLQGHUYROXPHLVIL[HG 3  03D  9   7q & 9 8               

7        7 q &

   P NJ

9

  a  

 8     8    N- NJ       4 NJ u     N- NJ N F 6WHDPDVDQLGHDOJDV¥FRQVWDQWSUHVVXUH 1

39 39 Ÿ   57 57

39  EXW9  57

9   3

3

Solutions to Chemical and Engineering Thermodynamics, 3e

39 7 

3 9 Ÿ7 7 



u7









      .  u 7 .   q&

7 7





4



Chapter 2



N J NJ u   - PRO. u     . u  J PRO

1' +  N-

I

 3'9

 3G9

:



3

 157  157   3 3  

0



 15 7  7 



5



 u  u   

  N-

G ,GHDOJDVFRQVWDQWYROXPH 39 57 

39 KHUH9 57 



 3 ˜9  7 7

39 7 

6RDJDLQ





4









9  3





3









7



. 



1'8

 J NJ  u    u     u  J PRO  &  5  4

&

9

3

N-

 0 8 Z

0Z

Z I

 0 8 Z

0 ZHLJKW

0

NJ u &3 7I  7L



V

0 ZHLJKW u J u P

NJ

5

NJ u  P V u P u

  - J. u NJ u  '7

:

Z L

J u '7 NJ

 . u   

P NJ V 

 -



 u  .

0

5 0

5

)URP,OOXVWUDWLRQZH KDYH WKDW + 7 3 + 7  3  IRU D -RXOH7KRPVRQ H[SDQVLRQ2QWKH0ROOLHUGLDJUDPIRUVWHDP)LJDWKHXSVWUHDPDQG GRZQVWUHDPFRQGLWLRQVDUHFRQQHFWHGE\DKRUL]RQWDOOLQH7KXVJUDSKLFDOO\ ZHILQGWKDW 7 a . $OWHUQDWLYHO\RQHFRXOGDOVRXVHWKH6WHDP7DEOHV RI$SSHQGL[,,,

Solutions to Chemical and Engineering Thermodynamics, 3e

Chapter 2

)RU WKH LGHDO JDV HQWKDOS\ LV D IXQFWLRQ RI WHPSHUDWXUH RQO\  7KXV + 7 3 + 7  3  EHFRPHV + 7 + 7  ZKLFK LPSOLHV WKDW

0

7 

5 0

7

05 0 5

5

q & 

6\VWHP&RQWHQWVRI'UXPRSHQV\VWHP PDVVEDODQFH 0   0  '0 W

W

HQHUJ\EDODQFH '0+ LQ  4  :V  3G9 08  08 W

EXW 4 DQG 9 7

I

I

W

 E\SUREOHPVWDWHPHQW :V

VWHDP



3'9  LV QHJOLJLEOH  1RWH 9 7

3G9

 q &  u   P NJ 

 q &  u   P NJ $OVRIURPWKH6WHDP7DEOHV + LQ

+ 7

q & 3

EDU 

N3D

 N- NJ

DQG UHFRJQL]LQJ WKDW WKH LQWHUQDO HQHUJ\ RI D OLTXLG GRHV QRW GHSHQG RQ SUHVVXUH JLYHV 8

W

8 7

q & EDU 8 VDW 7

q &  N- NJ

8 7

q & EDU 8 VDW 7

q &

DQG 8

W

1RZXVLQJPDVVEDODQFHDQGHQHUJ\EDODQFHVZLWK 0

W

 N- NJ

NJ \LHOGV

Solutions to Chemical and Engineering Thermodynamics, 3e

0

W

u N-   u N-

0

W

Chapter 2

  u N-

7KXV 0      u    W

0 

W

NJ DQG '0

0

W

0

NJ RIVWHDPDGGHG

W

D &RQVLGHUDFKDQJHIURPDJLYHQVWDWHWRDJLYHQVWDWHLQDFORVHGV\VWHP 6LQFHLQLWLDODQGILQDOVWDWHVDUHIL[HG 8  8   9  9  3  3  HWF DUH DOO IL[HG7KHHQHUJ\EDODQFHIRUWKHFORVHGV\VWHPLV

I

8   8 ZKHUH :

I

:V  3G9

DGLDEDWLF7KXV 8   8

4  :V  3G9

WRWDOZRUN$OVR 4

4 :  VLQFHWKHFKDQJHRIVWDWHLV

:

6LQFH 8 DQG 8  DUHIL[HGWKDWLVWKHHQGVWDWHVDUHIL[HGUHJDUGOHVVRIWKH SDWK  LW IROORZV WKDW : LV WKH VDPH IRU DOO DGLDEDWLF SDWKV  7KLV LV QRW LQ FRQWUDGLFWLRQZLWK,OOXVWUDWLRQZKLFKHVWDEOLVKHGWKDWWKHVXP 4  : LV WKH VDPH IRU DOO SDWKV  ,I ZH FRQVLGHU RQO\ WKH VXEVHW RI SDWKV IRU ZKLFK 4  LWIROORZVIURPWKDWLOOXVWUDWLRQWKDW:PXVWEHSDWKLQGHSHQGHQW E &RQVLGHU WZR GLIIHUHQW DGLDEDWLF SDWKV EHWZHHQ WKH JLYHQ LQLWLDO DQG ILQDO VWDWHVDQGOHW : DQG :

EHWKHZRUNREWDLQHGDORQJHDFKRIWKHVHSDWKV LH Path 1: 8   8 : ; Path 2: 8   8 :

1RZ VXSSRVH D F\FOH LV FRQVWUXFWHG LQ ZKLFK SDWK  LV IROORZHG IURP WKH LQLWLDO WR WKH ILQDO VWDWH DQG SDWK  LQ UHYHUVH IURP WKH ILQDO VWDWH VWDWH  EDFNWRVWDWH7KHHQHUJ\EDODQFHIRUWKLVF\FOHLV

0

8   8

 8   8

5

: :

 :  :

7KXV LI WKH ZRUN DORQJ WKH WZR SDWKV LV GLIIHUHQW LH : z :

 ZH KDYH FUHDWHGHQHUJ\



6\VWHP FRQWHQWVRIWDQNDWDQ\WLPH PDVVEDODQFH 0  0 '0 '0+ HQHUJ\EDODQFH 08  08

2 7 2 7 



LQ

Solutions to Chemical and Engineering Thermodynamics, 3e

Chapter 2

D 7DQNLVLQLWLDOO\HYDFXDWHG Ÿ 0  7KXV 0 '0  DQG 8  + LQ + EDU q &  N- NJ  E\ LQWHUSRODWLRQ   7KHQ 8  8  3 EDU 7 "  N- NJ   %\ LQWHUSRODWLRQXVLQJWKH6WHDP7DEOHV$SSHQGL[,,,  7 q & 9  3

q & #  P NJ

P  P NJ

2

9 9

7KHUHIRUH 0

EDU 7

7

 NJ 

E 7DQN LV LQLWLDOO\ ILOOHG ZLWK VWHDP DW  EDU DQG q& 8  N- NJ  DQG   P NJ  Ÿ 9 9  3 EDU 7 q &   NJ 7KXV 0  0 9 9  9    '0NJ (QHUJ\EDODQFH u  6ROYHE\JXHVVLQJYDOXHRI LV 0 8     u   0   



EDU  WR ILQG 9  DQG 8   LQ WKH 6WHDP 7DEOHV $SSHQGL[ ,,,   6HH LI HQHUJ\ EDODQFH DQG 0  P 9  DUH VDWLVILHG  %\ 7  XVLQJ 7  DQG 3

WULDO DQG HUURU  7 a q &  DQG 0 #   NJ  RI ZKLFK  NJ ZDV SUHVHQWLQWDQNLQWLDOO\7KXV '0 0  0  NJ 



D 8VHNLQHWLFHQHUJ\ PYWRILQGYHORFLW\ NJ u

Y  P  VHF

-



NJ VRY PVHF P VHF 

E +HDWVXSSOLHG VSHFLILFKHDWFDSDFLW\uWHPSHUDWXUHFKDQJHVR PRO u   u '7 - VR'7 . J u J PRO ˜ .  6\VWHP UHV...