34 PROBLEMS4.70 Bose Condensation Critical Parameters (MIT)
Consider an ideal Bose gas of N particles of mass and spin zero in a
volume V and temperature above the condensation point.
a) What is the critical volume below which Bose–Einstein condensa-
tion occurs? An answer up to a numerical constant will be sufficient.
b) What is the answer to (a) in two dimensions?4.71 Bose Condensation (Princeton, Stony Brook)
Consider Bose condensation for an arbitrary dispersion law in D dimensions
(see Figure P.4.71). Assume a relation between energy and momentum of
the form Find a relation between D and for Bose condensation
to occur.4.72 How Hot the Sun? (Stony Brook)
The total radiant energy flux at the Earth from the Sun, integrated over
all wavelengths, is observed to be approximately erg
The distance from the Earth to the Sun, is cm and the solar
radius, is Treating the Sun as a“blackbody,” make a
crude estimate of the surface temperature of the Sun (see FigureP.4.72).
To make the numerical estimate, you are encouraged to ignore all factors of
2’s and to express any integralsthat you mighthave in dimensionless
form, and to take alldimensionlessquantities tobe unity.