**Problem : **

Take a system with a multiplicity function such that *g*(*N*, *U*) = 100. What
is the entropy of the system, and in what units?

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!

**Problem : **

What is the conventional entropy *S* of the system in the above problem?

Recall that *S* = *k*_{B}*σ*, so we calculate *S* = 6.360×10^{-23}*J*/*K*.

**Problem : **

Say that in a large system, adding one Joule of energy increases the
entropy by 10^{20}. What is the approximate temperature of the
system?

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

**Problem : **

What is the temperature in kelvin of the system in the previous problem?

We use the relation *τ* = *k*_{B}*T* and find that *T* = 1000*K*.