Upload File

d Æ Á o o r } o Ì u v v u } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hl 4/y1cl...

  • Home
  • Documents
  • D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
18
PHYS 3014: Statistical Mechanics Lecture Notes Part 13 Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics 2 Programme: B. Sc. Physics Semester: VI Dr. Ajai Kumar Gupta Professor Department of Physics Mahatma Gandhi Central University Motihari-845401, Bihar E-mail: [email protected]

Upload: others

Post on 17-Sep-2020

0 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai

PHYS 3014: Statistical MechanicsLecture NotesPart 13

Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics 2

Programme: B. Sc. PhysicsSemester: VI

Dr. Ajai Kumar GuptaProfessor

Department of PhysicsMahatma Gandhi Central

UniversityMotihari-845401, Bihar

E-mail: [email protected]

Page 2: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 3: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 4: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 5: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 6: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 7: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 8: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 9: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 10: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 11: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 12: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 13: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 14: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 15: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 16: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai
Page 17: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai

• Statistical Mechanics by R. K. Pathria

• Statistical Mechanics by B. K. Agarwal and M. Eisner

• An Introductory Course of Statistical Mechanics by P. B. Pal

References:

• Elementary Statistical Physics by C. Kittel

• Fundamentals of Statistical and Thermal Physics by F. Reif

• Statistical and Thermal Physics by R. S. Gambhir and S. Lokanathan

Page 18: D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] î · 2020. 4. 29. · 4-hL 4/Y1cL ØB-de so Rc)cL V 9/2 2— Title: Microsoft PowerPoint - Presentation13 Author: gajai

Thank You

For any questions/doubts/suggestions and submission of assignments

Write at E-mail: [email protected]


LGS Presentation Ne · KDD Z / > lZ d /> µ ] v U µ ] u v o ] v P } u v ] U o ] À } l v ] v P U u ] v v v Wh >/ tKZ

K ( ( ] } ( Z } u u ] ] } v ( } v v Æ u ] v ] } v U d Z ...€¦ · K ( ( ] } ( Z } u u ] ] } v ( } v v Æ u ] v ] } v U d Z ] µ À v v Z µ u

1n( g(V,=,~):V:,dX - ~(po~':,dXoden/Dr._Oden_Reprints/...1 (1. e, H is element u~ U,] (2.10) v V,w E U limrr- inf 0 Vv€u n n-lim inf

^ µ } ] v P / v ( } u ] } v } ~// & u Á } l ] À ( } u

SUPR - Clanton Project Acceptance and Update 09 16 2020 Fï } ( ð } v ( } } ( ( µ µ µ o U ] u } ( u } µ v v } Ç u ] v o v µ u ] } v } ( u v P u v X v Ç u v Z Æ } ] v À }

} v v ] } v µ v u } ] ( ] } u } o u v v µ u o ] u ] v } o ...€¦ · } v v ] } v µ v u } ] ( ] } u } o u v v µ u o ] u ] v } o ] } ] ] } v W î ì í ô ¶ . Ô Ï Ë Ð Ñ Õ

K v } v } u Ç v o } } v } u Ç

W µ ] } v } ( ^ · 2020. 5. 8. · Microsoft PowerPoint - Presentation17 Author: gajai Created Date: 5/7/2020 8:09:53 PM

P ] U / v X · 2018-12-11 · { K À ] v P v ] ] v P } u v Ç u v P u v ] v Z À o } u v } ( } µ v µ ] v P ] X

W µ o ] ^ À ] } u u ] ] } v U t v P opscwbapplication.in/pdf20/QUALIFIED_ROLL_NO_WISE_LIST.pdf · W µ o ] ^ À ] } u u ] ] } v U t v P o. W µ o ] ^ À ] } u u ] ] } v U t v P

CONSTRUCCIîN...> }o]u v ] v µ }v} ]u] v } µu]u } v ]U Z_ µ ]vÀ] ] (} u À µv } o } v o}]v ] µ U (} u o µ } ] v(} o o} v ] }V ^ o Àoµ ] v µ o]Ì o ]v] ]} µ v ] ] Ç µ u

i U ] v v } o } v P u } ] ( ] v µ u ] v Z v µ Á ] o o v

K ( ( ] } ( Z } u u ] ] } v ( } v v Æ u ] v ] } v U d Z ... · W r o r u v } o o P } ( v P ] v ] v P U W u ] X ^ o XE } X Z } o o E } X E u Z v l } µ v v µ o / v } u í í ó õ

m|;ubl !;rou| -m -u K m; t t |bl; b] t -u|;u b| v|uom] u;v t|v · v u v v

v v } v ] o v u o · Afoo I,QT ) I,QT — -u Vcr . Title: Microsoft PowerPoint - Presentation10 Author: gajai Created Date: 4/28/2020 12:56:39 PM

UITNODIGING ]Pv} ]vPu]o }Pv] À ]u ] u v v u v ]v ]u Ç · } }( }Pv] }vv ]Pv} ] ]v ]u Ç v (} ÁÇ }]u }À Z ] v . }v }( } o Á] Z }Pv] À ]u ] u v } u v ÁZ}uÇ v . ( }u u oÇ X

~ ' } À v u v } ( D Z Z v ] } ( , v ] Z Z } ( u Ç ^ } W ] u ' } À …...~ ' } À v u v } ( D Z Z v ] } ( , v ] Z Z } ( u Ç ^ } W ] u ' } À X , ] P ... ... K v

W } u } ] v P Z t o o v } ( D ] v U } Ç U v ^ ] ] d Z } µ ... · u v'E U , u ] o } v :W U ] o Ç ' X d Z ] u } ( v µ Æ ] v } v Z µ u v } P v ] ] À ( µ v ] } v v u v o Z o Z

Æ v u v } ( Z } ] o ] u } ( Z P µ ] } v } ( v P o Z ( } u Z P } Ç ......^ ] } ( Z } u u ] ( } À o } u v W } o ] Ç U h v ] E ] } v u v ( } } v } u ] v ^ } ] o ( ( ] U í U î ì

W } µ / v P ] v ^ u v o o P v ^ u v } o o ] } v W ] Ì Ì...v v } U W } v ] ~D / v o µ ] v P W } l U ^ o U ^ ] U D ] v o ^ o ~ ð ñ ì U ð ñ í U ð ñ î U v ] } Æ ] v ~ ï

Z & o µ P o Ì v v v Á ] º l v E EEhE' Ì µ u ...€¦ · v P v X / Z l v v U µ Z ] u E u v î X & Z U ] º l ] ] P v d ] o v Z u ] v P µ v P v ] v À } o o u h u ( v P v X

u ] o ^ Ç u } ] µ u > v } v ( v v U > v h v ] À ] Ç U h v ... · > v } v ( v v U > v h v ] À ] Ç U h v ] < ] v P } u U í í r í î l î l î ì í õ ^ Ç u

v P o v W ] u } ( u } o ] Ç } ( Z } u ] v o ] v l } Z Ks/ r í õ v u ] · 2020. 6. 13. · o } À ] X } P n v P o v W ] v ] v ] u } o ] Ç u } v P Z } u ] v ï } v ] v P Z ] U }

D Æ Á o o r } o Ì u v v U } r ] v ] v v & u ] r ] ^ ] ] í · Microsoft PowerPoint - Presentation12 Author: gajai Created Date: 4/28/2020 12:51:30 PM

^ µ } ] v P ] v ( } u ] } v · 2019. 7. 31. · ^ í ^ µ } ] v P ] v ( } u ] } v ^ Ç v Z ] } ( Ç u u ] ^ W } o Ç u Ç W } r } o Ç u ] ] } v D } ] ( ] ] } v v W Z } } u ] W }

New v v µ o ^ µ À Ç } ( D ] v ] ] o } ] v u v v Z } ] v u v Ç Z } u u ] ] } v ( } W ... · 2019. 9. 10. · ó ' E Z d o ñW }]v u v v r }]v u v ÇP v U }o v } Çîìíñríò

C.V. arabic 30-9-2020 · 2020. 9. 30. · K ] } v Z v v P ] v ] v P u v P u v U 3ODQQLQJ DQG 6FKHGXOLQJ U d } o Y µ o ] Ç D v P u v ~dYD U } µ ] } v u v P u v v Z u Z } } o } P

u } ( ] } ] v ] } ] W u } ( Z , µ u v' µ } v v } Z u } Z P ] Z ] Z ] } o ......^ ] P v ] ( ] v ] o P } Á Z ] v Z i i µ v µ u v ] o µ u U u } o Ç ] v Z ] o Z } µ o o X U W

v ] µ ] } v o & u Á } l } ( Z v ] r } µ ] } v } u u ] } ( Z W o ] u v ......W } o ] Ç ] ( ^/ v ] µ ] } v o & u Á } l } ( Z v ] r } µ ] } v } u u ] } ( Z W o ] u v } ( D }

^ Æ u ] v ] } v } U ' µ i / v u ] Á ] v P Æ u ] v ] } v Z µ o î ì í ó } v ...sebexam.org/.../IntermediateDrawingExamResult2017.pdf^ Æ u ] v ] } v } U ' µ i / v u ] Á ]

0...E o }o P]} Z]oo o } ^}v} ~ K , U o]u o u v ] v oZ (} u/v Po o µ ] vD ]^µ ]} vîììóU (} u } ]ou v }v o U ]}]v] ]}o µ ] v µWov F > }o]u v ] v µ }v} ]u] v } µu

s } o µ u î W v À ] } v u v o / u u v Z } · ^ ] o ^ v < v } µ ~> v À ] } v ' } µ

µ ] v ] P W u ] µ ] v K v o ] v ] · 2020-04-10 · } ( Ç } v À Ç u o Z ] U } Z v P u U µ Z Z v P } } o o u } µ v U ] v ] } v } µ v U X

h v ] v } ( } o ] } v D Z o Ç l v } Á o P } ( ( Ç u v P u ... · , wz< î ì ñ Ç } µ v ] u o U u ] v v v v u v } P u ] v u µ o µ Ç u , W Z ï ì ð

v } · v u U µ ] ( ( v P µ u v Ç ~ } À o } ] v P tt } l ( } o o ( µ v ] } v U v } i µ o u u