Thermal Physics - Maxwell-Boltzmann Statistics

In a Maxwell-Boltzmann system with two states of energies ε and 2ε respectively, and a degeneracy of 2 for each state, the partition function is

A. e ^{−ε / kT}
B. 2e^{−2ε / kT}
C. 2e^{−3ε / kT}
D. e^{−ε / kT} + e^{−2ε / kT}
E. 2(e^{−ε / kT}+ e^{−2ε / kT})

(GR0177 #49)

Solution:

Canonical partition function:  Z = Σ_i e^−βE_i
β = 1/kT

For Maxwell-Boltzmann System:  Z = Σ_i g_i e^−βE_i
g_i = degeneracy

Thus, the partition function is
Z = 2e^−βε + 2e^−2βε = 2(e^{−ε / kT} + e^{−2ε / kT})

Answer: E