IYPT 2000 Problem No. 3 PLASMA

Transcription

1 IYPT 000 Problm No. 3 PLASMA Tam Austria Invstigat th lctrical conducivity of th flam of a candl. Examin th influnc of rlvant paramtrs, in particular, th shap and polarity of th lctrods. Th xprimnts should b carrid out with a voltag not xcding 150 V.

2 IYPT 000 Masurmnts 9 currnt I [µa] ,5 5,3 4,6 3,4,3 xprimntal data: sharp lctrods on th sam lvl in th flam voltag: 150 V, DC horizontal distanc d [mm]

3 IYPT 000 Masurmnts currnt I [µa] xprimntal data: sharp lctrods abov ach othr Intrsction: about 4 mm 0 voltag: 150 V, DC vrtical distanc d [mm]

4 IYPT 000 Conclusions from th masurmnts Th problm is not compltly solvabl! Only th influnc of various paramtrs can b xamind: lctric fild (shap and arrangmnt of th lctrods) tmpratur gas flow compositon of th gas

5 IYPT 000 Gas Flow - Exprimnt lft mass: g; right mass: 1g; connctd with a circular Al plat (in th flam: F plat);tmpratur masurmnt with Pt-100 or thrmocoupl Th straming forc F Str is an upward forc on th right mass and producs an additional downward forc on th lctronic scals. This causs th scals to show a highr wight, so F Str can b calculatd using this mass diffrnc m.

6 IYPT 000 Gas Flow - Calculations F Str c w A ρ v F C w 1,1 (for circular plats) Str v A r².π (ara of th circular plat) c A ρ w F Str... has bn masurd ρ... dnsity of air: calculatd (s following transparnt) xampl of calculation: distanc from th flam: 50 cm m 510 F Str kg ϑ,5 C ρ 1,195 3 m v 6 4,90510 FStr c A ρ w m v 0,4 s [kg] 5 [N] 5 4, ,1 1,5610 1,195

7 IYPT 000 Gas Flow - Calculations Calculation of air dnsity: idal gas quation p V m p V R T M m p M R T V p M ρ R T ρ n R T p M R T calculation of th molcular wight M: air at 0 C, 1 bar: ρ 1,93 [kg/m³] R T 1,938,31 73,15 0 M ρ 5 p0 10 M 0,0935[kg] (ρ [kg/m³] M [kg]) p prssur [Pa] V volum [m³] n numbr of mols R gas constant ( 8,31) [ J / (K. mol) ] T tmpratur [K] M molcular wight ρ dnsity [kg/m³]

8 IYPT 000 Gas Flow - Rsults Spd of th gas flow spd [m/s] 1,5 1,5 1 0,75 0,5 0, vrtical distanc from th cntr of th flam [cm]

9 IYPT 000 Thory about plasma Plasma in thrmic qulibrium: 3 distributions Boltzmann distribution Maxwll distribution Saha distribution For a plasma in thrmic qulibrium, all 3 distributions hav to b fulfilld.

10 IYPT 000 Maxwll distribution N(v) 4π N mm π k T 3 v mmv k T N...numbr of molculs k...boltzmann constant ( 1, [J/K]) m M...mass of on molcul T...tmpratur [K]

11 IYPT 000 Ionisation through hits calculation of th rquird minium spd for ionisation: E x i m M 4π v min Maxwll distribution to calculat th fraction of molculs which ar fastr than v min : N...numbr of molculs m π k M T 3 v min v mmv k T rsults:.g. for O : x for N : x d v k...boltzmann constant ( 1, [J/K]) m M...mass of on molcul T...tmpratur [K]

12 IYPT 000 Saha distribution Th Saha quation indicats th ionisation balanc btwn th lctrons and th ions vrsus nutral particls: S N N N ( π m ) + i 3 m...mass of th lctron h...planck constant k...boltzmann constant T...tmpratur E i...ionisation nrgy h 3 E i 5 kt ( k T ) lik chmical quilibrium: + X X + Chmical quation for th ionisation of an lmnt X. [ X ] [ ] + K f, [ X ] ( T ) E i

13 IYPT 000 Influnc of th lctric fild Th lctric fild causs lctrons to drift through th plasma with a currnt dnsity j: N...numbr of lctrons j N v d morovr: j σ E vd τ E m v d µ E λ v τ v 8k T π m...lmntary charg v d...drifting spd E...lctric fild strngth m..mass of th lctron τ...avrag tim btwn hits σ...conductivity µ...mobility of th lctrons λ...fr distanc btwn hits v...avrag spd of th lctrons (Maxwll distribution) k...boltzmann constant T...tmpratur

14 IYPT 000 calculation m 1 ~ N T k m 1 E E µ N j σ λ π σ σ using th shown formulas: Taking an lmnt with an avrag mass from th priodic systm of th lmnts w can show that th shar of ions of th currnt is < 0,4 %. So w can rstrict ourslvs to th considration of drifting lctrons only.

15 IYPT 000 Richardson quation j AT kt A 4π m k T h 3 W A W A...work function k...boltzmann constant T...Tmpratur h...planck constant m...rst mass of th lctron Th Richardson quation shows only th influnc of th tmpratur and is not considring th point ffct!

16 IYPT 000 Fild influnc fild mission: Schottky-ffct (point ffct) Fowlr-Nordhim quation: E j ~ F Q E F c E E 0 E...lctric fild strngth F...forc Q...charg c...lmntary charg j...currnt dnsity