Question

The magnetic susceptibility of a paramagnetic substance at $-173^{\circ}C$ is $1.5 \times 10^{-2}$. To have the susceptibility $0.5 \times 10^{-2}$ the change in temperature in $^{\circ}C$ is

• A. 100
• B. 180
• C. 200
• D. 220

Answer 1

Answer: (C)

Given, magnetic susceptibility of a paramagnetic substance,
$\chi_{m_{1}}=1.5 \times 10^{-2}$
$T_{1} =-173^{\circ} C$
$=(-173+273)=100\, K $
$\chi_{m_{2}} =0.5 \times 10^{-2},$
According to the Curie's law,
$ \chi_{m} \propto \frac{1}{T} $ or $ \frac{\chi_{m_{1}}}{\chi_{m_{2}}}=\frac{T_{2}}{T_{1}}$
$\Rightarrow T_{2}=T_{1}\left(\frac{\chi_{m_{1}}}{\chi_{m_{2}}}\right) $
$\Rightarrow T_{2}=100\left(\frac{1.5 \times 10^{-2}}{0.5 \times 10^{-2}}\right)=300\, K$
$ T_{2}=(300-273) $
$ T_{2}=27^{\circ} C$
Hence, change in temperature,
$\Delta T=T_{2}-T_{1}$
$\Delta T=27-(-173)=200^{\circ} C$