Question

The susceptibility of a paramagnetic material is $K$ at ${27^ \circ }{\text{ }}C$. At what temperature will its susceptibility be $\dfrac{K}{2}$?
A. ${600^ \circ }\,C$
B. ${287^ \circ }\,C$
C. ${54^ \circ }\,C$
D. ${327^ \circ }\,C$

Answer 1

Hint: Magnetic susceptibility of a material is defined as the ratio of magnetization or magnetic moment per unit volume to applied magnetic field intensity. In other words it can be said that it is the measure of how much a magnetic material will acquire the magnetic property in a magnetic field.

Complete step by step answer:
The susceptibility of a magnetic material is inversely proportional to the temperature. Magnetic susceptibility is denoted by $\chi $. The relation is as follows-
$\chi \propto \dfrac{1}{T}$
The magnetic material at ${27^ \circ }{\text{ }}C$ is given as $K$.
We have to convert the degree-Celsius scale into Kelvin Scale.

Therefore, the conversion formula is as follows:
$K' = C + 273$
where $K'$ denotes the Kelvin reading and $C$ denotes the degree-Celsius reading.
So, the Kelvin reading of ${27^ \circ }{\text{ }}C$ is,
$K' = 27 + 273 = 300$
So, the temperature is $300{\text{ }}K$.
So, we get,
$K = k\dfrac{1}{{300}} - - - - - \left( 1 \right)$
where $k$ is a constant of proportionality.
Again when magnetic susceptibility is $\dfrac{K}{2}$ then the temperature be $t$.Thus, we get,
$\dfrac{K}{2} = k\dfrac{1}{t} - - - - - \left( 2 \right)$

Dividing equation $\left( 1 \right)$ by equation $\left( 2 \right)$ we get,
$\dfrac{K}{{\dfrac{K}{2}}} = \dfrac{t}{{300}}$
$\Rightarrow t = 600$
By converting it into Celsius by using the formula, we get,
$C = K' - 273$
where $K'$ denotes the Kelvin reading and $C$ denotes the degree-Celsius reading
So, $600{\text{ }}K$ can be converted into Celsius as,
$\therefore C = 600 - 273 = 327$
So, the temperature when the magnetic susceptibility changes to $\dfrac{K}{2}$ is ${327^ \circ }{\text{ }}C$.

So, the correct option is D.

Note: It must be noted that in any temperature related question we must convert the reading to Kelvin scale. Magnetic susceptibility helps to distinguish between paramagnetic and diamagnetic materials. If the $\chi > 0$, then the material is having paramagnetism and when $\chi < 0$ then the material shows diamagnetism.