11/19/2013. PHY 113 C General Physics I 11 AM 12:15 PM MWF Olin 101
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1 PHY 113 C General Pyss I 11 AM 12:15 PM MWF Oln 101 Plan or Leture 23: Capter 22: Heat engnes 1. ermodynam yles; work and eat eeny 2. Carnot yle 3. Otto yle; desel yle 4. Bre omments on entropy 11/19/2013 PHY 113 C Fall Leture /19/2013 PHY 113 C Fall Leture 23 2 Comment ab Exam 3: Part I take ome porton (1 problem): avalable ursday 11/21/2013 ater lass; must be turned n beore Part II n-lass porton (3 problems): uesday 11/25/2013 Some speal arrangements or early exams ave been (or wll be) arranged by pror agreement O ourse, all setons o te exam are to be taken under te gudelnes o te onor ode 11/19/2013 PHY 113 C Fall Leture
2 Important equatons or marosop and mrosop desrptons o termodynam propertes o matter Frst Law o ermodynams : ΔE W ermodynam Work : Ideal Gas Law : P nr Mrosop analyss o gas moleules: (assume N moleules o mass m or n moles o molar mass M ) P N m0vrms n Mv Mvrms R 3 For moleules wt C / C nr 1 P nt Fall /19/2013 PHY 113 C 2013 Leture 4 : 0 2 rms nt W Pd nr E Webassgn Assgnment 20 e rms speed o an oxygen moleule (O 2 ) n a ontaner o oxygen gas s 563 m/s. Wat s te temperature o te gas? From te knet analyss o gas moleules: (assume N moleules o mass m0 or n moles o molar mass M ) P N m0vrms n Mvrms nr Mvrms R 3 11/19/2013 PHY 113 C Fall Leture 23 5 Webassgn Assgnment 20 In a onstant-volume proess, 213 J o energy s transerred by eat to 0.99 mol o an deal monatom gas ntally at 299 K. (a) Fnd te work done on te gas. For onstant volume proess, W=0. (b) Fnd te nrease n nternal energy o te gas. DE nt = + 0 = 213J + 0 = 213 J () Fnd ts nal temperature. nc 11/19/2013 PHY 113 C Fall Leture
3 Webassgn Assgnment 20 A 2.00-mol sample o a datom deal gas expands slowly and adabatally rom a pressure o 5.06 atm and a volume o 12.2 L to a nal volume o 29.6 L. (a) Wat s te nal pressure o te gas? (b) Wat are te ntal and nal temperatures? () Fnd or te gas durng ts proess. (d) Fnd ΔE nt or te gas durng ts proess. (e) Fnd W or te gas durng ts proess. 11/19/2013 PHY 113 C Fall Leture 23 7 Dgresson: Adabat proess (=0) DEnt W n RD PD γ-1 P nr DP PD nrd nrd γ-1pd DP PD D DP γ P γ P γ ln ln P γ P P γ 11/19/2013 PHY 113 C Fall Leture 23 8 Webassgn Assgnment 20 A 2.00-mol sample o a datom deal gas expands slowly and adabatally rom a pressure o 5.06 atm and a volume o 12.2 L to a nal volume o 29.6 L. For datom deal gas: 1.4 (a) Wat s te nal pressure o te gas? γ γ P P P P / 5.06atm12.2/ b) Wat are te ntal and nal temperatures? P=nR ) Fnd or te gas durng ts proess. =0 d) Fnd ΔE nt or te gas durng ts proess. ΔE nt =W e) Fnd W or te gas durng ts proess. 11/19/2013 PHY 113 C Fall Leture
4 Webassgn Assgnment 20 (a) How mu work s requred to ompress 4.95 mol o ar at 19.6 C and 1.00 atm to one-tent o te orgnal volume by an sotermal proess? (b) How mu work s requred to produe te same ompresson n an adabat proess? () Wat s te nal pressure n part (a)? (d) Wat s te nal pressure n part (b)? 11/19/2013 PHY 113 C Fall Leture Webassgn Assgnment 20 (a) How mu work s requred to ompress 4.95 mol o ar at 19.6 C and 1.00 atm to one-tent o te orgnal volume by an sotermal proess? W Pd For an sotermal proess : nr P nr W d nr ln W ln 11/19/2013 PHY 113 C Fall Leture Webassgn Assgnment 20 (b) How mu work s requred to ompress 4.95 mol o ar at 19.6 C and 1.00 atm to one-tent o te orgnal volume by an adabat proess? Note: assume 1.4 For an adabat proess : DE For an adabat proess : R C 2.5R 1 nt W nc /19/2013 PHY 113 C Fall Leture
5 ermodynam yles or desgnng deal engnes and eat pumps ttp://auto.owstuworks.om/engne1.tm Engne proess: P (1.013 x 10 5 ) Pa P P B A C D Work o engne : Eeny : W W eng eng n W Heat nput to system : n 11/19/2013 PHY 113 C Fall Leture Examples proess by an deal gas: P B C AB BC CD DA P (1.013 x 10 5 ) Pa ( P P ) γp ( ) ( P P ) -γp ( ) W 0 -P ( - ) 0 P ( - ) A D P DE nt ( P P ) P ( ) ( P P ) -P ( ) Weng Eeny : n P P 11/19/2013 PHY 113 C Fall Leture 23 AB BC 14 Example rom omework Eeny : W eng P P n AB BC Also : W W eng n n 1 CD AB DA BC n 1 n 11/19/2013 PHY 113 C Fall Leture
6 Most eent termodynam yle -- Carnot Sad Carnot /19/2013 PHY 113 C Fall Leture Carnot yle: AB Isotermal at BC Adabat CD Isotermal at DA Adabat Eeny o Carnot yle n n ε 1 1 n 11/19/2013 PHY 113 C Fall Leture lker exerse: We dsussed te eeny o an engne as n 1 n n Is ts result A. Speal to te Carnot yle B. General to all deal termodynam yles lker exerse: We dsussed te eeny o an engne runnng wt ot and old reservors as 1 Is ts result A. Speal to te Carnot yle B. General to all deal termodynam yles 11/19/2013 PHY 113 C Fall Leture
7 Note tat or a Carnot yle: WAB nr ln( C / D) n WCD nr ln( B / A) For adabatproess 1 1 B C 1 1 A D C / D B / A n For Carnot yle: 1 11/19/2013 PHY 113 C Fall Leture lker exerse: Wy sould we are ab te Carnot yle? A. We souldn t B. It approxmately models some eatng and oolng tenologes C. It provdes nsgt nto anoter termodynam varable -- entropy 11/19/2013 PHY 113 C Fall Leture /19/2013 PHY 113 C Fall Leture
8 Webassgn Assgnment 21 A eat engne operates between a reservor at 28 C and one at 362 C. Wat s te maxmum eeny possble or ts engne? e Carnot yle s te most eent proess operatng between ot and old temperatures : /19/2013 PHY 113 C Fall Leture Webassgn Assgnment 21 An deal gas s taken troug a Carnot yle. e sotermal expanson ours at 260 C, and te sotermal ompresson takes plae at 50.0 C. e gas takes n 1.28 x10 3 J o energy rom te ot reservor durng te sotermal expanson. (a) Fnd te energy expelled to te old reservor n ea yle (b) (b) Fnd te net work done by te gas n ea yle. 11/19/2013 PHY 113 C Fall Leture e Otto yle eoretal eeny : / 2 s te ompresson rato -- typally 1 / 2 = 8 = /19/2013 PHY 113 C Fall Leture
9 11/19/2013 PHY 113 C Fall Leture e Desel yle eoretal eeny: 1 D A 1 C B In prnple, ger eeny tan omparable Otto yle. 11/19/2013 PHY 113 C Fall Leture Engne vs eatng/oolng desgns Heat pump; eatng mode: (Carnot) W Heat pump; oolng mode: (Carnot) W 11/19/2013 PHY 113 C Fall Leture
10 Bre omments ab entropy marosop pture Carnot yle Note tat or a Carnot yle : WAB nr ln( C / D ) WCD nr ln( B / A) For adabat proess 1 1 B C 1 1 A D C / D B / A 11/19/2013 PHY 113 C Fall Leture Bre omments ab entropy ontnued For a Carnot yle : Dene : d ds For a Carnot yle S "state varable" (lke D S yle Oter examples o entropy : 0 E nt Cange o entropy wle meltng : ) o o J For meltng1kg water at 0 C ( K) DS 1219J / K o 11/19/2013 PHY 113 C Fall Leture K 29 DS d ml uson meltng 10
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