Request:While I have provided the final answers for each of the problem statements, I need help with how to get to those problem statements. Can you please help me in that area with trying to answer as best as you can? Also, please only answer parts (d), (e), and (f). Thank youQuestion:Call placement of a particle in box A, “heads” and placement in box B, “tails.” Given one particle, there are two ways of arranging it, H or T. For two particles, there are four ways of arranging them, {HH, HT, TH, TT}. We can treat the microstates by considering each particle in order. For example, {H T H H} means the first particle is in box A, the second in box B, the third in box A and the fourth in box A. (a) List and count the ways of arranging three particles. Now consider four particles. What is the general formula for the number of arrangements versus the number of particles? (ANS. 2N)(b) How many arrangements correspond to having two particles in box A and one in box B? What is the probability of {2H, 1T}? (ANS. 3/8)(c) How many arrangements correspond to {2H, 2T}? {3H, 2T}? {4H, 2T}? {3H, 3T}? (ANS. N!/[(N – m)!m!])(d) List the macrostates and corresponding number of microstates for an eight-particle, two-box system. What portion of all microstates are parts of either 5:3, 4:4, or 3:5 macrostates? (ANS. 71%)(e) What is the change of entropy in going from a 5:3 macrostate to a 4:4 macrostate? (ANS. 3.08E-24 J/K)(f) Use Stirling’s approximation to estimate the change of entropy in going from a distribution of 50.1% of 6.022E23 in box A to a distribution of 50.001%, and from 50.001% to 50.000%. (ANS. 1.2E18 J/K)

Name: Request:While I have provided the final answers for each of the proble
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Description: Request:While I have provided the final answers for each of the problem statements, I need help with how to get to those problem statements. Can you please help me in that area with trying to answer as best as you can? Also, please only answer parts

The probability of an event that happens can be written as,

Answered: While I have provided the final answers…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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While I have provided the final answers for each of the problem statements, I need help with how to get to those problem statements. Can you please help me in that area with trying to answer as best as you can? Also, please only answer parts (d), (e), and (f). Thank you

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Call placement of a particle in box A, “heads” and placement in box B, “tails.” Given one particle, there are two ways of arranging it, H or T. For two particles, there are four ways of arranging them, {HH, HT, TH, TT}. We can treat the microstates by considering each particle in order. For example, {H T H H} means the first particle is in box A, the second in box B, the third in box A and the fourth in box A.

(a) List and count the ways of arranging three particles. Now consider four particles. What is the general formula for the number of arrangements versus the number of particles? (ANS. 2^N)
(b) How many arrangements correspond to having two particles in box A and one in box B? What is the probability of {2H, 1T}? (ANS. 3/8)
(c) How many arrangements correspond to {2H, 2T}? {3H, 2T}? {4H, 2T}? {3H, 3T}? (ANS. N!/[(N – m)!m!])
(d) List the macrostates and corresponding number of microstates for an eight-particle, two-box system. What portion of all microstates are parts of either 5:3, 4:4, or 3:5 macrostates? (ANS. 71%)
(e) What is the change of entropy in going from a 5:3 macrostate to a 4:4 macrostate? (ANS. 3.08E-24 J/K)
(f) Use Stirling’s approximation to estimate the change of entropy in going from a distribution of 50.1% of 6.022E23 in box A to a distribution of 50.001%, and from 50.001% to 50.000%. (ANS. 1.2E18 J/K)

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