# Heat Diffusion and Specific heat

Consider two slabs - Slab A and Slab B, insulated on "latereal" faces as shown, initially at the same temperature, and having identical dimensions. The slabs at t= 0 are brought in contact with two heat reservoirs (on left and right) at temperatures $$T_1$$ and $$T_2$$. Slabs have the same thermal conductivity but different specific heats, with $$c_A > c_B$$

Since specific heat of A > that of B I argue that the temperature profiles at any instant of time t, would be as follows:

i.e. since $$c_A > c_B$$ A will have a hard time raising it's temperature than B. As a result the temperature gradients in A will be smaller (in magnitude) than in the case of B. This would mean that the heat transferring to A from the left reservoir in any time dt is smaller in A than in B. Furthermore, the rate of heat transfer in intermediate layers will also be lower in A than B. I've often read that a higher specific heat restricts thermal diffusion, could this be one way of explaining it why?

• Are you considering the steady state or the transient case?
– NMech
Jan 26, 2022 at 17:53
• @NMech Transient Jan 26, 2022 at 18:12
• You are describing a transient process, which lends itself to straightforward analysis that gives the temperature profile in the insulator and the bulk temperature of the slabs as a function of time. But I don't see a concise question. I suggest you re-write this with a clear question about what you want to know. Feb 13, 2022 at 16:58

You are right. What you are referring to maybe the property called Thermal diffusivity, $$\alpha$$
$$\alpha =\frac{k}{\rho C_p}$$
• $$\rho$$= density So Thermal diffusivity is inversely related to specific heat.