Question

The magnetic susceptibility of a paramagnetic material is $1.0\times {10}^{-5}$ at ${27}^{o}C$ temperature. Then, at what temperature its magnetic susceptibility would be $1.5\times {10}^{-5}$?

• A. ${200}^{o}C$
• B. ${18}^{o}C$
• C. ${-73}^{o}C$
• D. ${-18}^{o}C$

Answer 1

The correct option is C ${-73}^{o}C$

The susceptibility of a paramagnetic substance varies inversely as the Kelvin temperature of the substance.
${\chi }_m\propto 1/T$
$\frac{{\chi }_{m_1}}{{\chi }_{m_2}}=T_2/T_1$
where ${\chi }_{m_1}=1.0\times {10}^{-5}$
${\chi }_{m_2}=1.5\times {10}^{-5}$
$T_1={27}^{o}C+273=300K$
$T_2=$?
$T_2=\frac{300\times 1.0\times {10}^{-5}}{1.5\times {10}^{-5}}$
$=100\times 2=200K$
$=200-273={-73}^{o}C$