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3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB = ________ kB (upto 2 decimal places)
Correct answer is between '1.23,1.30'. Can you explain this answer?
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3- particles are to be distributed in 5 non degenerate energy levels. ...
If the particles are distinguishable, then
If the integral spin particles are indistinguishable, then
If the integral spin particles are indistinguishable, then
Most Upvoted Answer
3- particles are to be distributed in 5 non degenerate energy levels. ...
Given:
- Number of particles, N = 3
- Number of energy levels, W = 5
To find:
SD - SB = ? (in terms of kB)
Explanation:
In order to calculate the difference between the entropy of distinguishable particles (SD) and indistinguishable particles (SB), we need to determine the values of SD and SB individually.
Calculating SD:
The entropy of distinguishable particles (SD) is given by the formula:
SD = kB * ln(W^N)
Here, W is the number of energy levels and N is the number of particles.
Substituting the given values:
SD = kB * ln(5^3)
SD = kB * ln(125)
SD ≈ 2.079 * kB
Calculating SB:
For indistinguishable particles of integral spin, we need to use the formula:
SB = kB * ln(C)
Here, C represents the number of ways the particles can be distributed among the energy levels. To find C, we can use the concept of combinatorics.
Since the particles are indistinguishable, we can use the concept of "stars and bars" to calculate the number of ways to distribute them. The formula for C is given by:
C = (N+W-1)C(N)
Substituting the given values:
C = (3+5-1)C(3)
C = 7C3
C = 7! / (3! * 4!)
C = 7 * 6 * 5 / (3 * 2 * 1)
C = 35
Substituting the value of C into the equation for SB:
SB = kB * ln(35)
Calculating SD - SB:
Now, we can subtract SB from SD to find the difference:
SD - SB = kB * ln(125) - kB * ln(35)
SD - SB = kB * (ln(125) - ln(35))
SD - SB ≈ kB * (4.828 - 3.555)
SD - SB ≈ kB * 1.273
Approximate Answer:
SD - SB ≈ 1.273 * kB
Since the correct answer is between 1.23 and 1.30, the value of kB must be approximately 1. Therefore, SD - SB ≈ 1.273 * 1 ≈ 1.273 kB, which falls within the given range.
- Number of particles, N = 3
- Number of energy levels, W = 5
To find:
SD - SB = ? (in terms of kB)
Explanation:
In order to calculate the difference between the entropy of distinguishable particles (SD) and indistinguishable particles (SB), we need to determine the values of SD and SB individually.
Calculating SD:
The entropy of distinguishable particles (SD) is given by the formula:
SD = kB * ln(W^N)
Here, W is the number of energy levels and N is the number of particles.
Substituting the given values:
SD = kB * ln(5^3)
SD = kB * ln(125)
SD ≈ 2.079 * kB
Calculating SB:
For indistinguishable particles of integral spin, we need to use the formula:
SB = kB * ln(C)
Here, C represents the number of ways the particles can be distributed among the energy levels. To find C, we can use the concept of combinatorics.
Since the particles are indistinguishable, we can use the concept of "stars and bars" to calculate the number of ways to distribute them. The formula for C is given by:
C = (N+W-1)C(N)
Substituting the given values:
C = (3+5-1)C(3)
C = 7C3
C = 7! / (3! * 4!)
C = 7 * 6 * 5 / (3 * 2 * 1)
C = 35
Substituting the value of C into the equation for SB:
SB = kB * ln(35)
Calculating SD - SB:
Now, we can subtract SB from SD to find the difference:
SD - SB = kB * ln(125) - kB * ln(35)
SD - SB = kB * (ln(125) - ln(35))
SD - SB ≈ kB * (4.828 - 3.555)
SD - SB ≈ kB * 1.273
Approximate Answer:
SD - SB ≈ 1.273 * kB
Since the correct answer is between 1.23 and 1.30, the value of kB must be approximately 1. Therefore, SD - SB ≈ 1.273 * 1 ≈ 1.273 kB, which falls within the given range.
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3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer?
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3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. 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 3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer?.
3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. 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 3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer?.
Solutions for 3- particles are to be distributed in 5 non degenerate energy levels. Let 'SD' be the entropy of such a system if the particles are distinguishable and 'SB be the entropy if they are indistinguishable particles of integral spin. Then SD - SB =________ kB (upto 2 decimal places)Correct answer is between '1.23,1.30'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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