With the Debye model (a single group velocity u p,g, and a specific heat capacity calculated above), this becomes k p = ( 48 π π 2 ) 1 / 3 k B 3 T 3 a h P 2 T D ∫ ∫ 0 T / T D τ τ p x 4 e x ( e x − − 1 ) 2 d x ,