Problem set (3) By Sayantan Bhattacharya

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

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

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

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

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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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Ankit kumar

7 months ago

thanks for describ very deeply

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