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Suppose you flip four fair coins.(a) Make a list of all

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 1P Chapter 2

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 1P

Suppose you flip four fair coins.

(a) Make a list of all the possible outcomes, as in below Table.

(b) Make a list of all the different “macrostates” and their probabilities.

(c) Compute the multiplicity of each macrostate using the combinatorial formula 2.6, and check that these results agree with what you got by brute-force counting.

TABLE:  A list of all possible “microstates” of a set of three coins (where H is for heads and T is for tails).

Penny

Nickel

Dime

H

H

H

H

H

T

H

T

H

T

H

H

H

T

T

T

H

T

T

T

H

T

T

T

Step-by-Step Solution:

Step 1 of 5</p>

(a) Make a list of all the possible outcomes, as in below Table.

All the possible outcomes (microstates) for the four coils is shown in below table.

Coin 1

Coin 2

Coin 3

Coin 4

H

H

H

H

H

H

H

T

H

H

T

H

H

H

T

T

H

T

H

H

H

T

H

T

H

T

T

H

H

T

T

T

T

H

H

H

T

H

H

T

T

H

T

H

T

H

T

T

T

T

H

H

T

T

H

T

T

T

T

H

T

T

T

T

For head= H and Tail = T, hence the total number of microstates =16=.

Step 2 of 2

Chapter 2, Problem 1P is Solved
Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

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