Question

The susceptibility of magnesium at $200K$ is $18\times {10}^{-5}$. At what temperature will the susceptibility decrease by $6\times {10}^{-6}$ ?

Answer 1

Given, $T=200K,x_1=1.8\times {10}^{-5}$
$x_1-x_2=6\times {10}^{-6}=0.6\times {10}^{-5}$
$\Rightarrow x_2=x_1-0.6\times {10}^{-5}$
$=1.8\times {10}^{-5}-0.6\times {10}^{-5}$
$\therefore x_2=1.2\times {10}^{-5}$
$\therefore xT=Constant$
$\because x_1{T}_1=x_2{T}_2$
$\Rightarrow T_1=\frac{x_2{T}_2}{x_1}$
$\therefore T_2=\left(\frac{1.8\times 0^{-5}}{1.2\times {10}^{-5}}\right)\times 200K$
$\therefore T_2=300K$