
(a)
Interpretation: In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.
Concept Introduction:
A
Where
The entropy and thermodynamic probability is related by Boltzmann equation. As the number of possible arrangements increases the entropy also increases.
Where,
(a)

Answer to Problem 14.6QP
The number of possible arrangements of the system with barrier
The entropy for the given system,
The number of possible arrangement of the system without barrier
The entropy for the given system,
Explanation of Solution
To record the given data
The number of particles in the system,
The degeneracy of the system with the barrier,
The degeneracy of the system without the barrier,
To calculate the probability of arrangements of particles in the system with barrier
The probability of arrangements of the particles in the system with barrier is 1024
There are ten particles in the system. With the barrier there are two cells in the system. That is degeneracy is two. On plugging in the values of
Explanation:
To calculate the entropy of the given system with the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
Explanation:
To calculate the probability of arrangements of particles in the system without barrier
The probability of arrangement of particles in the system without barrier is
There are 10 particles in the system. Without the barrier there are four cells in the system. That is degeneracy is four. On plugging in the values of
Explanation:
To calculate the entropy of the given system without the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
The number of possible arrangements and the entropy for the given setup has been calculated in accordance with the given conditions.
(b)
Interpretation: In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.
Concept Introduction:
A thermodynamic system can have degenerate and non degenerate energy levels. There can be different possible arrangements of the particles in the various energy levels. These possible arrangements are defined as thermodynamic probability
Where
The entropy and thermodynamic probability is related by Boltzmann equation. As the number of possible arrangements increases the entropy also increases.
Where,
(b)

Answer to Problem 14.6QP
(b)
The number of possible arrangements of the system with barrier
The entropy for the given system,
The number of possible arrangement of the system without barrier
The entropy for the given system,
Explanation of Solution
To record the given data
The number of particles in the system,
The degeneracy of the system with the barrier,
The degeneracy of the system without the barrier,
To calculate the probability of arrangement of particles in the system with barrier
The probability of arrangement of particles in the system with barrier is
There are fifty particles in the system. With the barrier there are two cells in the system. That is degeneracy is two. On plugging in the values of
To calculate the entropy of the given system with the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
To calculate the probability of arrangement of particles in the system without barrier
The probability of arrangement of particles in the system without barrier is
There are fifty particles in the system. Without the barrier there are four cells in the system. That is degeneracy is four. On plugging in the values of
To calculate the entropy of the given system without the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
The number of possible arrangements and the entropy for the given setup has been calculated in accordance with the given conditions.
(c)
Interpretation: In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.
Concept Introduction:
A thermodynamic system can have degenerate and non degenerate energy levels. There can be different possible arrangements of the particles in the various energy levels. These possible arrangements are defined as thermodynamic probability
Where
The entropy and thermodynamic probability is related by Boltzmann equation. As the number of possible arrangements increases the entropy also increases.
Where,
(c)

Answer to Problem 14.6QP
(c)
The number of possible arrangements of the system with barrier
The entropy for the given system,
The number of possible arrangement of the system without barrier
The entropy for the given system,
Explanation of Solution
To record the given data
The number of particles in the system,
The degeneracy of the system with the barrier,
The degeneracy of the system without the barrier,
To calculate the probability of arrangement of particles in the system with barrier
The probability of arrangement of particles in the system with barrier is
There are hundred particles in the system. With the barrier there are two cells in the system. That is degeneracy is two. On plugging in the values of
To calculate the entropy of the given system with the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
To calculate the probability of arrangement of particles in the system without barrier
The probability of arrangement of particles in the system without barrier is
There are hundred particles in the system. Without the barrier there are four cells in the system. That is degeneracy is four. On plugging in the values of
To calculate the entropy of the given system without the barrier
Entropy of the system with barrier is found to be,
The entropy of the system is calculated by plugging in the values of
The number of possible arrangements and the entropy for the given setup has been calculated in accordance with the given conditions.
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Chapter 14 Solutions
Chemistry: Atoms First
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