Entropy, heat, and temperature are related through the following expression:

This expression can be rearranged to provide an expression for T in terms of heat and weight (W, the number of microstates for a given configuration of energy):

a. Substitute the expression for W for a two-level system into the equation to define T in terms of heat, Boltzmann€™s constant, the total number of two-state particles (N), and the number of particles in the excited state (n).

b. Determine the temperature for a two-level system where N = 20, the separation between energy levels is 100 cm^ˆ’1, and q_rev = n (100. cm^-1). To perform this calculation, determine q_rev and lnW for n = 0 to 20 for integer values of n. The temperature can then be determined by expressing Δq_rev and ΔlnW as:

c. Inspect the dependence of T on n. Can you explain this dependence?

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