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Introduction to Thermodynamics and Statistical Physics phần 7

Hãy VA1 = Nτ A / p (VB1 = Nτ B / p) là khối lượng ban đầu của tàu (B) và để cho VA2 (VB2) là khối lượng cuối cùng của tàu A (B) Trong điều kiện nhiệt độ cuối cùng của cả hai mạch, được ký hiệu là f τ, một trong những đã VA2 = VB2 = Nτ f. p giữa tổng năng lượng của U hệ thống và các Fermi năng lượng εF. | 2.9. Solutions Set 2 Using pV Nt yields n 1 Td - Tc 1 P2 Vd - V Tb - Ta P1 Vb - Va 2.295 Along the isentropic process pVY is constant where Y Cp Cv thus 1 P2 P1 Y Va - Vb 1 - P2 P1 Vb - Va P1 2.296 28. No heat is exchanged in the isentropic processes thus the efficiency is given by Q_ Qh 1 Qc -I Qa--b 1 cv Td - Tc cv Tb - Ta 2.297 Since tV7 1 remains unchanged in an isentropic process where cp cv 2.298 one finds that V Ý 2.299 TdV -1 Ta 7-1 2.300 or Tc Td V r 2.301 thus n 1 - Vr 2.302 29. Let VA1 Nta p VB1 Ntb p be the initial volume of vessel A B and let Va2 Vb2 be the final volume of vessel A B . In terms of the final temperature of both vessels which is denoted as Tf one has VA2 VB2 P 2.303 Eyal Buks Thermodynamics and Statistical Physics 95 Chapter 2. Ideal Gas The entropy of an ideal gas of density n N V which contains N particles is given by N logV- 1 where nQ M r or as a function of T and p 2.304 2.305 o N flog T 2 5 ỵ p 2 2.306 Thus the change in entropy is given by Ao ofinal initial 5N T log T T f T at B 2.307 In general for an isobaric process the following holds Q W AU p V2 - V1 cv t2 - T1 2.308 where Q is the heat that was added to the gas W the work done by the gas and AU the change in internal energy of the gas. Using the equation of state pV Nt this can be written as Q N cv t2 - T1 . 2.309 Since no heat is exchanged with the environment during this process the following holds Qa Qb 0 where Qa N Cv Tf - Ta 2.310 Qb N Cv tf - Tb 2.311 thus T A T B 2.312 Tf 2 and therefore Ao 5N log Tb 2 . 2 4tatb 2.313 Eyal Buks Thermodynamics and Statistical Physics 96 3. Bosonic and Fermionic Systems In the first part of this chapter we study two Bosonic systems namely photons and phonons. A photon is the quanta of electromagnetic waves whereas a phonon is the quanta of acoustic waves. In the second part we study two Fermionic systems namely electrons in metals and electrons and holes in semiconductors. 3.1 Electromagnetic Radiation In this section we study an .