When 100 coins are tossed, there is one way in which all can come up heads. There are 100 ways in which only one tail comes up. There are about
The change in entropy of coins when 100 coins placed in the box with only one head up is shaken and then there are
Answer to Problem 19SP
Solution:
Explanation of Solution
Given data:
There is one way in which all heads come up if 100 coins are tossed.
There are100 ways in which only one tail comes up if 100 coins are tossed.
There are about
A total of 100 coins are placed in a box with one head up.
The coins are shaken until there are
Formula used:
Entropy is calculated by the formula:
Here,
The number of ways in which a number of things can be arranged is calculated by the formula:
Here,
Explanation:
Recall the expression for calculating the number of ways in which the 100coins can be arranged with one head up:
Understand that thenumber of ways is to be calculated for the case in which one coin with its head facing up can be arranged at100 different places.
Substitute
Understand that the number of ways in which 100 coins can be arranged with one coin withits head facing up is equal to the number of ways in which one coin with its head facing up can be arranged at100 different places. Therefore,
Substitute
Here,
Recall the expression for entropy when 100 coins are arranged with one head up:
Here,
Consider the standard value of Boltzmann constant is
Substitute
Recall the expression for entropy when 100 coins are arranged with
Here,
According to the problem, 100 coins can be arranged with
Substitute
Calculate the change in entropy when the box is shaken till there are
Here,
Substitute
Conclusion:
The change in entropy is
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Chapter 21 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)