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# THERMODYN & STAT MECH PHYS 4420

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This 8 page Class Notes was uploaded by Diamond Kirlin MD on Monday October 19, 2015. The Class Notes belongs to PHYS 4420 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/224885/phys-4420-rensselaer-polytechnic-institute in Physics 2 at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15

PHY S4420 TIEERMODYNAMICS K STATISTICAL MECHANICS SPRING 2006 Nega ve Abxabmz Temperwmnz Nuelel study statrstaeally The Hamrltoman for the mteraetror between amagrretae moment and a m u h a dl V wd tth eomporlerlt H 4mg ofthe 5pm operator The energy levels forthls system are glyer by w ere m ean have values of11117 2 1and1ls the 5pm ofthe nucleus under exammatlor flaEH y Hm717my H Then the transltaor frequency ls a yH The probablllty offlndmg anueleus m a state ofenergy Emls m 7 m E u 25uEeE2 1 52 sum 73a a 5mm 1 42 5 5mm la 4 suEeuz 3Q 725mm 50 u m U2 as no Prnh Temperature 300 K r t s m state Tu r t Tu th t th states Th quot temperature Ttrs foundthat the system does come to equrlrlmum for the rmelear ease andthe energy r rs hot 25mm 52 seem 732 g 5mm em 5 5mm m 45mm 3Q 725uEeu2 52 u U1 as no Prnh Temperature 300K r A r r m r nmhhnuw F mm mm m MW m m m emselves by temperature u y y would m y wn r m rrrfrmcevalue Further L A w m mum to highest energy rs 70 aw gt roe aew j Interestingly H 1 Adiabatic Demagnetization When a magnetic eld is turned on a system of spins goes into a lower energy state a state of negative energy so it gives off energy If this is done while the entire system is in contact with a constant temperature heat reservoir the temperature can be held constant Then the magnetic material can be isolated from the reservoir and the magnetic eld can be turned off adiabatic demagnetization The system of spins rises to a state of zero energy so it must absorb energy or heat from its surroundings That means that the crystal lattice loses energy and cools down This is the principle method used to cool to ultra low temperatures PHYS 4420 THERMODYNAMICS amp STATISTICAL MECHANICS SPRING 2006 Class Activity Class 7 February 7 2006 Name Do problem 73 from the textbook Since many of you do not have the textbook with you it is given here Hint Do not believe all the answers in the back of the book Calculate the change in the entropy of the universe as a result of each of the following processes a A copper block ofmass 04 kg and heat capacity 150 JK at 100 C is placed in a lake at 10 C b The same block at 10 C is dropped from a height of 100 m into the lake c Two similar blocks at 100 C and 10 C are joined together Hint See problem 78 or today s lecture notes d One kilomole of a gas at 0 C is expanded reversibly and isothermally to twice its initial volume e One kilomole of a gas at 0 C is expanded reversibly and adiabatically to twice its initial volume PHYS 4420 THERMODYNAMICS amp STATISTICAL MECHANICS SPRING 2006 Class Activity Class 7 February 7 2006 Name ANSWERS Do problem 73 from the textbook Since many of you do not have the textbook with you it is given here Hint Do not believe all the answers in the back of the book Calculate the change in the entropy of the universe as a result of each of the following processes a A copper block ofmass 04 kg and heat capacity 150 JK at 100 C is placed in a lake at 10 C b The same block at 10 C is dropped from a height of 100 m into the lake c Two similar blocks at 100 C and 10 C are joined together Hint See problem 78 or today s lecture notes d One kilomole of a gas at 0 C is expanded reversibly and isothermally to twice its initial volume e One kilomole of a gas at 0 C is expanded reversibly and adiabatically to twice its initial volume r dT T 283 K a ASHES C j C ln 150 JK 1117 414 JK T 373 ASW g CPT1 T2 2 150 JK373 K 283 K MINK T T 283 K ASuniveme ASblock ASlake 7 AS1miverxe b ASblock 0 mighz 04kg98ms2100 m ASW 139 JK T2 T2 283 K ASuniveme ASblock ASlake 0 AS1miverse JK c ASWS 2CP1n 2150 JK1n w 285 JK 2T1T2 2 373 K283 K Asmrroundings 0 AS universe ASblockx ASmrroundirng K 0 A Svunivervei5 lIlt d Since the process is reversible ASmivme 0 For the isothermal process dU 0 so dQ dW PdV 2V L W Edi1 2V LVR1n Rln2 576gtlt103 JK VD T VD V T VD V V0 7 576 x103 JK gas AS mrroundings e Since the process is reversible Asumvme 0 AS 0 and AS gas surroundings 7 0 PHYSJAZO TIEERMODYNAMICS R STATISTICAL MECHANICS SPRING 2005 Meamn39ng yby Ruchhmd Method Drop a steel ball ofmass m down an exaetly frttrhg glass tube of m eross secuonal areaA rhto a large sealed ask ofvolume VD eohtarhrhg an at atmospherre pressure Pu The gas m the ask erI be Compressed and exert an upward force on the ball A Apply Newton39s 2quot 1awto the ball emgAAPmy whereyrs the vemcal dASLanCe from the porht atwhreh the ball rs released The posrtrve duecuon ofyxs upward a PM AP7 AV andsmce PWE V p and BVV W t E PM new 5V V V V VI Pn 7mgA 47M my and AVAy so n P A 4A mg 7 y my 3A2 my y y mg 0 Va 3A2 0 y men y E PA Let y quot o so yo yg0 mVr Frheny Change the ongm so that y y and y y39 Thrs shxfts the ohgrh to the ethanm posrtroh of the ball Theh 39vquota 2y 0 Thrs rs srrhpIe harmom mohoh aboutye 0 so 2 2 2 472 E FHA andfmally y Wquot 21 T my FHA2 T We heedto measure T the penod ofthe mohoh to determrhe y Turn lhepagzer over 7712quot is man an the bark mV0 27139 2 7 P0142 T J The values of the constants in the equation above are m 167 x10392 kg V0 109 x10392m3 m 10 L P0 101 x 105 Nm2 A 201 x 10394 m2 diameter 16 mm Record the data taken in class here T average 7 Use the data collected in class to nd y

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