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Q.

At a temp of 300 K, the susceptibility of a ferromagnetic material is found to be $χ$ . Its susceptibility at 450 K is $χ^{1}$ . Then $\frac{χ^{1}}{χ} =$

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a

$\frac{2}{3}$

b

$\frac{1}{2}$

c

$\frac{1}{3}$

d

$\frac{3}{2}$

answer is C.

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Detailed Solution

Curie’s law $χ_{m} = \frac{μ_{0} C}{T}$
$T_{1} =300 K$ ; $T_{2} =450 K$
$U \sin g, χ_{m} \propto \frac{1}{T}$
$\Rightarrow \frac{χ_{m_{1}}}{χ_{m_{2}}} = \frac{T_{2}}{T_{1}}$
$\Rightarrow χ_{m_{2}} = (\frac{T_{1}}{T_{2}}) χ_{m_{1}}$
$\Rightarrow χ_{m_{2}} = (\frac{300}{450}) χ$
$\Rightarrow χ_{m_{2}} = \frac{2}{3} χ$ or $\frac{2 χ}{3} = χ^{1}$
$\Rightarrow \frac{χ^{1}}{χ} = \frac{2 χ / 3}{χ} = \frac{2}{3}$ .

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At a temp of 300 K, the susceptibility of a ferromagnetic material is found to be χ . Its susceptibility at 450 K is χ1 . Then χ1χ=