Thermodynamics: Building Blocks

The entropy is σ(N, U) = log g(N, U) = log 100 = 4.61 . There are no units, since entropy is a dimensionless quantity. Remember that log means ln !

Recall that S = k _B σ , so we calculate S = 6.360×10^-23 J/K .

Since = , a small increase in energy causing a decrease in entropy means that is negative. Therefore the temperature is negative! But doesn't that violate our understanding of absolute zero? It turns out that this solution really does exist, but only in systems of nuclear spins and similar examples where one cannot actually "feel" the temperature of the system.

We know that = . We approximate the partial derivative by , and can therefore determine that τ = 10^-20 J .

We use the relation τ = k _B T and find that T = 1000K .