Problem mol. T r. P r. a) NIST Database

Transcription

1 roblem a) NIST Daabase Use your browser o poin o hp://webbook.nis.gov/hemisry/fluid. Sele mehane as he speies of ineres. Choose Celsius, bar, and m /mol for he unis and sele isohermal properies. Coninue o he nex page in whih you ener 7 C as he required emperaure. Sine we only need informaion for wo poins, we hoose low 1 high in 199 Coninue o he nex page in whih you will find a plo indiaing ha he firs poin is in he vapor range and he las poin ( bar) is in he superriial range. Clik he view able buon o ge he required resuls: A 1 bar,.4914 m /mol A bar,.141 m /mol To alulae he volume of he ank, we need o alulae he number of moles using he informaion given a 1 bar. 4 m m mol n mol The required ank volume * m b) The ideal gas law Using n from par a, we apply he ideal gas law a bar ) Lee/Kesler generalized orrelaion Criial properies of Mehane from S+N Appendix B T 19.6 K bar ω.1 Calulae he redued variables: K T r K ( molk) * K m n R T mol* 8.14 m bar / ig. m bar 1m bar r bar 4.49

2 We use Lee/Kesler ables in Appendix E o ge Z and Z 1 for he equaion Z Z + ωz 1 There are no olumns in he able for r of 4.5 nor here are any rows for T r of So we need o inerpolae beween he values given in he able. We an esimae a value based on our inuiion wihou doing any alulaions (e.g..8) bu i is beer o linearly inerpolae beween he given values o ge Z a he needed T r and r. To do his we will inerpolae as illusraed in he diagram. Inerpolaing beween he wo values of pressure ( T, ) Z ( T, ).86 + We an do he same o ge Z 1 (T r, r ) of.5 (lef as an exerise) We now an alulae he volume ( Z ( T, ) Z ( T, ) r r r r1 ( ) Z r r r r1 + r r1 r r1 Z ( ) ( 4.49.). 84 ( 5..) ( T, ) * r r LK Zig.846 *. m.169 m

3 d) an der Waals EOS RT b a The onsans a and b an be esimaed from he riial onsans of mehane 7 R T a 64 7 * ( 8.14 m bar /( mol K) ) 64*45.99 bar *19.6 K m 1 m 6.5 *1 6 m mol bar b R T 8 ( ) 8.14 m bar / molk 19.6 K 8* bar m 1m 4.7 *1 5 m mol Muliplying an der Waals equaion hrough by (-b)/ o give RT a b For ieraion, we wrie RT a b + ( b) ( b) i i + 1 i Using Exel spreadshee o ierae for (see he seion on how o use formulas in Exel), we ge a b R T.E ieraio n i i+1 1.E-4 1.1E E E E E E E E E E E-4 The ank volume is

4 4 dw mol*1.66*1 m / mol.1648m e) The Redlih-Kwong EOS Calulae a and b using equaions (.4) and (.41) and ierae using equaion (.7) in an Exel spreadshee as follows T a b R T E-5.99E E- 5 ieraio n i i+1 1.E E E E E E E-4 1.5E E E E E-4 The ank volume is 4 RK mol*1.54*1 m / mol.169 m

5 f) Mehod Ease of Use Auray % error (ompared o a) NIST Exel help on how o use formulas ery easy o use Limied o small number of ompounds Bes auray beause i is a ompilaion of experimenal daa.166 Ideal Gas Law ery easy Bad. Lee/Kesler Easy if poins are found, oherwise requires inerpolaion dw Tedious as i requires ieraion for RK Tedious as i requires ieraion for Good Good Good How formulas alulae values A formula is an equaion ha analyzes daa on a workshee. Formulas perform operaions suh as addiion, mulipliaion, and omparison on workshee values; hey an also ombine values. Formulas an refer o oher ells on he same workshee, ells on oher shees in he same workbook, or ells on shees in oher workbooks. The following example adds he value of ell B4 and 5 and hen divides he resul by he sum of ells D5, E5, and F5. Abou formula synax Formulas alulae values in a speifi order ha is known as he synax. The synax of he formula desribes he proess of he alulaion. A formula in Mirosof Exel begins wih an equal sign (), followed by wha he formula alulaes. For example, he following formula subras 1 from 5. The resul of he formula is hen displayed in he ell. 5-1 Abou ell referenes A formula an refer o a ell. If you wan one ell o onain he same value as anoher ell, ener an equal sign followed by he referene o he ell. The ell ha onains he formula is known as a dependen ell; is value depends upon he value in anoher ell. Whenever he ell ha he formula refers o hanges, he ell ha onains he formula also hanges. The following formula muliplies he value in ell B15 by 5. The formula will realulae whenever he value in ell B15 hanges. B15*5 Formulas an refer o ells or ranges of ells, or o names or labels ha represen ells or ranges.

6 Abou workshee funions Mirosof Exel onains many predefined, or buil-in, formulas known as funions. Funions an be used o perform simple or omplex alulaions. The mos ommon funion in workshees is he SUM funion, whih is used o add ranges of ells. Alhough you an reae a formula o alulae he oal value of a few ells ha onain values, he SUM workshee funion alulaes several ranges of ells. The differene beween relaive and absolue referenes When you reae a formula, referenes o ells or ranges are usually based upon heir posiion relaive o he ell ha onains he formula. In he following example, ell B6 onains he formula A5; Mirosof Exel finds he value one ell above and one ell o he lef of B6. This is known as a relaive referening. When you opy a formula ha uses relaive referenes, he referenes in he pased formula updae and refer o differen ells relaive o he posiion of he formula. In he following example, he formula in ell B6 has been opied o ell B7. The formula in ell B7 has hanged o A6, whih refers o he ell ha is one ell above and o he lef of ell B7. If you don' wan referenes o hange when you opy a formula o a differen ell, use an absolue referene. For example, if your formula muliples ell A5 wih ell C1 (A5*C1) and you opy he formula o anoher ell, boh referenes will hange. You an reae an absolue referene o ell C1 by plaing a dollar sign ($) before he pars of he referene ha do no hange. To reae an absolue referene o ell C1, for example, add dollar signs o he formula as follows: A5*$C$1