Ideal Bose gas below condensation point occupies volume 1m³ at pressure 1Pa and temperature 1K?

Question

What is entropy of the gas?
(Hint: compress the gas isothermally to zero volume)

Virial theorem might also come handy

Answer 1

Since this question has been hanging around for a while, I thought I'd give it a try. I can plug and chug the numbers, but I don't understand that much beyond the perfect gas law.
Ref: http://en.wikipedia.org/wiki/Bose_gas#Thermodynamics

TS = U + PV - G

For T<< Tc G(free energy) = 0 , and

U (heat energy)=3/2PV, assuming perfect gas monatomic gas

therefore

TS= 5/2 PV
= 2.5 Newtons

I'd love to know the correct answer if I am wrong and any better references. Thx.