Question 2.172: Sketch the temperature dependence of the heat conductivity o...

The thermal conductivity of a solid is \kappa=c v_{ s } \lambda / 3, where c is thermal capacity per unit volume, v_{ s } \text { is velocity of sound, } \lambda is mean free path of phonons. κ versus T is shown in Fig. 2.37.

(a) At low temperatures the heat capacity c \propto T^{3}, v_{ s } \text { and } \lambda are constants, hence \kappa \propto T^{3}.

(b) At high temperatures  v_{ s } is constant and  \lambda \propto \frac{1}{T}, the thermal capacity c is constant, hence \kappa \propto \frac{1}{T}.