7/24/2019 Expansion Work
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1. Expansion work
Given:
Pressure(kPa) Volume (m3)
420 0.5368 2333 3326 4326 5312 6242 10207 11
Required: ork in k!
Solution:
"#ep 1: Plo##in$ Pressure %s. Volume
0 2 4 6 8 10 120
50
100
150
200
250
300
350
400
450
&(x) ' 0.03x4 1.12x3 * 13.05x2 66.+5x * 451.62,- ' 1
Polnomial ()
7/24/2019 Expansion Work
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"#ep 2: /alula#in$ work &rom #e $ure o#aine nal#ial e#o
"ine work ue #o expansion is
' pV
en work ue #o expansion is #e area elow #e ur%e plo##e ase on #ea#a $i%en. a# is #e in#e$ral o& #e e9ua#ion o& #e ur%e in#e$ra#e &rom x' 0.5#o x' 11. "ine #e e9ua#ion an e reail in#e$ra#e; #e work ue #o expansionan e sol%e anal#iall &rom #e o#aine e9ua#ion.
is is one in #e &ollowin$
'
0.5
11
0.0274x4 1.1182x3* 13.046x2 66.+5x * 451.62) x
' (0.0274 x
5
5 1.1182 x
4
4 *13.046 x
3
3 66.95 x
2
2 *
451.62 x )< 11
0.5
' 3277.12 k! (approxima#e work ue #o expansion &romanal#ial me#o)
"#ep 3: /alula#in$ work &rom #e $ure o#aine =umerial >n#e$ra#ion
is an also e es#ima#e =ew#on/o#e?s @ormulas usin$ #e &ormulas&or #rapeAoial "impson?s 1B3 an "impson?s 3B8 as sown #e &ollowin$ solu#ion
(Cur#?s solu#ion)