The susceptibility of a paramagnetic material is x at 27 °C. At what temperature will its susceptibility will be $\frac{x}{3}$?

627 °C

The correct answer is Option (2) → 627 °C

Curie's law: $\chi = \frac{C}{T}$

Given: $\chi_1 = x$ at $T_1 = 27^\circ C = 300\ \text{K}$

We want: $\chi_2 = x/3$ at $T_2$

Using Curie's law:

$\frac{\chi_2}{\chi_1} = \frac{T_1}{T_2} \text{ implies } \frac{x/3}{x} = \frac{300}{T_2} \text{ implies } \frac{1}{3} = \frac{300}{T_2}$

$T_2 = 900\ \text{K}$ (absolute temperature)

If temperature is asked in °C: $T_2(^\circ C) = T_2(K) - 273 = 900 - 273 = 627^\circ C$

Final Answer: $T = 627^\circ C$