Statistical Physics

172 10 Dense Gases – Ideal Gases at Low Temperaturechemical potential increases towards zero. If we use the original summation in(10.80) to determine the chemical potential, we can always find a solution: theright-hand side tends to zero as µ →−∞, and it diverges as µ → 0. However,it turns out that the right-hand side of the integral in (10.81) remains finiteeven at µ = 0, and the limiting value decreases as the temperature is lowered.The temperature at which the limiting value coincides with N is the criticaltemperature T c for Bose–Einstein condensation. For T>T c , the right-handside of (10.81) at µ = 0 is larger than the number of bosons, and the finitenegative chemical potential can be determined. On the other hand, for T