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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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BuyFindarrow_forward

Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
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

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