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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?

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  • $\begingroup$ Are you considering the steady state or the transient case? $\endgroup$
    – NMech
    Jan 26 at 17:53
  • $\begingroup$ @NMech Transient $\endgroup$ Jan 26 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 at 16:58

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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.

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  • $\begingroup$ 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 at 18:36
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    $\begingroup$ 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 at 18:43

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