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Problem 6.43 (Schroeder’s Intro to Thermal Physics)

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Problem 6.43

Some advanced textbooks define entropy by the formula

S=-k \sum_s P(s) \ln{P(s)}

where the sum runs over all microstates accessible to the system and P(s) is the probability of the system being in microstate s.

(a) For an isolated system, P(s) = 1/ \Omega for all accessible states s. Show that in this case the preceding formula reduces to our familiar definition of entropy.

(b) For a system in thermal equilibrium with a reservoir at temperature T, P(s) = e^{-E(s)/kT}/Z. Show that in this case as well, the preceding formula agrees with what we already know about entropy.

Solution:

Problem 6.43 (Schroeder's Intro to Thermal Physics)

Problem 6.43 Solution (Download)

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