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As I see, there are many examples of object with low specific heat capacity and high thermal conductivity and vice versa. Since they are different properties of matter and their definitions are not same, is it possible for an object to have low specific heat capacity and low thermal conductivity?

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I am not quite sure what kind of examples you have in mind, the standard kinetic theory estimate of the thermal conductivity is $$ \kappa = \frac{1}{3} n\bar{v} c_V l_{mfp} $$ where $n$ is the density, $\bar{v}\sim T/m$ is the mean velocity of the molecules, $l_{mfp}$ is the mean free path, and $c_V$ is the specific heat. This says that keeping the mean free path fixed, thermal conductivity is proportional to the specific heat (and indeed this is the every day experience, a metal pot is a good conductor and has large specific heat, the wooden handle is the opposite).

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  • $\begingroup$ Metal pot has small specific heat, isn't? $\endgroup$ – Chin Huan Sep 16 '15 at 3:44
  • $\begingroup$ Part of that is related to the annoying chemists, who quote specfic heat per mass. I mean $c_v$ as in $\partial {\cal E}/\partial T$, where ${\cal E}$ is internal energy. $\endgroup$ – Thomas Sep 16 '15 at 3:57
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Yes of course, the materials that are used for thermal insulation applications,like polystyrene, mineral wool and polyurethane have such characteristics.

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the relation between the specific heat and the temperature is inversely relationship so all the materials in which has low specific heat will be good conductor while the materials in which has high specific heat has bad conductivity for the heat

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