# Temperature storage question

1. Dec 30, 2011

### njl

Hi all - this is my first post. I have two questions if anyone knows the answer or how to go about finding out.

1. Considering the design of an icebox or cooler, would sandstone (talc) be a better storage medium for coldness than ice? I did some research and found that the volumetric heat capacity of ice is 1.9 (in J/cm^3K) while sandstone is about 3. Also paraffin wax is about 2.3. Am I correct that the same size block of sandstone or paraffin wax would keep an icebox cold for longer?

2. My other question has to do with storing heat. If the heat capacity of sandstone is 3, and I heated a 20lb block of sandstone to 200 degrees Fahrenheit, how long would it take for it to cool to 70F? I have no idea how to model this question into a mathematical equation. Sorry if this is really basic.

2. Dec 30, 2011

### 256bits

For question 2 - This involves some knowledge the conduction and convection aspects of your sandstone block with the surrounding air. The block would cool at different rates depending upon whether on not the air is still ( conduction ) or moving around it ( convection ). Is the block hanging from a cable and all 6 sides are surrounded by air or is it sitting on a surface. If you add insulation around the block that would also affect the cooling rate.

Question 1 - That is a little tricky because when the ice melts, the volumetric heat capactiy of the water becomes about 4.18 in the units you specified, which is more than the figures you cited for talc or sandstone.
The tricky part is that ice melts. And in order to melt it has to "absorb" a certain amount of heat from the surroundings. For water, this value is 334 kJ/Kg and is called the heat of fusion of water or enthalpy of fusion. One kilogram of ice melting, with the heat of fusion, provides more cooling effect than just plain ice rising in temperature, with its volumetric heat capacity.
You can calculate how much talc or sandstone you would need in your ice box to supply the same amount of cooling as 1 kg of ice does when it melts. I think your icebox would become somewhat heavy to carry around.

3. Dec 30, 2011

### njl

The block would be sitting on a wire stovetop (turned off after the initial heating) and would not be insulated. Basically all 6 sides would be exposed, and the air would be still.

4. Dec 30, 2011

### 256bits

In that case the block would be subject to natural convection ( versus forced concvection ).

You could model your block as:
Assuming the block has an even temperature throughout, and that h does not depend upon temperature then,

dQ/dt = - h A ( $\Delta$T(t) ) ; $\Delta$T(t) = T(t) - Tair

where
h is the Heat transfer coefficient W/(m2K)
A is the surface area
T is the temperature of the object's surface
Tair is the temperature of the air

h would be different for the top, the bottom and 4 sides.
We do not know h, and you would have to estimate it, or calculate it for your block, from expressions of heat flow from plates that are horizontal and vertical.

You might want to treat your block as a lumped system with a heat capacitance of C, where C= dQ/dT. And where r=hA/C which gives units of 1/sec ; and t0 is the time constant t0 of the system . Then t0 = (delta T )(dT(t)/dt ) = 1/r .

Happy New Year and happy modeling.
check the wiki's, internet, and your heat transfer books for more comprehensive explanations and equations.

5. Dec 31, 2011

### phinds

Just as a minor side issue to your post, you might give some consideration to the point of view that sloppy terminology leads to (or may in fact be cause by) sloppy thinking.

"temperature" and "cold" are not things you can store. Temperature is just a measurement of heat and "cold" is just a name we give to low amounts of heat. SO ... you can store heat and you can isolate things from heat (what you call "storing cold") but you cannot "store temperature" or "store cold".