FrontierScience / 218df0c2-18db-495f-8c53-eb6758feaff2 / A paramagnetic sample is subjected to magnetic cooling. Assume that magnetic…

A paramagnetic sample is subjected to magnetic cooling. Assume that magnetic susceptibility per unit volume χ can be approximated by Curie's law χ=a/τ and that the heat capacity at constant magnetic H field, C_(H) at zero magnetic field is given by C_(H)(τ,0)=(Vb)/(τ²) where a and b are constants. For an adiabatic process, calculate the ratio of the final and initial temperatures (τ_(f))/(τ_(i)) as a function of a, b, the final magnetic field H_(f) and the initial magnetic field H_(i). In this problem, we consider high temperatures and do not need to consider the quantum effects of magnetic moments or the interactions between magnetic moments.

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.

A paramagnetic sample is subjected to magnetic cooling. Assume that magnetic susceptibility per unit volume \( \chi \) can be approximated by Curie's law \( \chi = a / \tau \) and that the heat capacity at constant magnetic \( H \) field, \( C_H \) at zero magnetic field is given by \( C_H(\tau, 0)=\frac{V b}{\tau^2} \) where \( a \) and \( b \) are constants. For an adiabatic process, calculate the ratio of the final and initial temperatures \( \frac{\tau_{f}}{\tau_{i}} \) as a function of \( a \), \( b \), the final magnetic field \( H_f \) and the initial magnetic field \( H_i \). In this problem, we consider high temperatures and do not need to consider the quantum effects of magnetic moments or the interactions between magnetic moments.

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.