Thermal energy: Part III
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1 Thrmal nrgy: Part III 1. ach molcul occupis a crtain volum. th molculs attract ach othr Kywords 1. Th importanc of thrmodynamics: various ngins. Prssur/ kintic intrprtation 3. Idal gas 4. Avrag molcul vlocity 5. Spcific hat of idal gas 6. First law of thrmodynamics 7. Carnot cycl 8. Efficincy/ Carnot thorm 9. Entropy 1. Enthalpy 11. Gas turbin/stirling/otto ngins 1. an dr Waals gas 13. Ronald Stam Grissn turbin 8 rij Univrsitit, Amstrdam vrij Univrsitit amstrdam 1. ach molcul occupis a crtain volum. th molculs attract ach othr 1. ach molcul occupis a crtain volum. th molculs attract ach othr idal gas p nrt R: Intraction rang ral gas ach mol of molculs occupis a volum b nb p nb nrt (Clausius quation of stat) d: avrag distanc btwn molculs Forc on a singl surfac molcul is proportional to th numbr of th molculs within rang f N/ f N/ R: Intraction rang Numbr of molculs that ar within a rang R of th surfac and hnc fl th influnc th surfac n surf N/ Total inward forc on subsurfac molculs N f nsurf Prssur is incrasd by: f n psubsurfac R p incrasd by a subsurfac n N p nb nrt p n b RT n pa b RT n (Clausius quation of stat) p incrasd by a n i.. apart from p xt thr is an xtra cohsiv prssur Th an dr Waals Equation of Stat a and b dpnd on th gas undr considration 1
2 Ral gas: Th an dr Waals cofficints n pa b RT n Gas an dr Waals Cofficints a (Pa m 6 mol - ) b (m 3 /mol) Hlium 3.46 x x 1-6 Non.14 x x 1-6 Hydrogn.48 x x 1-6 Carbon dioxid 3.64 x x 1-6 Watr vapour 5.54 x x an dr Waals 5K isothrm for CO liquid liquid+gas gas 8 4 obsrvabl in Prssur [1 5 Pa] n p a b RT n obsrvabl in Maxwll construction suprsaturatd gas 5 K suprhatd liquid Molar olum volum [litr] [litr/mol] an dr Waals isothrm an dr Waals isothrms for CO p [Pa] p RT a n b x Molar volum [litr/mol] n ngativ prssur? Watr at 473 K Prssur [1 5 Pa] K K 4 K 35 K 3 K Molar olum volum [litr/mol] [litr] an dr Waals isothrms for CO an dr Waals isothrms for CO 1 Prssur [1 5 Pa] critical point 5 K K 4 K 35 K 3 K Prssur critical point Molar olum volum [litr/mol] [litr] olum
3 Us of an dr Waals isothrms 1 gas liquid (undr atmosphric conditions, p = 1 atm) : volum of 1 mol changs: litr cm 3 (vry roughly) ry usful for storag: mor mass pr volum CO to squstration 8 atm at 3K 8 m dp in ocan Mthod 1: cooling Liquid natural gas CH 4 (11 K) Mthod : prssur Butan C 4 H 1 at o C liquid undr atm (roughly) 1 km km ~3 GtCO /yar Us of an dr Waals isothrms undr atmosphric conditions (p = 1 atm) liquid gas volum of 1 mol changs: cm 3 litr (roughly) larg xpansion ratio, larg prssur obtainabl larg forc larg xpansion ratio mor work pr cycl dispnsabl, chap liquid high hat capacity WORK watr stam ngin p Prssur [1 5 Pa] olum [litr] an dr Waals isothrms for H O At rathr high T, still coxistnc watr droplts: harm turbins K K 473 K K - 83 K Molar olum volum [litr/mol] [litr] Tmpratur [K] Hating watr at constant prssur ΔS Q Q TΔS T Q T c Hat Q [kj/kg] p Tmpratur [K] S T T c Entropy S [kj/k/kg] p Tmpratur [ o C] T-S diagram for watr bar Entropy S [kj/kg/k] 3
4 From th book: TS diagram of watr Th problm with Carnot isothrm is rquird T is limitd whol loop: watr/stam mixtur bad for turbin blads hug comprssor a solution: Rankin c b Rankin cycl without rhat W turbin Still som watr formd in th turbin d Rankin cycl with rhat prvnt watr condnsing a f Q in W pump Q out a Q in c 1 3 f b W turbin W pump Q out d Organic Rankin cycl Us an organic fluid with boiling point lowr than watr Wast hat Solar hat (parabolic troughs) Solar ponds Organic Rankin cycl Us an organic fluid with boiling point lowr than watr Wast hat Solar hat (parabolic troughs) Solar ponds ordinary pond solar pond convction cooling STG salt gradint prvnts convction bottom layrs hat up 4
5 Waigaoqiao II coal-fird stam turbin powr plant by Simns in Shanghai 1.8 GW Coal and China Officially, 6, wr killd in China's coal mins just last yar - that's a day. Mthan xplosions ar th main culprit. But it's not just a safty hazard - mthan's also a grnhous gas, tims as damaging as carbon dioxid. 4 wr killd in China's coal mins in 1. Engins fr from th Carnot cycl China is building on coal-fird powr station a wk. NaS x accumulator: th ida NaS x accumulator Na + S - moltn sodium Na Porous Al O 3 S Na + S x- moltn sulphur Na S 3 5
6 anod oxidation Lad accumulator H SO 4 4+ Pb PbO + PbSO 4 SO SO 4-4H + idntical: + PbSO 4 +H O cathod rduction Car with lad accumulator La jamais contnt, km/h Ful cll Elctrolyzr Full Cl hydrogn air cathod lctrolyt nitrogn +watr Enrgy Storag: H gas Ful clls / Hydrogn busss Efficincy of a ful cll W lctric Q But w ar not rally applying hat! How to solv? Gibbs Fr Enrgy (lctric nrgy out) G H 85.8 Enthalpy (total nrgy ndd for crating) 6
7 Summary n an dr Waals gas pa b RT n volum of 1 mol changs: cm 3 litr (roughly) Rankin cycl Ful cll: xtrnal lctrical work chmical nrgy ΔG ΔH Nxt: fluid dynamics: watr (Tsunami) and wind(mill) 7
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