PX154 - C10 - heat capacity of solids

prediction

[YF 18.4]

atoms may vibrate in 3D
- each direction contributes $k_{B} T$ per atom
$\frac{1}{2} k_{B} T$ each from the $K E$ and the $P E$
so, for 3D (x, y, z), $⟹ t o t a l 3 k_{B} T$
so, per mole $C_{V} = 3 R = 24.9 J m^{- 1} K^{-} 1$
- the rule of Dulong and Petit
  -
experimental heat capacities approach the prediction at high $T$
$C_{V}$ drops at low $T$ as modes of vibration are frozen out