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Consider a system of ideal bosons of zero spin (r = 1), within a container of volume V .
(a)Show that the entropy above the condensation tempera- ture To is given by
where
and
(b) Given N and V , what is the expression of the entropy below To? What is the entropy associated with the particles of the condensate?
(c)From the expression for the entropy, show that the specific heat at constant volume above To is given by
(d) Below To, show that the specific heat at constant volume is given by
(d) Given the specific volume v, sketch a graph of cV /kB versus λ-2 (that is, in terms of the temperature in convenient units). Obtain the asymptotic expressions of the specific heat for T → 0 and T → ∞. Obtain the value of the specific heat at T = To.
Physics
Note the asymptotic limits of the specific heat,
for T →0, in agreement with Nernst´s third law of thermody- namics, and
for T→∞ (z→0), according to the classical theorem of equipartition of energy. Also, note the value of the specific heat at the temperature of the Bose-Einstein condensation,
Sketch a graph of cV versus T.
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