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Consider a system of 5 non-interacting distinguishable particles. Each particle can occupy only two energy levels ∈ and 2∈. If the total energy of the system 8∈. Then, the entropy of the system is _____ kB. (answer must be given upto 2 decimal places)
Correct answer is '2.30'. Can you explain this answer?
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Consider a system of 5 non-interacting distinguishable particles. Each...
Let N1 and N2 be the number of particles occupying energy levels ∈ and 2∈ respectively.
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Consider a system of 5 non-interacting distinguishable particles. Each...
Let's label the energy levels as 1 and 2. Since there are 5 particles, the total number of possible configurations is 2^5 = 32. We can list all the possible configurations as follows:
1. All particles in level 1: 11111
2. One particle in level 2, rest in level 1: 11112, 11121, 11211, 12111, 21111
3. Two particles in level 2, rest in level 1: 11122, 1112, 11212, 12112, 21112, 1122, 1212, 2112, 22211, 22112, 21212
4. Three particles in level 2, rest in level 1: 111222, 11122, 11222, 12222, 22211, 22112, 21212, 1222, 2122, 2212
5. Four particles in level 2, rest in level 1: 1112222, 111222, 112222, 122222, 22221, 22212, 22122, 21222
6. All particles in level 2: 22222
Note that we can count the number of configurations in each category by using the binomial coefficient formula:
n choose k = n!/(k!(n-k)!)
where n is the total number of particles and k is the number of particles in level 2. For example, the number of configurations with one particle in level 2 is:
5 choose 1 = 5!/(1!(5-1)!) = 5
Similarly, the number of configurations with two particles in level 2 is:
5 choose 2 = 5!/(2!(5-2)!) = 10
We can use this formula to count the number of configurations in each category and add them up to get the total number of configurations.
1. All particles in level 1: 11111
2. One particle in level 2, rest in level 1: 11112, 11121, 11211, 12111, 21111
3. Two particles in level 2, rest in level 1: 11122, 1112, 11212, 12112, 21112, 1122, 1212, 2112, 22211, 22112, 21212
4. Three particles in level 2, rest in level 1: 111222, 11122, 11222, 12222, 22211, 22112, 21212, 1222, 2122, 2212
5. Four particles in level 2, rest in level 1: 1112222, 111222, 112222, 122222, 22221, 22212, 22122, 21222
6. All particles in level 2: 22222
Note that we can count the number of configurations in each category by using the binomial coefficient formula:
n choose k = n!/(k!(n-k)!)
where n is the total number of particles and k is the number of particles in level 2. For example, the number of configurations with one particle in level 2 is:
5 choose 1 = 5!/(1!(5-1)!) = 5
Similarly, the number of configurations with two particles in level 2 is:
5 choose 2 = 5!/(2!(5-2)!) = 10
We can use this formula to count the number of configurations in each category and add them up to get the total number of configurations.
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Consider a system of 5 non-interacting distinguishable particles. Each particle can occupy only two energy levels ∈ and 2∈. If the total energy of the system 8∈. Then, the entropy of the system is _____ kB. (answer must be given upto 2 decimal places)Correct answer is '2.30'. Can you explain this answer?
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Consider a system of 5 non-interacting distinguishable particles. Each particle can occupy only two energy levels ∈ and 2∈. If the total energy of the system 8∈. Then, the entropy of the system is _____ kB. (answer must be given upto 2 decimal places)Correct answer is '2.30'. 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 Consider a system of 5 non-interacting distinguishable particles. Each particle can occupy only two energy levels ∈ and 2∈. If the total energy of the system 8∈. Then, the entropy of the system is _____ kB. (answer must be given upto 2 decimal places)Correct answer is '2.30'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of 5 non-interacting distinguishable particles. Each particle can occupy only two energy levels ∈ and 2∈. If the total energy of the system 8∈. Then, the entropy of the system is _____ kB. (answer must be given upto 2 decimal places)Correct answer is '2.30'. Can you explain this answer?.
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