Suppose that the specific heat is a function of position and temperature, c(x, u)....

Suppose that the specific heat is a function of position and temperature, c(x, u).

(a) Show that the heat energy per unit mass necessary to raise the temperature of a thin slice of thickness Δx from 0°to u(x, t) is not c(x)u(x, t), but instead

(b) Rederive the heat equation in this case. Show that (1.2.3) remains unchanged.