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1 Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether the enthlpy () nd the entropy (S) o the system ncrese, decrese or remn unchnged durng the ollowng processes: A) condensng sturted vpor; decreses (Δ < 0); S system decreses (ΔS sys < 0) B) dtc reversle compresson o superheted vpor; ncreses (Δ > 0); S remns constnt (ΔS 0) ) Joule-homson throttlng. remns constnt (Δ 0); S ncreses (ΔS > 0) (0 ponts). A closed nsultng cylnder s tted wth non-conductng, rctonless lotng pston whch dvdes the cylnder nto Sectons A nd B. he two sectons contn r wth equl numer o moles, n 0, nd ntlly t the sme condtons, 00 K nd tm. An electrcl hetng element Q & n Secton A s ctvted nd the r tempertures slowly ncrese: A n Secton A ecuse o het trnser nd B n Secton B ecuse o dtc compresson y the slowly movng pston. Assume r to e n del gs wth p 7. I the nl pressure s.5 tm, clculte: A) B, temperture n Secton B; B) A, temperture n Secton A; ) Q/n A, het sored per mole o gs A. Dt: 8.06 cm. tm.mol -.K -

2 n A n B n A, B,.0 tm A, B, 00 K A, n A A, / A, n / B, n B B, / B, n / A, B, A, + B, A, + B, n n n n A, B, + + n n ( ) A, + A, + B, B, onsder just secton B. hs secton undergoes n dtc compresson, whch we hve lredy seen oeys the ormul γ γ Applyng ths ormul to secton B gves p.5, B K.00 We cn then solve or A, usng the equton ove:.5 A, B, * K.00 7 Fnlly, to solve or het dded, we wrte n energy lnce or the comned system (whch s rgd!) ΔU n (ΔU A + ΔU B ) n [ ( A, ) + ( B, ) ] Q/n ( A, + B, ),8 J/mol Alternte Soluton Strt y solvng secton B s ove to get B, 9.75 K I we solve the del gs lw, we nd tht A, B,,68 cm /mol. Snce we know the nl pressure nd temperture o secton B, we cn use the del gs lw to solve or B, 0,99 cm /mol. Snce totl system volume s conserved, we thereore hve A, 8,5 cm /mol. (Secton A gns the volume tht secton B loses.) Now, usng the del gs lw we cn solve or A, A, / 0.5 K.

3 Next, wrte the energy lnce or secton B: ΔU W Δ W (, ) W W (5/) (, ) J Now snce the work done on secton B s done y secton A, the energy lnce or secton A ecomes ΔU Q W ΔU Q J ( A, ) Q J Q (5/) (0.5 00) + 0.5,8 J/mol.

4 (5 ponts). A cr drvng long the rod ccdentlly runs over nl, puncturng one tre. he tre ws ntlly nlted to n solute pressure o.78 r, nd the r nsde hd n ntl temperture o 0 K. For smplcty we ssume the volume remns constnt t 5 L s the tre deltes. I the tre deltes untl ts nternl pressure s.05 r: A) Wht s the temperture o the r tht remns n the tre mmedtely ter? B) ow mny moles o gs hve escped the tre? You my tret r s n del gs wth constnt pressure het cpcty o 7/. Assume good mxng nd tht the tre delton s dtc. Mss lnce: dn N& Energy lnce: & n & + Q& W& Note tht we re neglectng potentl nd knetc terms. No mterl lows nto the system, so n 0. he process s dtc, so Q 0. Lkewse, there s no sht work eng done, nd the system oundres re not movng, so the only work eng done s low work done y the escpng r. hs low work hs een comned wth U to orm the terms. d comned lnce: ( NU ) & N& dn N + U dn rerrnge: N ( U ) drop : U dn N dn del gs lw: N dn d d

5 susttute: U ( ) d * d o del wth, we recognze tht the molr enthlpy tht ech unt o gs escpes wth s equl to the molr enthlpy the gs hd just eore escpng (ths s why the good mxng ssumpton s necessry). hus, system, nd or n del gs, U. omnng ths wth d gves d ( ) d ntegrte: ln ln + nd or n del gs, + p K.9.78 o determne the numer o moles tht escpe, we must know the numer o moles ntlly n the tre, nd the numer o moles tht re let n the tre. (.78)( 5) ( 0.08)( 0) (.05)( 5) ( 0.08)( 8.) N ntl 5.7 moles N nl.55 moles N lost moles

6 (0 ponts). onsder cycle tht conssts o the ollowng reversle processes: () Isotherml compresson rom to () onstnt-volume hetng rom to () Isotherml expnson rom to (v) onstnt-volume coolng rom to Assume constnt het cpcty, nd tht the workng lud oeys the vn der Wls equton o stte: A) Drw the pths on qulttve - dgrm. Lel ech stte,,, nd ccordng to ther respectve pressures. Also lel the sotherms nd or the hotter temperture nd the colder temperture, respectvely. B) For step, clculte ΔU, Q, nd W n terms o expermentlly ccessle vrles. Use the sgn conventon ΔU Q W, nd leve these qunttes n molr unts. ) Show tht: ( ) ( ) ( ) ( ) Soluton A.) B, D A,

7 B.) here re severl wys to do ths prt. ere s one soluton: d d W Step () s sotherml compresson, so s constnt. nd re lso constnts. d d W + ln W o get U, we wrte U U(,) d U d U + Snce step () s sotherml, the d term goes to zero. o get the d term, we wll use the reltonshp ds d to get S U he second term s just. he rst term requres Mxwell relton: S uttng t ll together (nd rememerng tht s constnt nd d 0), d Now we pply ths equton to the vn der Wls equton: d d

8 Δ U Fnlly, snce ΔU Q W, we cn wrte Q ΔU + W + + ln Q Q ln.) We wll strt y wrtng the equtons or the pressure t ech pont: notce tht nd lkewse Now, determne wht nd re: ( ) ( ) Fnlly, dvde one derence y the other. he temperture terms cncel, levng ( ) ) ( ) ( ) (

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