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A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is 4∈, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.
Correct answer is '6.1 to 6.3'. Can you explain this answer?
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A microcanonical ensemble consists of 12 atoms with each taking either...
The number of ways having total energy 4∈, out of 12 atom is
12 x 11 x 10 x 9 / 4 x 3 x 2 = 495
Hence, entropy, S = kB lnw = kB In(495) = kB (6.204) = 6.204kB
Hence, entropy, S = kB lnw = kB In(495) = kB (6.204) = 6.204kB
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A microcanonical ensemble consists of 12 atoms with each taking either...
To find the possible configurations of this microcanonical ensemble, we need to distribute the total energy of 4 among the 12 atoms.
Since each atom can take either energy 0 state or energy 1 state, there are two possibilities for each atom. Therefore, the total number of configurations is given by 2^12 = 4096.
However, we need to find the number of configurations that have a total energy of 4. Let's denote the number of energy 1 states as x. Then, the number of energy 0 states is (12 - x).
The total energy of the ensemble is given by 1*x + 0*(12 - x) = x.
To have a total energy of 4, we need to solve the equation x = 4.
There is only one solution to this equation, which is x = 4. This means that there are 4 energy 1 states and 8 energy 0 states in the ensemble.
Therefore, there is only one configuration in this microcanonical ensemble that has a total energy of 4.
Since each atom can take either energy 0 state or energy 1 state, there are two possibilities for each atom. Therefore, the total number of configurations is given by 2^12 = 4096.
However, we need to find the number of configurations that have a total energy of 4. Let's denote the number of energy 1 states as x. Then, the number of energy 0 states is (12 - x).
The total energy of the ensemble is given by 1*x + 0*(12 - x) = x.
To have a total energy of 4, we need to solve the equation x = 4.
There is only one solution to this equation, which is x = 4. This means that there are 4 energy 1 states and 8 energy 0 states in the ensemble.
Therefore, there is only one configuration in this microcanonical ensemble that has a total energy of 4.
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A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is 4∈, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.Correct answer is '6.1 to 6.3'. Can you explain this answer?
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A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is 4∈, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.Correct answer is '6.1 to 6.3'. 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 A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is 4∈, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.Correct answer is '6.1 to 6.3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is 4∈, its entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann constant.Correct answer is '6.1 to 6.3'. Can you explain this answer?.
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