Dielectrics: An Atomic View — Question 5

Question 5

Two temperatures separate induced and orientational susceptibility

At fixed number density a material obeys $\chi(T)=A+B/T$ with positive constants. Measurements give $\chi(T_0)=.600$ and $\chi(2T_0)=.400$. A is induced response and B/T is orientational response.

1. Find A and B/T0.

2. For unchanged capacitor geometry find the capacitance ratio C(2T0)/C(T0) and the infinite-temperature limiting relative permittivity within this model.

Question 5 - Solution

Two temperatures separate induced and orientational susceptibility

(a) Method and calculation

$$A+B/T_0=.600,\quad A+B/(2T_0)=.400.$$$$B/T_0=.400,\quad A=.200.$$

(b) Interpretation and further calculation

$$\frac{C(2T_0)}{C(T_0)}=\frac{1+.400}{1+.600}=.875.$$$$\kappa(T\to\infty)=1+A=1.200.$$

Physical check

Temperature changes the alignment contribution in this supplied model, while the induced contribution remains constant.