The susceptibility of a paramagnetic material is \( \chi \) at 27 °C. At what temperature will its susceptibility be \( \frac{\chi}{3} \)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 627 °C
For a paramagnetic material, Curie's law says that the susceptibility is inversely proportional to the absolute temperature.
\( \displaystyle \chi \propto \frac{1}{T} \;\Rightarrow\; \frac{\chi_2}{\chi_1} = \frac{T_1}{T_2} \)
\( \displaystyle T_1 = 27 + 273 = 300\,\mathrm{K} \)
\( \displaystyle \frac{\chi/3}{\chi} = \frac{300\,\mathrm{K}}{T_2} \;\Rightarrow\; T_2 = 3 \times 300\,\mathrm{K} = 900\,\mathrm{K} \)
\( \displaystyle T_2 = 900 - 273 = 627\,^\circ\mathrm{C} \)