# Statistical physics exam

Almost no one has answered.To take some external help, i write all questions here, maybe someone have an answer.

1)An aluminium cube cooled down to 90 Kelvin.At this point there is too many microstates available.how much heat we need, to increase these microstates in factor of 10$$^{10}$$ ? Answer in Joule unit.

2)In a simple October's forecast, days are tagged as rainy or shiny. Probability of a shiny day followed a shiny day is 0.8 .Probability of a rainy day followed by shiny air is 0.4 .Probability of 1st October to be shiny is 0.75
a)Find probability of 2nd and 3rd October be shiny.
b) If 1st October is shiny, what's probability is 3rd October to be rainy?

3)Two heat tanks, with constant volume and heat capacity, are used to power up a heat machine.Their startup temperature is T$$_{a}$$ and T$$_{b}$$.Assume that this heat machine gives as most possible product.(Net entropy change is zero).What is highest work that can be obtained from this machine?

4) A solid, has N count, 1/2 spinned atoms.In a enough temperature, these spins rotated randomly.But enough low temperatures, they are acted ferromagnetically.Due this reason, all spins are rotated same in T->0 K .In a rough given formula spin oriented addition to heat capacity is C(T)

C(T) = C$$_{1}$$ = ($$\frac{2T}{T_{1}}$$ - 1 ) if T$$_{1/2}$$ < T < T$$_{1}$$
( 1 and 1/2 are subscripts. Sown wrongly)
0 else

So take maximum probable of C$$_{1}$$ using entropy. (C subscript 1)

5) In a fermi gase,related to $$\epsilon$$$$_{f}$$ , state density D($$\epsilon$$$$_{f}$$) , show that heat capacity is written as

C$$_{v}$$ = $$\frac{\pi^{2}}{3}$$ D($$\epsilon$$$$_{f}$$) k$$^{2}$$ T