/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q11.3P In statistical mechanics, we fre... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q11.3P (page 554)

In statistical mechanics, we frequently use the approximationN! = N In N-N, where N is of the order of Avogadro鈥檚 number. Write out ln N! using Stirling鈥檚 formula, compute the approximate value of each term for N = 1023 , and so justify this commonly used approximation.

Short Answer

Expert verified

The approximation is justified.

Step by step solution

01

Given Information

The approximation is N! =N InN- N .

02

Definition of the sterling’s formula.

Sterling鈥檚 formula is used to simplify formulas involving factorial.

n!鈻�nne-n2蟺苍.

03

Justify the approximation.

The approximation is N! = N In N - N.

The sterling鈥檚 formula is n!鈻�nne-n2蟺苍.

Take log on both side on the formula mentioned above.

The equation becomes as follows.

Inn!=Innne-n2蟺苍1+112n=Innn+Ine-n+Inn+In1+112n=nInn-n+12Inn+In1+112n

Substitute n = 1023 in the above equation.

The equation becomes as follows.

nInn=5.526脳1026where,n=1023Inn=55In1+112n鈮�0

Hence, In(n!) = nIn n - n .

The approximation is justified.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

A particle starting from rest at x=1 moves along the xaxis toward the origin.

Its potential energy is V=12mlnx. Write the Lagrange equation and integrate it

to find the time required for the particle to reach the origin.

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.

13. 鈭�-12349-4t21-t2dt

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.

8. 鈭�03249-4t21-t2dt

Use the term 1/(12p)in (11.5) to show that the error in Stirling鈥檚 formula (11.1) is < 10%for p > 1; < 1%for p > 10; < 0.1%for p > 100; < 0.01%for p > 1000.

Express as a function
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Electric Charge Field and Potential

Read Explanation

Medical Physics

Read Explanation

Fluids

Read Explanation

Dynamics

Read Explanation

Electricity

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.