Question:
Consider a linear collection of \( N \) independent spin 1/2 particles, each at fixed location. The entropy of the system is:
Consider a linear collection of \( N \) independent spin 1/2 particles, each at fixed location. The entropy of the system is:
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For an ideal spin system, entropy depends on the number of accessible spin states.
Updated On: Mar 26, 2025
- \( 0 \)
- \( \frac{N k_B}{2} \)
- \( \frac{N k_B}{2} \ln 2 \)
- \( N k_B \ln 2 \)
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The Correct Option is D
Solution and Explanation
For \( N \) independent spin-1/2 particles, each spin can be in two possible states.
The number of accessible microstates is:
\[ W = 2^N \] The entropy is given by Boltzmann’s relation:
\[ S = k_B \ln W = k_B \ln(2^N) = N k_B \ln 2 \]
\[ W = 2^N \] The entropy is given by Boltzmann’s relation:
\[ S = k_B \ln W = k_B \ln(2^N) = N k_B \ln 2 \]
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