Consider a system of N free particles in which the energy of each particle can assume only two distinct values, 0 and E (E > 0). Denote n0 and n1 the occupation numbers of the energy levels 0 and E, respectively. The total energy of the system is U. (i) Find the entropy of such a system. (ii) Find the most probable values of n0 and n1 and find the mean square fluctuations of these quantities. (iii) Find the temperature as a function of U and show that it can be negative.
Consider a system of N free particles in which the energy of each particle can assume only two distinct values, 0 and E (E > 0). Denote n0 and n1 the occupation numbers of the energy levels 0 and E, respectively. The total energy of the system is U. (i) Find the entropy of such a system. (ii) Find the most probable values of n0 and n1 and find the mean square fluctuations of these quantities. (iii) Find the temperature as a function of U and show that it can be negative.
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Consider a system of N free particles in which the energy of each particle
can assume only two distinct values, 0 and E (E > 0). Denote n0 and n1
the occupation numbers of the energy levels 0 and E, respectively. The
total energy of the system is U.
(i) Find the entropy of such a system.
(ii) Find the most probable values of n0 and n1 and find the mean square
fluctuations of these quantities.
(iii) Find the temperature as a function of U and show that it can be
negative.
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