# Is it possible for an object to have low specific heat capacity and low thermal conductivity?

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?

• – dmckee Sep 16 '15 at 3:45
• Think of air. Thermal underwear works because air has a very low thermal conductivity, despite the fact that it also has a low specific heat. – David White May 15 '16 at 0:57

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).
• 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. – Thomas Sep 16 '15 at 3:57