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Chapter 9: Q20E (page 403)

A two-sided room contains six particles, a, b, c, d, e and f, with two on the left and four on the right.

(a) Describe the macrostate.

(b) Identify the possible microstates. (Note: With only six particles, this isn't a thermodynamic system, but the general idea still applies, and the number of combinations is tractable.)

Short Answer

Expert verified

a) The macrostate of the system is the particle concentration on the right side is twice as large as that on the left side. As such, the corresponding ratio must be23 is to13.

b) The possible microstates corresponding to this macrostate are:

ab cdef

ac bdef

ad bcef

ae bcdf

af bcde

bc adef

bd acef

be acdf

bf acde

cd abef

ce abdf

cf abde

de abcf

df abce

ef abcd

Step by step solution

01

Formula used

Formula is:

NR=23N

02

Given information from question

In this problem, we are given six particles: a, b, c, d, e and f inside a two-sided room that are arrange in a way that four particles are on the right region and two are on the left region

03

Describe the macrostate of the system

(a)

In this two-sided room with six particles, since there are four particles on the right side, thenNR must be:

NR=23N

WhereN=6 Now for this NR=23Nmacro-state, the particle concentration on the right side is twice as large as that on the left side. As such, the corresponding ratio must be 23is to13.

04

Calculate the possible microstates corresponding to this macrostate

The possible microstates corresponding to this macrostate are:

ab cdef

ac bdef

ad bcef

ae bcdf

af bcde

bc adef

bd acef

be acdf

bf acde

cd abef

ce abdf

cf abde

de abcf

df abce

efabcd

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