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,
${\chi }_{m_1}=1.5\times 10^{-2}$
$T_1=-173^{\circ }C$
$=(-173+273)=100K$
${\chi }_{m_2}=0.5\times 10^{-2},$
According to the Curie's law,
${\chi }_m\propto \frac{1}{T}$ or $\frac{{\chi }_{m_1}}{{\chi }_{m_2}}=\frac{T_2}{T_1}$
$\Rightarrow T_2=T_1\left(\frac{{\chi }_{m_1}}{{\chi }_{m_2}}\right)$
$\Rightarrow T_2=100\left(\frac{1.5\times 10^{-2}}{0.5\times 10^{-2}}\right)=300K$
$T_2=(300-273)$
$T_2=27^{\circ }C$
Hence, change in temperature,
$\Delta T=T_2-T_1$
$\Delta T=27-(-173)=200^{\circ }C$