Consider N two-state systems at temperature T. All systems are identical, with one state at energy 0 and the other at energy ϵ.
Using the Boltzmann factor for the two states, compute a formula for the energy U(T) as a function of N,ϵ, and T.
Using C(T)=dU/dT, derive a formula for the heat capacity in terms of the same variables.
Use the formulas for U(T) and C(T) to answer the questions below, assuming that N=6.022 × 1023 and ϵ= 2.07 × 10-21 J for all questions:
1) Compute the internal energy U when T-200 K.
2) Compute the heat capacity when T-200 K.
3) Compute the heat capacity when T-250 K.
4) Compute the heat capacity when T-20 K.