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Problem Set 3
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This video contains problems on Statistical Mechanics and more videos on this course to follow. Do follow my page for more lessons: unacademy.com/user/sayantan34

Sayantan Bhattacharya
"Educating India For a Better Tomorrow" ||Ph.D student,U mass Lowell,Massachusetts,USA|| M.Sc,University Of Hyderabad,2018|| B.Sc,B.H.U,2016

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thanks for describ very deeply
1. Problem set (3) By Sayantan Bhattacharya

2. GATE2017 Consider N non-interacting, distinguishable particles in atwo-level system at temperature T . The energies of the levels are 0 and , where >0. In the high temperature limit kT>e ,what is the population of particles in the level with energy : e-ElkT) Probability is given by:P(e)= So, the population in a particular energy level will be given by: NP(E) ee/kT) 1 +e-Elk ->In the limit kTSe,e -lkT So, NP()N 1+1 2

3. GATE2015 The average energy U of a one dimensional quantum oscillator of frequency and in contact with a heat bath at temperature T is given by: . 2 Because,energy of quantum Harmonic oscillator is: 0 En ntho; and we know: U I Z) 2 sinh Bho 2sinh Pho

4. GATE 2014 . Consider a system of 3 fermions which can occupy any of the 4 available energy states with equal probability. The entropy of the system is: a) kgln2 b)2kgln2 c) 2k g In 4 d) 3kB In4

5. Number of ways that 3 fermions will adjust in 4 available energy is: 4 So,number of micostate: 2 4 We know that Entropy S=kB In So, In this case entropy: S-kBIn4 2kB In2

6. Thank you