Suppose you toss 100 coins starting with 60 heads and 40 tails, and you get the most likely result, 50 heads and 50 tails. What is the change in entropy?

Strategy

Noting that the number of microstates is labeled W in Table 15.4 for the 100-coin toss, we can use ΔS = S_f - S_i = klnW_f - klnW_i  to calculate the change in entropy.

Data given in Table 15.4

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Macrostate Heads Tails 100 99 95 90 75 60 55 51 50 0 1 5 10 25 40 45 49 50 Number of microstates (W) 1 1.0x10² 7.5x107 1.7x1013 2.4x1023 1.4x1028 6.1x1028 9.9x1028 1.0×102⁹