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MECH 424/524, Fall 2011. 2ndLaw.

This coverage of he Firs and !econd Laws is a"en fro# a wonderf$l %oo" %&

'sh%& and (ones)

Engineering Materials 2. An Introduction to Microstructures, Processing

and Design, %& Michael F. 'sh%& and *avid +. H. (ones, $erworh-Heine#ann, 1, 2nd Ediion, Ch. 5, The driving force for sr$c$ral

change

*efine free wor" or ofen, s3onaneo$s wor" or ac$al wor" as follows)

Wf free wor"

#a6i#$# availa%le wor" #in$s inefficiencies

driving force in che#isr& and #aerials science

7 %e e6ra caref$l) driving force in che#./#a.sci. has

$nis of wor"

Free wor" is he a#o$n of s&se# energ& freel& availa%le o do $sef$l wor" aferhe s&se# sors o$ is inernal irreg$lariies8 e.g., an engine c&linder soring o$

$neven co#%$sion res$ls in inefficien energ& conversion. The a%ove

irreg$lariies are closel& relaed o entropy, which #eans a $rning inwards.

Consider a car rolling down an incline fig. a. To #eas$re he car9s a%ili& o

generae free wor", we can i#agine a #ass %eing raised fig. %)

a %

Loosel&, he a%ili& of he car o raise #ass mells $s how #$ch free wor" Wf: 0

ha we can ge free in he sense ha he car s3onaneo$sl& does wor" for $s.

eca$se a dropin he car9s elevaion is he indicaor of free wor", we define free

wor" wih a negaive sign he car9s i#agined 3oenial-energ& lossis he #eas$re

of he a#o$n of free wor" 3ossi%le)

ccf ygmW ;=

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=where ;vc vc,final= vc,ini> 08 ha is, a lossin "ineic energ& is needed o 3$ll $3

he #ass mfor free.

Le9s go f$rher)

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a %

( ) !pvmgymUW ccccf ;;;

+ 2inin

2

1

More generall& alho$gh no in he car si$aion, #echanical energ& can %e sored

in he environ#en %& increasing he environ#en 3ress$re a consan vol$#e, %$

ha also leaves $s wih less Wf)

( ) p!!pvmgymUW ccccf ;;;;

+ 2inin

2

1

Boe 1) The p;! er# is 3o3$lar wih che#iss) che#ical reacions al#osalwa&s wor" agains he a#os3here and his cos is a$o#aicall& charged

as 3ar of he re?$ired energ& %$dge. eca$sepis al#os alwa&s consan

pa# for he che#is, enhal3& has a co#3ac iner3reaion of oal hea

added) ;" ;Uinp!. For $s,pvaries %$ we can sill iner3re ;Uinp!

as oal hea e.g., co#%$sion ha #$s %e 3lanned for.

Boe 2)

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s&se# fro# all ca$ses, dUin, and incl$de s3onaneo$s s&se# e63ansion

agains he s$rro$nding 3ress$re,pd!, hen he res$l #$s %e greaer han

he hea a33lied across he %o$ndar& of he s&se#, in8 ha is, dUinpd!=

in: 0. This is anoher wa& of sa&ing ha he conversion of availa%le

#echanical wor" Wshafino energ& sorage dmcgyc dImcvc2( !dpand

free wor" Wf is never 100J) dUinpd! infor 3erfec conversion.

ased on his disc$ssion, we definedUinpd! = inas a change in he

s&se# dissi3aion :0. For inco#3ressi%ili&,pd! 0, which is ass$#ed in

he e69s coverage of 3i3e flow Ch. 5.

Boe ) For he case of a Ke engine, i #a"es sense o define he in3$

enhal3& as Uinp! Imv2, since he in3$ energ& %$dge is also

res3onsi%le for he "ineic energ& of gas flow. The er# Uinp! Imv2is

"nown as stagnation ent)alpy. ' he $3srea# hea so$rce where here is

$s$all& no flow, i is si#3l& Uinp!, which #oivaes he word sagnaion.

Boe 4) o$ are 3ro%a%l& #ore fa#iliar wih he following sae#en of he

Firs Law

s&se%&in WdU = 2

%$ he following sae#en is he sa#e hing)

( ) 0ins&se#on = dUWThe analogo$s $sage in Fl$ids Mechanics is goen %& seing

Won s&se# ( ) ( )p!dvmdgymdW cccc

2shaf2

1so ha

( ) ( ) 02

1in

2

shaf =+

pd!dU!dpvmdgymdW cccc 29

'noher 3o3$lar for# of he energ& e?$aion es3. for Ke-engine calc$laions

is

( ) ( )cccc gymdvmdp!UdW +

++=+ 2inshaf2

1299

Co#3are and conras he energ& e?$aions 2 and he ine?$aliies 1.

Le9s release a free-wheeling car or an& %lac"-%o6 #echanis# down a hill.

Firs Law 29 sa&s ha he oal s&se# energ& change #$s %e e?$al o

dmcgyc, 3l$s dImcvc2, 3l$s he irreversi%le hea generaed. !econd Law

1, on he oher hand, as"s $s o imaginea #ass ;m%eing dragged %& he

rolling car. *oes he rolling car sill roll on is own if ;mis s#all eno$gh

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are co#3leel& differen. Nnl& e?$aions 1 give $s %d& * dac$al, which is

he %asis for he !econd Law.

Boe 5) Le9s regro$3 he free-wor" e63ression as follows)

( ) ( )inin2

shaf

2

1pd!dU!dpvmdgymdWW ccccf +

+=

The er# dUinpd!= in is defined as he +is free energy, ;+, in

che#isr& and #aerials science. eca$se e6ernal energ& so$rces s$ch as

mg), Imv2canno r$n a s&se# conin$o$sl&, Oi%%s9 sandard definiion of

free energ& e6cl$des N Pmg), Imv2Q8 f$rher, che#iss and #aerials

scieniss rarel& deal wih shaf wor".