Question

The susceptibility of magnesium at $300K$ is $2.4\times {10}^{-5}$. At what temperature will the susceptibility increase to $3.6\times {10}^{-5}$?

Answer 1

Given ${\chi }_{m_1}=2.4\times {10}^{-5},T_1=300K,{\chi }_{m_2}=3.6\times {10}^{-5},T_2=?$
$\because {\chi }_m\propto \frac{1}{T}$
$\Rightarrow \frac{{\chi }_{m_1}}{{\chi }_{m_2}}=\frac{T_2}{T_1}$
$\Rightarrow \frac{2.4\times {10}^{-5}}{3.6\times {10}^{-5}}=\frac{T_2}{300}$
$\Rightarrow T_2=200K$