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)