Question

The magnetic susceptibility of a paramagnetic substance at $-173^{\circ} C$ is $1.5 \times 10^{-2}$. If its value at $-73^{\circ} C$ is $b \times 10^{-3}$, then find $b$.

Answer 1

In paramagnetic substance, the magnetic susceptibility is given by
$\chi=\frac{C}{T} \Rightarrow \frac{\chi_{1}}{\chi_{2}}=\frac{T_{2}}{T_{1}}$
Then $\chi_{2}=\chi_{1} \times \frac{T_{1}}{T_{2}}$
Here, $\chi_{1}=1.5 \times 10^{-2}$,
$T_{1}=273-173=100\, K$
$T_{2}=273-73=200\, K $
$\therefore \chi_{2}=1.5 \times 10^{-2} \times \frac{100}{200}$
$=7.5 \times 10^{-3}$