Chapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale.

Transcription

1 Chapters 18 & 19: Themodynamcs revew ll macroscopc (.e., human scale) quanttes must ultmately be explaned on the mcroscopc scale. Chapter 18: Thermodynamcs Thermodynamcs s the study o the thermal energy o the systems. Need to dene another parameter: Temperature Formal denton wll come later, now let s become amlar wth t. SI unt (nature s unt) or temperature: Kelvn (K) room temperature: 90 K water reezes: 73 K absolute zero: 0 K

2 The Zero th Law o Thermodynamcs Thermal equlbrum: Two bodes n contact come to a stable condton. Zeroth law o thermodynamcs: I bodes and B are each n thermal equlbrum wth a thrd body T, then they are n thermal equlbrum wth each other. Temperature s the property that determnes whether one object s n thermal equlbrum wth the other object. I T T T and T B T T then T T B Thermal Expanson Most objects expand when they are heated to a hgher temperature Lnear expanson. L α L T α : coecent o lnear expanson, α ( L/L)/ T unt: 1/K, 1/ o C α s derent or derent materals olume expanson β T β : coecent o volume expanson β 3α

3 Heat Heat s an energy, but t s not an ntrnsc property o a system. It s a physcal property assocated wth a process, whch means the amount o heat transerred s path-dependent. Work s also a physcal property (an energy) assocated wth a process, and so t also s path-dependent. The absorpton o heat by solds and lquds Heat capacty: when the temperature o an object s rased rom T to T, heat s absorbed: Q C (T T ) The constant C s called the heat capacty o the object. Unt o C: energy/degree, e.g. J/K, cal/ o C

4 Specc heat: It takes more heat to rase same T or a larger pot o water Q s proportonal to both (T T ) and mass Q c m ( T T ) c: specc heat, derent or derent materal e.g, 1 cal s the heat to rase 1 C o or 1 g water: c water Q/[m(T T )] 1 cal/(1g. 1C o ) 4190 J/(kg. K) c Tungsten 134 J/(kg. K) ; c l 900 J/(kg. K) Specc heat s heat capacty per unt mass C m c Heat o Transormaton: When ce melts or water bols, heat s absorbed, but T does not change. The system undergoes a phase transton. Q m L m mass, L Latent heat o transormaton. Heat o vaporzaton L : For lqud vaporzng to gas, or gas condenses to lqud. water, L 539 cal/g 56 kj/kg Heat o uson L F : For sold meltng to lqud, or lqud reezng to sold. water, L F 79.5 cal/g 333 kj/kg

5 Molar specc heat o an deal gas Molar specc heat: Q c n ( T T ) The specc heat c s a value that depends on the ablty o a substance to absorb energy. s such, c depends on both the type o materal and whether the process s a constant volume process or a constant pressure process. 1) Constant-volume process ) Constant-pressure process 3) rbtrary process Heat Transer Mechansms There are three heat transer mechansms: conducton, convecton, and radaton Conducton: heat transer through drect contact. TH TL Q k t L k: thermal conductvty, derent or derent materal. The hgher the k value, the better a thermal conductor t s. e.g. l: k 35; wndow glass: k 1 (unt: W/m.K) Conducton rate: P cond Q/t k (T H T L ) /L

6 Heat and Work Energy can be transerred as heat and work between a system and ts envronment. To take a system rom an ntal state: p,, T to a nal state: p,, T s called a thermodynamc process. Work done by the gas on the pston: r r dw F ds (p)(ds) p d From to : W dw p d > Non-zero work *needs* a volume change! Summary o work Work done at constant pressure p s constant, W p ( ) p Work done at constant volume d 0, so W 0 Work done by deal gas at constant temperature nrt d W pd d nrt nrt[ln ] nrt ln

7 The Frst Law o Thermodynamcs Q and W are process (path)-dependent. (Q W) E nt s ndependent o the process. E nt E nt, E nt, Q W (rst law) Q: + heat nto the system; heat lost rom the system W: + work done by the system. work done on the system Frst law o thermodynamcs s an extenson o the prncple o energy conservaton to systems that are not solated. Some specal cases o the Frst Law o Thermodynamcs dabatc processes: system nsulated, no heat transer Q 0 thereore E nt Q W W Constant-volume process: s xed dw pd 0, W 0 thereore E nt Q W Q Cyclc processes: System goes back to the ntal state E nt 0 thereore Q W

8 Ideal Gases t low gas denstes, all gases can be treated as deal gases. Ideal gases obey the relaton: p nrt (deal gas law) IF n s constant, then p T p T nr p: absolute (not gauge) pressure. : volume o the gas n: number o moles o gas present. T: the temperature n Kelvn. R: gas constant ( same or all gases) R 8.31 J/mol. K Ideal Gases p nrt Three varables n the deal gas law (4 you count n -- but let n be constant or now). Consder specal cases Pressure: Isobarc -- constant pressure olume: Isochorc (or sovolumc) -- constant volume Temperature: Isothermal -- constant temperature

9 p nrt Ideal Gases Three varables n the deal gas law (wth n beng constant). Consder specal cases Pressure: Isobarc -- constant pressure W pd p d p ( ) p Pressure olume p nrt Ideal Gases Three varables n the deal gas law (wth n beng constant). Consder specal cases olume: Isochorc -- constant volume W pd pd 0 Pressure olume snce the ntegral lmts are equal

10 p nrt Ideal Gases Three varables n the deal gas law (wth n beng constant). Consder specal cases Pressure Temperature: Isothermal -- constant temperature Gas expands rom to, p nrt/ olume W nrt pd d nrt d nrt[ ln ] nrt ln Denton o pressure: Pressure Force rea But now what s orce? Relate orce to mpulse and change n momentum. v F p x v dp dt p p v v dp Fdt Pressure ( mvx ) ( mvx ) mvx

11 Snce there are N molecules n the box, N nn and N s usually a *very* bg number, we can use the average speed nstead o the actual speeds. F mv x p L m 3 L m 3 L x1 ( v + v + K+ v ) x1 / L ( vx ) avg + mv x x / L L + K+ mv x N The volume o the box s L 3, so m nn p ( vx ) avg x N / L v rms Snce there are 3 dmensons, v x + v y + v z v and each dmenson s the same, v x v y v z > v 3v x m nn m nn 1 m nn ( vx ) v ( v ) avg p avg 3 avg (v ) avg s the average o the squared speed -- whch makes the speed the (square) root o the mean (average) squared speed --.e., root-mean-squared speed, v rms. 3 Rearrange (v ) avg v rms m nn 3 ( v ) p rms vrms 3p n mn

12 gas temperature mn s the molar mass M o the gas and usng the deal gas law p nrt : v 3p n mn 3nRT n M rms 3RT M Thus, the characterstc speed o the gas molecules s related to the temperature o the gas! Gas v rms (m/s) Hydrogen 190 Helum 1370 N 517 escape speed Earth 110 Maxwell-Boltzmann Dstrbuton M P(v) 4π πrt 3/ v e Mv / RT Thus, v avg v P(v)dv 0 8RT πm and 0 vavg ( vrms) v P(v) dv 3RT M

13 Mean Free path Dene the mean-ree-path λ as the dstance between collsons. 1 λ πd N/ Molecular szes Knetc Energes verage knetc energy: K avg ( ) m v 3RT M mv 3RT M / m 3RT N 3 R N ( m) () T kt 1 avg 1 rms Knetc energy only depends on the gas s temperature! K 1 3 avg m vrms kt The 3 comes rom the three dmensons: x, y, and z!