THERMODYNAMICS. For an ideal gas, Pv = RT or PV = mrt, and P 1

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1 HERMODYNAMICS PROPERIES OF SINGLE-COMPONEN SYSEMS Nomenclature. Intense propertes are ndependent of mass.. Extense propertes are proportonal to mass. State Functons (propertes Absolute Pressure, P (lbf/n or Pa Absolute emperature, ( R or K Volume, V (ft 3 or m 3 V m (ft 3 /lbm or m 3 /kg Internal Energy, U (Btu or kj u U m (usually n Btu/lbm or kj/kg Entalpy, H (Btu or KJ Entalpy, u + P H/m (usually n Btu/lbm or kj/kg Entropy, S (Btu/ R or kj/k s S/m [Btu/(lbm- R or kj/ Gbbs Free Energy, g s (usually n Btu/lbm or kj/kg Helmolz Free Energy, a u s (usually n Btu/lbm or kj/kg Heat Capacty at Constant Pressure, c p b l Heat Capacty at Constant Volume, c b u l Qualty x (apples to lqud-apor systems at saturaton s x m g /(m g + m f m g m f mass of apor, and mass of lqud. can be wrtten: x g + ( x f or f + x fg f g fg g f Smlar expressons exst for u,, and s: u xu g + ( x u f or u u f + xu fg x g + ( x f or f + x fg s xs g + ( x s f or s s f + xs fg P For an deal gas, P R or PV mr, and P / P / P pressure, m mass of gas, R gas constant, and absolute temperature. V olume R s but can be found from R R ^ mol. wt R te unersal gas constant,545 ft-lbf/(lbmol- R 8,34 J/(kmol K. For deal gases, c p c R Also, for deal gases: b P u l b l For cold ar standard, eat capactes are assumed to be constant at ter room temperature alues. In tat case, te followng are true: Δu c Δ; Δ c p Δ Δs c p ln ( / R ln (P /P ; and Δs c ln ( / + R ln ( /. For eat capactes tat are temperature dependent, te alue to be used n te aboe equatons for Δ s known as te mean eat capacty `c p j and s gen by c p # cd p - Also, for constant entropy processes: k k - P P k ; P d n d n P k -, d n were k cp c For real gases, seeral equatons of state are aalable; one suc equaton s te an der Waals equaton wt constants based on te crtcal pont: P a c + m ^ - b R a 7 Rc Rc were c m f p, b 64 Pc 8Pc were P c and c are te pressure and temperature at te crtcal pont, respectely, and HERMODYNAMICS 73

2 FIRS LAW OF HERMODYNAMICS e Frst Law of ermodynamcs s a statement of conseraton of energy n a termodynamc system. e net energy crossng te system boundary s equal to te cange n energy nsde te system. Heat Q s energy transferred due to temperature dfference and s consdered poste f t s nward or added to te system. Closed ermodynamc System No mass crosses system boundary Q W ΔU + ΔKE + ΔPE were ΔKE cange n knetc energy, and ΔPE cange n potental energy. Energy can cross te boundary only n te form of eat or work. Work can be boundary work, w b, or oter work forms (electrcal work, etc. Work W bw W l m s consdered poste f t s outward or work done by te system. Reersble boundary work s gen by w b P d. Specal Cases of Closed Systems Constant Pressure ( : w b PΔ (deal gas / constant Constant Volume: w b (deal gas /P constant Isentropc (deal gas: P k constant w (P P /( k R( /( k Constant emperature ( : (deal gas P constant w b Rln ( / Rln (P /P Polytropc (deal gas: P n constant w (P P /( n Open ermodynamc System Mass crosses te system boundary P done by mass enterng te system. w re dp + Δke + Δpe Frst Law apples weter or not processes are reersble. FIRS LAW (energy balance Rmo 8 + V / + gzb- Rmo e8e + Ve / + gzeb + Qo - Wo d_ mu / dt, were n net s s Wo net rate of net or saft work transfer, ms us Qo rate of eat transfer (neglectng knetc and potental energy of te system. Specal Cases of Open Systems Constant Volume: w re (P P Constant Pressure: w re Constant emperature: (deal gas P constant w re R ln ( / R ln (P /P Isentropc (deal gas: P k constant w re k (P P /( k kr ( /( k w re ^k - / k k k P R > - d n H - P Polytropc: P n constant w re n (P P /( n Steady-State Systems e system does not cange state wt tme. s assumpton s ald for steady operaton of turbnes, pumps, compressors, trottlng ales, nozzles, and eat excangers, ncludng bolers and condensers. Rm o ` + V / + gzj- Rmo e`e + Ve / + gzej + Qo n - Wo out and Rmo Rmo were e mo and e refer to nlet and ext states of system, g acceleraton of graty, Z eleaton, V elocty, and Wo rate of work. Specal Cases of Steady-Flow Energy Equaton Nozzles, Dffusers: eleaton cange, no eat transfer, and no work. Sngle mass stream. + V / + V / e e Ve - V _ - es entalpy at sentropc ext state. urbnes, Pumps, Compressors: Often consdered adabatc (no eat transfer. Velocty terms usually can be gnored. e + w es 74 HERMODYNAMICS

3 - - e es es e - - rottlng Vales and rottlng Processes: No work, no eat transfer, and sngle-mass stream. Velocty terms are often e Bolers, Condensers, Eaporators, One Sde n a Heat Excanger: mass stream, te followng apples: + q e Heat Excangers: mo and mo : mo _ - mo _ - e e See MECHANICAL ENGINEERING secton. Mxers, Separators, Rm o Rm o e e and Rmo Rmo e BASIC CYCLES Heat engnes take n eat Q H at a g temperature H, produce a net amount of work W, and reject eat Q L at a low temperature L η of a eat engne s gen by: η W/Q H (Q H Q L /Q H Carnot Cycle. Its η c ( H L / H H and L absolute temperatures (Keln or Rankne. e followng eat-engne cycles are plotted on P- and -s dagrams (see later n ts capter: Carnot, Otto, Rankne Refrgeraton cycles are te reerse of eat-engne cycles. Heat s moed from low to g temperature requrng work, W. Cycles can be used eter for refrgeraton or as eat pumps. COP Q H /W for eat pumps, and as COP Q L /W for refrgerators and ar condtoners. Upper lmt of COP s based on reersed Carnot Cycle: COP c H /( H L for eat pumps and COP c L /( H L for refrgeraton. ton refrgeraton, Btu/r 3,56 W IDEAL GAS MIXURES,,, n consttuents. Eac consttuent s an deal gas. Mole Fracton: x N /N; N Σ N ; Σ x were N number of moles of component. Mass Fracton: y m /m; m Σ m ; Σ y Molecular Wegt: M m/n Σ x M Gas Constant: R R/ M o conert mole fractons x to mass fractons y : xm y R_ xm o conert mass fractons to mole fractons: y M x R_ y M mr Partal Pressures: P RP; P V mr Partal Volumes: V! V; V P P, V, te pressure, olume, and temperature of te mxture. x P /P V /V Oter Propertes: u Σ (y u ; Σ (y ; s Σ (y s u and are ealuated at, and s s ealuated at and P. PSYCHROMERICS We deal ere wt a mxture of dry ar (subscrpt a and water apor (subscrpt : P P a + P (absolute umdty, umdty rato ω: ω m /m a m mass of water apor and m a mass of dry ar. ω.6p /P a.6p /(P P Relate Humdty (r φ: φ P /P g P g saturaton pressure at. Entalpy : a + ω Dew-Pont emperature dp : dp sat at P g P HERMODYNAMICS 75

4 Wet-bulb temperature wb s te temperature ndcated by a termometer coered by a wck saturated wt lqud water and n contact wt mong ar. Humd Volume: Volume of most ar/mass of dry ar. Psycrometrc Cart temperature plotted for a alue of atmosperc pressure. (See cart at end of secton. PHASE RELAIONS Clapeyron Equaton for Pase ranstons: b d dp l sat fg s fg fg fg, were fg entalpy cange for pase transtons, fg olume cange, s fg entropy cange, absolute temperature, and (dp/d sat slope of pase transton (e.g.,apor-lqud saturaton lne. Clausus-Clapeyron Equaton s equaton results f t s assumed tat ( te olume cange ( fg can be replaced wt te apor olume ( g, ( te latter can be replaced wt P R from te deal gas law, and (3 fg s ndependent of te temperature (. P fg - lne d n P : R Gbbs Pase Rule (non-reactng systems P + F C + P number of pases makng up a system F degrees of freedom, and C number of components n a system COMBUSION PROCESSES Frst, te combuston equaton sould be wrtten and balanced. For example, for te stocometrc combuston of metane n oxygen: CH 4 + O CO + H O Combuston n Ar For eac mole of oxygen, tere wll be 3.76 moles of ntrogen. For stocometrc combuston of metane n ar: CH 4 + O + (3.76 N CO + H O N Combuston n Excess Ar e excess oxygen appears as oxygen on te rgt sde of te combuston equaton. Incomplete Combuston Some carbon s burned to create carbon monoxde (CO. Ar-Fuel Rato (A/F: A/F mass of ar mass of fuel Stocometrc (teoretcal ar-fuel rato s te ar-fuel rato calculated from te stocometrc combuston equaton. _ A F actual Percent eoretcal Ar # _ A F stocometrc _ A F - _ A F Percent Excess Ar _ A F actual stocometrc # stocometrc SECOND LAW OF HERMODYNAMICS ermal Energy Reserors ΔS reseror Q/ reseror Q s measured wt respect to te reseror. Keln-Planck Statement of Second Law No eat engne can operate n a cycle wle transferrng eat wt a sngle eat reseror. COROLLARY to Keln-Planck: No eat engne can ae a same reserors. Clausus Statement of Second Law No refrgeraton or eat pump cycle can operate wtout a net work nput. COROLLARY: No refrgerator or eat pump can ae a ger COP tan a Carnot Cycle refrgerator or eat pump. VAPOR-LIQUID MIXURES Henry s Law at Constant emperature At equlbrum, te partal pressure of a gas s proportonal to ts concentraton n a lqud. Henry s Law s ald for low concentratons;.e., x. P Py x Henry s Law constant, P partal pressure of a gas n contact wt a lqud, x mol fracton of te gas n te lqud, y mol fracton of te gas n te apor, and P total pressure. Raoult s Law for Vapor-Lqud Equlbrum Vald for concentratons near ;.e., x. P x P * P partal pressure of component, x mol fracton of component n te lqud, and P * apor pressure of pure component at te temperature of te mxture. 76 HERMODYNAMICS

5 ENROPY ds _ dqre s - s # _ dq Inequalty of Clausus # _ dq # re # re _ dq # s - s Isotermal, Reersble Process Δs s s Q/ Isentropc Process Δs ; ds A reersble adabatc process s sentropc. Adabatc Process δq ; Δs Increase of Entropy Prncple Dstotal Dssystem + Dssurroundngs $ Dso Rmo s - Rmo s - R_ Qo / total out out n n external external $ EXERGY Exergy s te porton of total energy aalable to do work. Closed-System Exergy (Aalablty (no cemcal reactons φ (u u o o (s s o + p o ( o were te subscrpt o desgnates enronmental condtons w reersble φ φ Open-System Exergy (Aalablty ψ ( o o (s s o + V / + gz w reersble ψ ψ Gbbs Free Energy, ΔG Energy released or absorbed n a reacton occurrng reersbly at constant pressure and temperature. Helmoltz Free Energy, ΔA Energy released or absorbed n a reacton occurrng reersbly at constant olume and temperature. emperature-entropy (-s Dagram Q re ds AREA HEA s Entropy Cange for Solds and Lquds ds c (d/ s s c (d/ c mean ln ( /, were c equals te eat capacty of te sold or lqud. Irreersblty I w re w actual HERMODYNAMICS 77

6 COMMON HERMODYNAMIC CYCLES Carnot Cycle Reersed Carnot Otto Cycle (Gasolne Engne η r k q r / Rankne Cycle Refrgeraton (Reersed Rankne Cycle w q q w c q q p p 3 p p 3 η ( ( COP ref 4 COP HP 3 78 HERMODYNAMICS

7 emp. o C Press. kpa p sat MPa Specfc Volume m 3 /kg lqud f apor g SEAM ABLES Saturated Water - emperature able Internal Energy Entalpy kj/kg kj/kg Eap. lqud apor lqud Eap. u f u fg u g f fg apor g lqud s f Entropy kj/(kg K Eap. s fg apor s g HERMODYNAMICS 79

8 Supereated Water ables u s u emp. m 3 /kg kj/kg kj/kg kj/(kg K m 3 /kg kj/kg kj/kg o C p. MPa (45.8 o C p.5 MPa (8.33 o C s kj/(kg K p. MPa (99.63 o C p. MPa (.3 o C p.4 MPa (43.63 o C p.6 MPa (58.85 o C p.8 MPa (7.43 o C p. MPa (79.9 o C HERMODYNAMICS

9 P- DIAGRAM FOR REFRIGERAN HFC-34a HERMODYNAMICS 8

10 ASHRAE PSYCHROMERIC CHAR NO WE BULB EMPERAURE - C ENHALPY - KJ PER KILOGRAM OF DRY AIR ENHALPY - KJ PER KILOGRAM OF DRY AIR SAURAION EMPERAURE - C DRY BULB EMPERAURE - C HUMIDIY RAIO - KILOGRAMS MOISURE PER KILOGRAM DRY AIR % 5 8% 5 7% 6% 5% VOLUME - CUBIC MEER PER KG DRY AIR ASHRAE PSYCHROMERIC CHAR NO. NORMAL EMPERAURE BAROMERIC PRESSURE:.35 kpa Copyrgt 99 R R AMERICAN SOCIEY OF HEAING, REFRIGERAING AND AIR-CONDIIONING ENGINEERS, INC. SEA LEVEL SENSIBLE HEA Qs OAL HEA Qt ENHALPY HUMIDIY RAIO W.84 4% 5 %.8 %.8 % RELAIVE HUMIDIY.78 8 HERMODYNAMICS

11 HERMAL AND PHYSICAL PROPERY ABLES GASES Substance Mol wt c p c kj/(kg K Btu/(lbm- R kj/(kg K Btu/(lbm- R k R kj/(kg K Gases Ar Argon Butane Carbon doxde Carbon monoxde Etane Helum Hydrogen Metane Neon Ntrogen Octane apor Oxygen Propane Steam SELECED LIQUIDS AND SOLIDS Substance c p Densty kj/(kg K Btu/(lbm- R kg/m 3 lbm/ft 3 Lquds Ammona Mercury Water , Solds Alumnum Copper Ice ( C; 3 F Iron Lead ,7 8,9 97 7,84, HERMODYNAMICS 83