Q155 / 180 · KCET 2015 · Physics

The magnetic susceptibility of a paramagnetic material at \( -73^{\circ} \mathrm{C} \) is \( 0.0075 \) and its value at
\( -173^{\circ} \mathrm{C} \) will be

  • A
    \( 0.0045 \)
  • B
    \( 0.0030 \)
  • Correct answer
    C
    \( 0.015 \)
  • D
    \( 0.0075 \)

Solution

Given, magnetic susceptibility of para-magnet at $T_{1}=73^{\circ} \mathrm{C}$ is $0.0075$ Let magnetic susceptibility at $T_{2}=-173^{\circ} \mathrm{C}$ be $\chi_{2}$ We know magnetic susceptibility is given by $\chi \propto \frac{1}{T}$ Therefore, $\frac{\chi_{1}}{\chi_{2}}=\frac{T_{2}}{T_{1}} \Rightarrow \frac{0.0075}{\chi_{2}}=\frac{-173^{\circ} \mathrm{C}}{-73^{\circ} \mathrm{C}}$ $\Rightarrow \frac{0.0075}{\chi_{2}}=\frac{(273-173) K}{(273-73) K} \Rightarrow \frac{0.0075}{\chi_{2}}=\frac{100}{200}$ $\Rightarrow \frac{0.0075}{\chi_{2}}=\frac{1}{2} \Rightarrow \chi_{2}=2 \times 0.0075=0.0150$ Therefore, magnetic susceptibility at $-173^{\circ} \mathrm{C}$ will be $0.0150$.

Hence, the correct answer is option: 'C'.

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