PHY 410. Final Examination, Spring May 4, 2009 (5:45-7:45 p.m.)

Transcription

1 PHY ina amination, Spring 9 May, 9 5:5-7:5 p.m. PLAS WAIT UTIL YOU AR TOLD TO BGI TH XAM. Wi waiting, carfuy fi in t information rqustd bow Your am: Your Studnt umbr: DO OT TUR THIS PAG UTIL TH XAM STARTS USUL COSTATS AD ITGRALS Avogadro s umbr A 6. Botzmann s constant k.8 - J/K /K Panck constant.5 - J.s ctron carg magnitud.6-9 C ctron mass m kg Spd of igt m/s atm. bar bar 5 /m.6-9 J

2 Tr ar 7 probms. To rciv fu crdit for ac answr, you must work naty, sow your work and simpify your answr to t tnt possib.. Probm 5 points A powr pant producs GW of ctricity at an fficincy of %. i Wat is t rat at wic t powr pant ps wast at to t nvironmnt? η W Q dw Givn ; W ηq GW η w W + Q av dq η W Q ; Q η η dw η ii Wat is t rat at wic it uss up nrgy at t ot nd? η W η. GW.5GW. dq dw η Atrnativy Probm 7.5 points dq GW.5GW. dq + dw.5gw + GW.5GW Considr a fu c tat uss mtan gas as fu. T raction is CH + O H O + CO T diffrnc in Gibb s fr nrgy fina initia is -8 kj pr mo of CH. i Assuming ida prformanc, ow muc ctrica work can b producd by t c for ac mo of CH. 8 kj iit two stps of tis raction ar At v ctrod CH +H O CO + 8H and At +v ctrod O + 8H H O Wat is t maimum votag gnratd by t c? 8 A 8kJ 8 8 Trfor ma votag A J 8 86 J.6. 9 J.

3 Probm points An ida gas of bosons of mass M is in a cubica bo of voum. T bosons ar nonrativistic. T dnsity of orbitas or stats is givn by. ; / / π M D iwrit down an prssion for t numbr of partics in trms of D and t Bos-instin distribution function. B f µ d D / ii Driv an prssion for t B condnsation tmpratur in trms M and t dnsity /.Us π.6 / d / / / / / / / / /.6 : M d M Put d M d D π π π iii How dos cang wn t mass of t boson doubs? It rducs by a factor of

4 Probm 7.5 points T masurd constant voum at capacity of a mta at ow tmpratur << << θ is givn by and B Dby k C A + B, wr A and B ar constants. iwat ar t pysica origins of t abov two diffrnt contributions to C? T inar trms coms from t rmi Dirac statistics of ctrons in a mta. T cubic trms coms from t ponons attic vibrations of t atoms ii Wat is t tmpratur dpndnc of ntropy of t mta? dq dσ C d d C ' dσ d ' ' σ σ C ' d ' ' A d ' + B ' d ' A + B Usuay σ

5 5 Probm 5 points Considr a dfct in a soid wic as two nrgy vs wit nrgy and >. T dgnracy of t ground v is and tat of t citd v is. T soid is at a tmpratur. i Wat is t partition function for tis dfct? ii Wat is its avrag nrgy U? Pot U as a function of. iii Wat is U at? iv ind t tmpratur U,. wn t avrag nrgy U is af t avrag nrgy at z + / U + U U U Sov for / / / / 6 + and tn n 5

6 6 Probm 6 5 points T nrgy pr unit voum of a back body radiation and t radiation prssur p ar givn by U u A ; wr A is aconst ant, p u A gas of poton is usd as t working mdium of a at ngin. T gas undrgos an isotrma pansion at tmpratur from voum to. i Wat is t work don by t poton gas, W? If instad of a poton gas w us an ida gas of Ar atoms, wat is t work don in tis cas? PHOTOS : W ARGO ATOMS : W p d A p d d A d n A n ii ow t poton gas undrgos an adiabatic pansion from, to, wr /,, and t work don by t poton gas is W. Wat is W /W? Start from tst aw of du dq+ dw or an adiabatic procss dq W Us rsut du U U for W trmo dynamics nrgy wr dw is t work don O t gas Work don BY t gas dw dq du Work don BY t gas dw du from i abov A A W A A W A / OW Pug in t diffrnt ratios. onsrvation

7 7 Probm 7 5 points Considr an ida -dimnsiona gas of non-rativisitic ctrons spin ½ of dnsity n/a at zro tmpratur. T dnsity of stats for tis systm is givn by A m D ;. π i Driv an quation rating t rmi nrgy as a function of n, mass m, and otr fundamnta constants. D + µ / m d D π A d A m π ii Cacuat t avrag nrgy nrgy/partic in trms of t rmi nrgy. U U D d π A m iii Wat is t rmi nrgy in ctron vots if n m..5 J. s 8 π m 9 9. kg.6 J 8

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