Specific Heat / Thermal Conductivity

[LittleTuc]

I had the following question on a Physics Quiz and I am wondering why the answer is D.

When you walk barefoot in a room, the floor feels cooler walking on a tile floor as compared to a wooden floor because
A) tile has a smaller specific heat than wood.
B) tile has a larger specific heat than wood.
C) tile has a smaller thermal conductivity than wood.
D) tile has a larger thermal conductivity than wood.

Though that answer does make since, it also seems as if A would be true. To me, both answers appear to be correct.

Can somebody please expain why the answer is D and not A. Please note, this is not a 'homework' problem. Instead it is just a question about the differece between Thermal Conductivity and specific heat with an example being a problem.

 

[Doc Al]

What makes an object feel cool is the rate at which it conducts heat away from you (thus cooling your skin). So something with greater thermal conductivity will feel cooler. Specific heat has to do with how much energy is needed to raise an object's temperature, which is something else entirely.

 

[LittleTuc]

Wouldnt SH also deal with how much energy is needed to raise an object's temperature.

 

[Doc Al]

Wouldnt SH also deal with how much energy is needed to raise an object's temperature.

Isn't that what I said?

 

[LittleTuc]

Quote from my book:
"If you take a bite of a pie that is just out tof hte oven, you are much more likely to burn your tongue on the fruit filling due to the fact that the filling has a higher specific heat."

Why doesn't this problem act like the floor problem above?

 

[Doc Al]

In order to burn your tongue, plenty of heat must flow. Because the pie filling has a much higher specific heat than the pie crust, it has much more internal energy that can transfer to your tongue and burn you.

The point is that just because the thermal conductivity may be high, if the object doesn't have much stored thermal energy to transfer--due to its low specific heat--it will have a harder time burning you. It will rapidly cool down as heat is removed--unlike the pie filling which retains its heat.

To complicate things, the pie filling--mostly water--has both high specific heat and good thermal conductivity.

 

[LittleTuc]

So, for the problem first stated, about the wood floor and tile, answer A is correct, but answer D is more correct?

 

[Doc Al]

No, answer A is not correct at all. Think about it. If the tile had a smaller specific heat than wood, then it would tend to heat up faster--thus the initial coolness would dissappear quicker. (Perhaps you were thinking of answer B, but chose A by mistake? If the tile had a larger specific heat than wood it would take a lot of heat to raise its temperature, thus keeping it cool longer.)

In any case, the best answer has to do with thermal conductivity, not specific heat, since that's what determines the initial feeling of coolness (or its lack).

 

[vaatmoly]

They can be somewhat related. For metals where thermal conductivity is dominated by free carriers, thermal conductivity(k) and specific heat(c_v) can be related by: k=(1/3)c_v*v*l, where v is the mean carrier speed and l the mean free path.