Question

The $\chi$ versus $\frac{1}{T}$ graph for an alloy of paramagnetic nature is shown in the figure. The Curie constant for this alloy is -

$[$Assume the states are far away from saturation$]$

• A. $50\text{K}$
• B. $2.8\times {10}^{-3}\text{K}$
• C. $570\text{K}$
• D. $1.5\times {10}^{-3}\text{K}$

Answer 1

The correct option is A $50\text{K}$

We know that, for paramagnetic material, at states far away from saturation,

$\chi =\frac{C}{T}$

$\Rightarrow \chi =C\times \frac{1}{T}$

Comparing the above expression with the equation of a straight line, passing through origin, $i.e.y=mx$, we can say that, the slope of $\chi$ versus $\frac{1}{T}$ curve is equal to the Curie constant.

Therefore, slope,

$m=C=\frac{y_2-y_1}{x_2-x_1}=\frac{{\chi }_2-{\chi }_1}{\frac{1}{T_2}-\frac{1}{T_1}}$

$\Rightarrow C=\frac{0.4-0}{(8-0)\times {10}^{-3}}$

$\Rightarrow C=50\text{K}$