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:

enter image description here

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?

  • $\begingroup$ Are you considering the steady state or the transient case? $\endgroup$
    – NMech
    Jan 26, 2022 at 17:53
  • $\begingroup$ @NMech Transient $\endgroup$ Jan 26, 2022 at 18:12
  • $\begingroup$ 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. $\endgroup$
    – ttonon
    Feb 13, 2022 at 16:58

1 Answer 1


You are right. What you are referring to maybe the property called Thermal diffusivity, $\alpha$

$$\alpha =\frac{k}{\rho C_p}$$

  • Cp = specific heat
  • k = thermal conductivity
  • $\rho $= density So Thermal diffusivity is inversely related to specific heat.

However in your example as soon as slab A reaches the T2, a bit after slab B, on the right side they both transfer heat at the same rate because they have the same thermal conductivity.

  • $\begingroup$ kamran, yes, I always had trouble wrapping my head around the concept of thermal diffusivity. I was reviewing my notes today, when this one of the ways of interpreting how high specific heat restricts thermal diffusion came to my mind. $\endgroup$ Jan 26, 2022 at 18:36
  • 1
    $\begingroup$ It's like 2 12 volt batteries one larger one smaller. the larger takes more energy to charge, but once the 2 batteries are charged both have a voltage of 12. $\endgroup$
    – kamran
    Jan 26, 2022 at 18:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.