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FrontierScience / b90fc8dc-2fca-4ff7-9c9f-a2e6a0ac7812 / Consider a large insulating lattice containing `N≫1` atoms. The entire system is placed in a uniform external magnetic field `B` and is in thermal equilibrium at temperature `T`. W…
Problem
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problem
Consider a large insulating lattice containing `` atoms. The entire system is placed in a uniform external magnetic field `` and is in thermal equilibrium at temperature ``. We focus on the quantum mechanical interaction between the magnetic moment of the atoms and the external field.
Suppose the system starts with a temperature `` and an external field ``. We gradually reduce the magnetic field to `` such that it is an adiabatic process. Determine the temperature `` of the final state.
Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.
Plain-text mathematical notation (without MathML)
Consider a large insulating lattice containing `N≫1` atoms. The entire system is placed in a uniform external magnetic field `B` and is in thermal equilibrium at temperature `T`. We focus on the quantum mechanical interaction between the magnetic moment of the atoms and the external field. Suppose the system starts with a temperature `T₀` and an external field `B₀`. We gradually reduce the magnetic field to `B₁` such that it is an adiabatic process. Determine the temperature `T₁` of the final state. Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.
Original LaTeX notation
Consider a large insulating lattice containing `\(N\gg1\)` atoms. The entire system is placed in a uniform external magnetic field `\(B\)` and is in thermal equilibrium at temperature `\(T\)`. We focus on the quantum mechanical interaction between the magnetic moment of the atoms and the external field. Suppose the system starts with a temperature `\(T_0\)` and an external field `\(B_0\)`. We gradually reduce the magnetic field to `\(B_1\)` such that it is an adiabatic process. Determine the temperature `\(T_1\)` of the final state. Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.
subject
physics
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