Two energy levels, 0 (non-degenerate) and ϵ (doubly degenerate), are available to N non-interacting distinguishable particles. If U is the total energy of the system, for large values of N the entropy of the system is \(k_B\left[N \ln N-\left(N-\frac{U}{\epsilon}\right) \ln \left(N-\frac{U}{\epsilon}\right)+X\right]\) In this expression, X is
1
\(-\frac{U}{\epsilon} \ln \frac{U}{2 \epsilon}\)
2
\(-\frac{U}{\epsilon} \ln \frac{2 U}{\epsilon}\)
3
\(-\frac{2 U}{\epsilon} \ln \frac{2 U}{\epsilon}\)
4
\(-\frac{U}{\epsilon} \ln \frac{U}{\epsilon}\)