Q131 / 150 · MHT CET 2025 (27 Apr Shift 2) · Physics

' $\chi_1{ }^{\prime},{ }^{\prime} \chi_2{ }^{\prime}$ and ' $\chi_3{ }^{\prime}$ are susceptibilities of a paramagnetic material at temperatures ' $\mathrm{T}_1{ }^{\prime} \mathrm{K}$, ' $\mathrm{T}_2{ }^{\prime} \mathrm{K}$ and ' $\mathrm{T}_3{ }^{\prime} \mathrm{K}$ respectively, then

  • Correct answer
    A
    $\chi_1: \chi_2=\mathrm{T}_1: \mathrm{T}_2, \chi_2: \chi_3=\mathrm{T}_3: \mathrm{T}_2$
  • B
    $\chi_1: \chi_2=\mathrm{T}_1: \mathrm{T}_2, \chi_2: \chi_3=\mathrm{T}_2: \mathrm{T}_3$
  • C
    $\chi_1: \chi_2=\mathrm{T}_2: \mathrm{T}_1, \chi_2: \chi_3=\mathrm{T}_3: \mathrm{T}_2$
  • D
    $\chi_1: \chi_2=\mathrm{T}_2: \mathrm{T}_1, \chi_2: \chi_3=\mathrm{T}_2: \mathrm{T}_3$

Solution

For a paramagnetic material, the magnetic susceptibility $\chi = \frac{C}{T}$ follows Curie's Law, where $C$ is the Curie constant.

The ratio $\frac{\chi_1}{\chi_2} = \frac{C / T_1}{C / T_2} = \frac{T_2}{T_1}$, so $\chi_1 : \chi_2 = T_2 : T_1$.

Similarly, $\frac{\chi_2}{\chi_3} = \frac{T_3}{T_2}$, giving $\chi_2 : \chi_3 = T_3 : T_2$.

These relationships correspond to option C.

Hence, the correct answer is option: 'A'.

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