The probability of a system being in the ith microstate is given by $P_i = frac{e^{-eta E_i}}{Z}$, where $E_i$ is the the energy of ith microstate. Show that the entropy is given by $frac{S}{K_B} = ln Z + eta U$, where $U$ is the internal energy given by $U = sum_i P_i E_i$

          The probability of a system being in the ith microstate is given by $P_i = frac{e^{-eta E_i}}{Z}$, where $E_i$ is the the energy of ith microstate. Show that the entropy is given by $frac{S}{K_B} = ln Z + eta U$, where $U$ is the internal energy given by $U = sum_i P_i E_i$

$The probability of a system being in the ith microstate is given by Pi = frace^-eta EiZ, where Ei is the the energy of ith microstate. Show that the entropy is given by fracSKB = ln Z + eta U, where U is the internal energy given by U = sumi Pi Ei$

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Supreeta N

05/20/2023

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The probability of a system being in the ith microstate is given by, where is the the energy of ith microstate. Show that the entropy is given by, where is the internal energy given by