Use the law of energy conservation to show that, when heat diffuses through a homogeneous medium whose

Question:

Use the law of energy conservation to show that, when heat diffuses through a homogeneous medium whose pressure is being kept fixed, the evolution of the temperature perturbation δT ≡ T − (average temperature) is governed by the diffusion equation

is called the thermal diffusivity. Here c_P is the specific heat per unit mass at fixed pressure, and ρc_P is that specific heat per unit volume. For the extension of this to heat flow in a moving fluid, see Eq. (18.4).