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Consider a systen of N non-interacting particles for which the energy of each particle can assume two and only two distinct values: 0 and E (E>0). denote N1 and N2 to be the occulation numbers of the levels 0 and E respectively. The fixed ttoal energy of the system is U.

a) Find the entropy of the system.

b) Find the temperature as a function of U. For what range of values is N1 is T<0?

c) In which direction does heat flow when a system of negative temerature is brought into thermal contact with a system of positive temperature? Why?

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