Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q31E (page 404)

Show that equation (9- 16) follows from (9-15) and (9- 10).

Short Answer

Expert verified

The value forkBTisln(1+NM)=hω0kBT

⇒kBT=hω0ln(1+NM)

Step by step solution

01

Given data

The angle between the vertices of a tetrahedron is109.5°, when the vertices of a tetrahedron are four vertices of a cube symmetrically chosen so that no two are adjacent.

02

Step 2:

Consider the cube in the given image. In order to find the angle between the vertices of a tetrahedron, let us form a tetrahedron using the following vertices.

03

To show the equation using natural logarithm.

MNhω0=hω0ehω0kBT-1

⇒MN=1ehω0kBT-1

⇒ehω0kBT-1=NM

⇒ehω0kBT=1+NMn

ln(ehω0kBT)=ln(1+NM)

⇒hω0kBT=ln(1+NM)

⇒ln(1+NM)=hω0kBT

⇒kBT=hω0ln(1+NM)

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

Consider a gas of atoms that might serve as a laser medium but that is inequilibrium, With no population inversions. A photon gas coexists with the atoms. Woulda photon whose energy is precisely the differencebetween two atomic energy states be more likely to be absorbed or to induce a stimulated emission or neither? We expect that inequilibrium the number. of atomsat different levels and the number of photons of a given energy should be stable. Is your answer compactible?

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.)

A. block has a cavity inside, occupied by a photon gas. Briefly explain what the characteristic of this gas should have to do with the temperature of the block.

The Stirling approximation.J!≡2πJJ+1/2e-J, is very handy when dealing with numbers larger than about100 . Consider the following ratio: the number of ways Nparticles can be evenly divided between two halves of a room to the number of ways they can be divided with60%on the right and40%on the left.

(a) Show, using the Stirling approximation, that the ratio is approximately4046065Nfor largeN.

(b) Explain how this fits with the claim that average behaviours become more predictable in large systems.

A scientifically untrained but curious friend asks, "When I walk into a room, is there a chance that all the air will be on the other side?" How do you answer this question?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Waves Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Fluids

Read Explanation

Turning Points in Physics

Read Explanation

Measurements

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