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 be $\frac{2}{3}$ is to $\frac{1}{3}$ .

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

Formula used

Formula is:

$N_{R} = \frac{2}{3} N$

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

Describe the macrostate of the system

(a)

In this two-sided room with six particles, since there are four particles on the right side, then $N_{R}$ must be:

$N_{R} = \frac{2}{3} N$

Where $N = 6$ Now for this $N_{R} = \frac{2}{3} N$ macro-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 $\frac{2}{3}$ is to $\frac{1}{3} .$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Formula used

Given information from question

Describe the macrostate of the system

Calculate the possible microstates corresponding to this macrostate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Famous Physicists

Physical Quantities And Units

Electricity

Fluids

Turning Points in Physics

Study anywhere. Anytime. Across all devices.