Curie Law And Temperature Dependence

Question

The magnetic susceptibility of a paramagnetic sample is measured as $0.006$ at a temperature of $300$ K; assuming Curie's law holds, its susceptibility when cooled to $150$ K will be

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NCERT Class 12, Chapter 5 (Magnetism and Matter) states Curie's law for paramagnetic materials: the susceptibility varies inversely with absolute temperature, $\chi = \dfrac{C}{T}$, where $C$ is the Curie constant. This arises because thermal agitation opposes the alignment of atomic dipoles with the field, so lowering the temperature allows stronger alignment and larger susceptibility. Since $\chi_1 T_1 = \chi_2 T_2 = C$, we have $\chi_2 = \chi_1 \dfrac{T_1}{T_2} = 0.006 	imes \dfrac{300}{150} = 0.012$. The value $0.003$ wrongly makes susceptibility increase with temperature. The value $0.006$ assumes no temperature dependence at all. The value $0.024$ uses a temperature ratio of 4 instead of 2. Plausibility check: halving the absolute temperature should double the susceptibility under an inverse relationship, and $0.012$ is exactly twice $0.006$, so both the direction (increase on cooling) and the factor are consistent with Curie's law. It is essential here to use absolute (kelvin) temperatures rather than Celsius, since the inverse proportionality is defined only on the absolute scale; had one mistakenly used a Celsius ratio the factor would be wildly wrong, so recognising the kelvin requirement is part of validating the answer.

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Curie Law And Temperature Dependence

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