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What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?
- a)6kB In 3
- b)3kB In 2
- c)kB (2 In 3 + In 2 + In 5)
- d)3kB (ln 3 + ln 2)
Correct answer is option 'C'. Can you explain this answer?
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What is the maximum entropy of the system when six distinguishable par...
For maximum entropy particles are distributed equally.
The number of microstates for equal distribution.
The number of microstates for equal distribution.
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What is the maximum entropy of the system when six distinguishable par...
To find the maximum entropy of the system, we need to determine the number of microstates that correspond to each macrostate. In this case, the macrostate is defined by the distribution of particles over the energy states.
We can use the formula for the number of microstates in a macrostate with distinguishable particles and non-degenerate energy states:
Ω = (n + k - 1)! / (n! * (k - 1)!)
where Ω is the number of microstates, n is the total number of particles, and k is the number of energy states.
In this case, we have n = 6 particles and k = 3 energy states. Plugging these values into the formula, we get:
Ω = (6 + 3 - 1)! / (6! * (3 - 1)!)
= (8)! / (6! * 2!)
= (8 * 7 * 6!) / (6! * 2)
= 8 * 7 / 2
= 28
Therefore, there are 28 microstates corresponding to the macrostate with 6 particles distributed over 3 non-degenerate energy states.
The maximum entropy of the system is given by the logarithm of the number of microstates:
S_max = k_B * ln(Ω)
where k_B is the Boltzmann constant. Assuming k_B = 1, we have:
S_max = ln(28)
≈ 3.33
Therefore, the maximum entropy of the system is approximately 3.33.
We can use the formula for the number of microstates in a macrostate with distinguishable particles and non-degenerate energy states:
Ω = (n + k - 1)! / (n! * (k - 1)!)
where Ω is the number of microstates, n is the total number of particles, and k is the number of energy states.
In this case, we have n = 6 particles and k = 3 energy states. Plugging these values into the formula, we get:
Ω = (6 + 3 - 1)! / (6! * (3 - 1)!)
= (8)! / (6! * 2!)
= (8 * 7 * 6!) / (6! * 2)
= 8 * 7 / 2
= 28
Therefore, there are 28 microstates corresponding to the macrostate with 6 particles distributed over 3 non-degenerate energy states.
The maximum entropy of the system is given by the logarithm of the number of microstates:
S_max = k_B * ln(Ω)
where k_B is the Boltzmann constant. Assuming k_B = 1, we have:
S_max = ln(28)
≈ 3.33
Therefore, the maximum entropy of the system is approximately 3.33.
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What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer?
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What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer?.
What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the maximum entropy of the system when six distinguishable particles are distributed over three non-degenerate energy states of energies 0, ∈ and 2 ∈ ?a)6kB In 3b)3kB In 2c)kB (2 In3 + In 2 + In 5)d)3kB (ln 3 + ln 2)Correct answer is option 'C'. Can you explain this answer?.
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