Consider nn two-state systems at temperature tt. all systems are identical, with one state at energy 0 and the other at energy ϵϵ. using the boltzmann factor for the two states, compute a formula for the energy u(t)u(t) as a function of nn,ϵϵ, and tt. using c(t)=dudtc(t)=dudt, derive a formula for the heat capacity in terms of the same variables. use the formulas for u(t)u(t) and c(t)c(t) to answer the questions below, assuming that n=6.022 × 1023 and ϵ=ϵ= 2.07 × 10-21 j for all questions.