Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q2Q (page 507)

What is the advantage of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms (natural logarithm of the number of microstates)?

Short Answer

Expert verified

The advantage of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms (natural logarithm of the number of microstates) is that the natural logarithms are used to express large numbers.

Step by step solution

01

Significance of natural logarithm

There are 3 reasons for finding a natural logarithm.

  • A quantity “e”that happens frequently and unavoidably in nature.
  • Natural logarithms consist of simple derivativesamong all the other logarithms.
  • While calculating logarithms to the base, we first need to calculate “e” andmultiply it by a constant.
02

Step 2: Advantages of plotting the (natural) logarithm

The following are the advantages of plotting the (natural) logarithm of the number of ways of arranging the energy among the many atoms;

  • The natural logarithm can be moderately skeweddata more generally distributed to constant variance.
  • We have to use astraight line to allow the data to fall in a curved pattern to be generated.
  • We canexpress large numbersby using natural logarithms.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

List explicitly all the ways to arrange 2 quanta among 4 one-dimensional oscillators.

Figure 12.59 shows the distribution of speeds of atoms in a particular gas at a particular temperature. Approximately what is the average speed? Is the RMS (root-mean-square) speed bigger or smaller than this? Approximately what fraction of the molecules have speeds greater than 1000 m/s?

A microscopic oscillator has its first and second excited states 0.05eVand 0.10eVabove the ground-state energy. Calculate the Boltzmann factor for the ground state, first excited state, and second excited state, at room temperature.

Object A and object B are two identical microscopic objects. Figure 12.55 below shows the number of ways to arrange energy in one of these objects, as a function of the amount of energy in the object.


(Figure 12.55)

(a)When there are\({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 20}}}}{\bf{J}}\)of energy in object A, what is the entropy of this object? (b) When there are\({\bf{1}}{\bf{.4 \times 1}}{{\bf{0}}^{{\bf{ - 20}}}}{\bf{J}}\)of energy in object B, what is the entropy of this object? (c) Now the two objects are placed in contact with each other. At this moment, before there is time for any energy flow between the objects, what is the entropy of the combined system of objects A and B?

In order to calculate the number of ways of arranging a given amount of energy in a tiny block of copper, the block is modeled as containing 8.7×105independent oscillators. How many atoms are in the copper block?
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Measurements

Read Explanation

Electricity

Read Explanation

Geometrical and Physical Optics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Mechanics and Materials

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free