Question

18. 11. A system of particles occupying single-particle states and obeying Boltz, mann statistics is in thermal contact with a heat bath at temperature 1. The populations are: 3.1% for 0.0281 eV: 8.5% for 0.0195 eV: 23% for 0.0109 eV 63% for 0.0023 eV. What is the temperature of the system?

Answer 1

Sol's Given date Energylev population E: 0.0281 3.17.20031 +5,20.0281012 0.0281x1602 x16 Trg % =0.08st Exo.0195212 00195*160221691 E20-0195 Ez a 0.0109 Eys 0.0023 23% 20:23 by E220.0109 EVO 0 0109 x1 602x1699 6342063 E420-001-32V20 63 E420-002.3eva O.OOL 3x1602x10191 distribution we know that the formule N(E) is the of particles in high energy state E NCE)= Noe tot boltzman is 7NCE) Nose fa E + NCG), e RT. 0.031 Ewhere ka 1.3506x17 235/K ! z 0.031 4- In (0.031) & Tis. E en (0.031) -0.0281 1602*1019 13806x16 23x en (0.031) 93.86K = 2. TI = 93.868

Similarly of Tza ~ Ez kan (0.085) -0.0195*1-60210'9 1:3806x1023 ln (0.085) 91.79K T2 = 91.79k kan (6:23) -0.0 109 x 11602 X169 1380681023x en (0.23) = 8606K " T3286.066 & Tao - E4 kln (0.63) -0.0023 X1602x1079 1:3806x16 23 x ln (0.63) = 57.76k 3. Tur 57.76k tempere tre of the system (T) Tit T2+ Tht Ty - 93.86 +9179+86.06+57176 - The 7 8237K 1. The temperature of the system (T) = 82.37k/