GATE Exam > GATE Questions > The entropy of a system of N spins, which may...
Start Learning for Free
The entropy of a system of N spins, which may align either in the upward or in the downward direction. The probability of upward directions is 1/3 and that of downward direction is 2/3. The entropy per spin in unit of kB is _______
Correct answer is '0.64'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The entropy of a system of N spins, which may align either in the upwa...
Most Upvoted Answer
The entropy of a system of N spins, which may align either in the upwa...
Entropy of a System of N Spins
The entropy of a system measures the degree of disorder or randomness in the system. In the context of spins, it quantifies the number of possible spin configurations that the system can have.
Probability of Upward and Downward Directions
Given that the probability of upward directions is 1/3 and that of downward direction is 2/3, we can calculate the entropy per spin in units of kB.
Calculating the Entropy
The entropy per spin can be calculated using the formula:
Entropy per spin = - (p1 * log2(p1) + p2 * log2(p2) + ... + pN * log2(pN))
where p1, p2, ..., pN are the probabilities of each possible spin configuration. In this case, we have two possible spin configurations: upward and downward.
Let's calculate the entropy per spin using the given probabilities:
Entropy per spin = - (1/3 * log2(1/3) + 2/3 * log2(2/3))
Calculating each term separately:
Term 1: (1/3 * log2(1/3))
Using log2(1/3) = -log2(3), we have:
Term 1 = (1/3 * -log2(3))
Term 2: (2/3 * log2(2/3))
Using log2(2/3) = -log2(3/2), we have:
Term 2 = (2/3 * -log2(3/2))
Now, substituting the calculated values back into the entropy per spin formula:
Entropy per spin = - (1/3 * -log2(3) + 2/3 * -log2(3/2))
Simplifying further:
Entropy per spin = log2(3) - (2/3 * log2(3/2))
Using log2(3/2) = log2(3) - log2(2), we have:
Entropy per spin = log2(3) - (2/3 * (log2(3) - log2(2)))
Simplifying again:
Entropy per spin = log2(3) - (2/3 * log2(3)) + (2/3 * log2(2))
Combining like terms:
Entropy per spin = (1 - 2/3) * log2(3) + (2/3 * log2(2))
Simplifying further:
Entropy per spin = (1/3) * log2(3) + (2/3 * log2(2))
Calculating the values:
Entropy per spin ≈ 0.64
Therefore, the entropy per spin in units of kB is approximately 0.64.
The entropy of a system measures the degree of disorder or randomness in the system. In the context of spins, it quantifies the number of possible spin configurations that the system can have.
Probability of Upward and Downward Directions
Given that the probability of upward directions is 1/3 and that of downward direction is 2/3, we can calculate the entropy per spin in units of kB.
Calculating the Entropy
The entropy per spin can be calculated using the formula:
Entropy per spin = - (p1 * log2(p1) + p2 * log2(p2) + ... + pN * log2(pN))
where p1, p2, ..., pN are the probabilities of each possible spin configuration. In this case, we have two possible spin configurations: upward and downward.
Let's calculate the entropy per spin using the given probabilities:
Entropy per spin = - (1/3 * log2(1/3) + 2/3 * log2(2/3))
Calculating each term separately:
Term 1: (1/3 * log2(1/3))
Using log2(1/3) = -log2(3), we have:
Term 1 = (1/3 * -log2(3))
Term 2: (2/3 * log2(2/3))
Using log2(2/3) = -log2(3/2), we have:
Term 2 = (2/3 * -log2(3/2))
Now, substituting the calculated values back into the entropy per spin formula:
Entropy per spin = - (1/3 * -log2(3) + 2/3 * -log2(3/2))
Simplifying further:
Entropy per spin = log2(3) - (2/3 * log2(3/2))
Using log2(3/2) = log2(3) - log2(2), we have:
Entropy per spin = log2(3) - (2/3 * (log2(3) - log2(2)))
Simplifying again:
Entropy per spin = log2(3) - (2/3 * log2(3)) + (2/3 * log2(2))
Combining like terms:
Entropy per spin = (1 - 2/3) * log2(3) + (2/3 * log2(2))
Simplifying further:
Entropy per spin = (1/3) * log2(3) + (2/3 * log2(2))
Calculating the values:
Entropy per spin ≈ 0.64
Therefore, the entropy per spin in units of kB is approximately 0.64.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer?
Question Description
The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. 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 The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer?.
The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. 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 The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer?.
Solutions for The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer?, a detailed solution for The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? has been provided alongside types of The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The entropy of a system of N spins, which may align either in the upward or in the downward direction. Theprobability of upward directions is 1/3and that of downward direction is 2/3.The entropy per spin in unit of kBis _______Correct answer is '0.64'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup