   Chapter 17, Problem 106CP

Chapter
Section
Textbook Problem

# 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

Explanation

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

### 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

#### The DRI are for all people, regardless of their medical history. T F

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

#### Define the following terms: a. chromosome b. chromatin

Human Heredity: Principles and Issues (MindTap Course List)

#### True or false? Some humans are genetically modified.

Biology: The Unity and Diversity of Life (MindTap Course List)

#### What sediments accumulate most rapidly? Least rapidly?

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