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change in entropy of the coins?

change in entropy of the coins?

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P-6 Please I need help with this question needed very clearly and step by step explanation and NEEDED ONLY TYPED SOLUTIONS PLEASE NO HANDWRITTEN please, will be really appreciated for your help.

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Question-1

a) Suppose you have four coins, all with tails up. You now rearrange them so two heads and two tails are up. What was the change in entropy of the coins?

(b) Suppose your system is the 100 coins of Table 20-1; what is the change in entropy of the coins if they are mixed randomly initially, 50 heads and 50 tails, and you arrange them so all 100 are heads? 

TABLE 20-1 Probabilities of Various Macrostates for 100 Coin Tosses Масrostate Number of Microstates Heads Tails Probability 100 1 7.9 x 10-31 99 1 1.0 x 10 1.7 x 103 7.9 x 10 29 1.4 x 10-17 4.2 x 10-10 90 10 80 20 5.4 x 1020 1.4 x 1028 6.1 x 1028 1.0 x 1029 60 40 0.01 55 45 0.05 50 50 0.08 45 6.1 x 1028 1.4 x 1028 55 0.05 40 60 0.01 20 80 5.4 x 1020 4.2 x 10 10 10 90 1.7 x 1013 1.4 x 10-17 7.9 x 10 29 7.9 x 10-31 1 99 1.0 x 10 100
Transcribed Image Text:TABLE 20-1 Probabilities of Various Macrostates for 100 Coin Tosses Масrostate Number of Microstates Heads Tails Probability 100 1 7.9 x 10-31 99 1 1.0 x 10 1.7 x 103 7.9 x 10 29 1.4 x 10-17 4.2 x 10-10 90 10 80 20 5.4 x 1020 1.4 x 1028 6.1 x 1028 1.0 x 1029 60 40 0.01 55 45 0.05 50 50 0.08 45 6.1 x 1028 1.4 x 1028 55 0.05 40 60 0.01 20 80 5.4 x 1020 4.2 x 10 10 10 90 1.7 x 1013 1.4 x 10-17 7.9 x 10 29 7.9 x 10-31 1 99 1.0 x 10 100
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