Paramagnetism — Question 9

Question 9

An inverse-susceptibility line determines a Curie-Weiss intercept

A material in its high-temperature paramagnetic regime follows $\chi=C/(T-\Theta)$. Measurements give $\chi=0.020$ at 300 K and $\chi=0.010$ at 400 K. Restrict use of this model to the measured regime.

1. Find C and Theta from the two measurements.

2. Predict susceptibility at 500 K and give the slope and temperature-axis intercept of a plot of inverse susceptibility versus T.

Question 9 - Solution

An inverse-susceptibility line determines a Curie-Weiss intercept

(a) Method and calculation

$$0.020(300-\Theta)=0.010(400-\Theta)\Rightarrow\boxed{\Theta=200\,\mathrm K}.$$$$\boxed{C=0.020(300-200)=2.00\,\mathrm K}.$$

(b) Interpretation and further calculation

$$\boxed{\chi(500)=2/(500-200)=6.667\times10^{-3}}.$$$$\chi^{-1}=(T-\Theta)/C\Rightarrow\boxed{\text{slope}=0.500\,\mathrm{K^{-1}},\quad T\text{ intercept}=200\,\mathrm K}.$$

Physical check

The extrapolated intercept alone does not validate the model near a phase transition or prove that the actual transition occurs there.