   # Entropy can be calculated by a relationship proposed by Ludwig Boltzmann: S = k In ( W ) where k = 1.38 × 10 −23 J/K and W is the number of ways a particular state can be obtained. (This equation is engraved on Boltzmann's tombstone.) Calculate S for the five arrangements of particles in Table 16- 1. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 16, Problem 108CP
Textbook Problem
20 views

## Entropy can be calculated by a relationship proposed by Ludwig Boltzmann: S = k   In ( W ) where k = 1.38 × 10−23 J/K and W is the number of ways a particular state can be obtained. (This equation is engraved on Boltzmann's tombstone.) Calculate S for the five arrangements of particles in Table 16- 1.

Interpretation Introduction

Interpretation: A relation between S and W is given. The value of S is to be calculated for the five arrangements of particles given in Table 16-1 .

Concept introduction: Ludwig Boltzmann proposed a probability equation that gives the relationship between entropy (S) and W , where W is the number of ways a particular state can be obtained.

### Explanation of Solution

The relation between S and W is,

S=kln(W)

Where,

• S is the entropy.
• k is the Boltzmann’s constant (1.38×1023J/K) .
• W is the number of ways a particular state can be obtained.

Refer to Table 16-1 .

For first arrangement,

The value of W for the first arrangement is 1 .

Substitute the values of k and W in the above equation.

S=kln(W)=(1.38×1023J/K)ln(1)=0_

The relation between S and W is,

S=kln(W)

Where,

• S is the entropy.
• k is the Boltzmann’s constant (1.38×1023J/K) .
• W is the number of ways a particular state can be obtained.

Refer to Table 16-1 .

For second arrangement,

The value of W for the second arrangement is 4 .

Substitute the values of k and W in the equation.

S=kln(W)=(1.38×1023J/K)ln(4)=1.91×1023J/K_

The relation between S and W is,

S=kln(W)

Where,

• S is the entropy.
• k is the Boltzmann’s constant (1.38×1023J/K) .
• W is the number of ways a particular state can be obtained.

Refer to Table 16-1 .

For third arrangement,

The value of W for the third arrangement is 4 .

Substitute the values of k and W in the equation

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
One way to evaluate any diet is to compare the total food amounts that it provides with those recommended by th...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Speed is a(n) ___ quantity. (2.2)

An Introduction to Physical Science

6.11 Define the term photon.

Chemistry for Engineering Students

List at least three major risk factors for developing severe hyperbilirubinemia.

Nutrition Through the Life Cycle (MindTap Course List)

A Carnot engine has a power output of 150 kW. The engine operates between two reservoirs at 20.0C and 500C. (a)...

Physics for Scientists and Engineers, Technology Update (No access codes included)

How is a free wave different from a forced wave?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin 