Stone heaters / Physics / Brains needed?

Question

We are a trainings center and as part of a course we are working on a project. We would like to build a stone heater.
The usually offered stone heaters are coming in the shape of a panel/slab and is aprox 1.2 x 0.5 x 0.03m and equipped and heated with by 1000 - 1200 Watt. The granit/marble panel/slab weights aprox 45 kgs.
The manufacturer is saying that this size(mass) - surface relation is the most efficient. aprox 0.5M2 to 1000 Watt.
As we ve got in our workshop only 5 blocks of granit, we would like to know is we also get a good result with our blocks.
Instead a granit panel, we thought to heat our block of granit (dimensions are 0.7m x 0.65m x 0.35m )aprox weight is 80kg and is equipped with 3 heating elements of each 800Watt.

Is a corrolation between the mass/surface/watt and heating efficiency???
Can we heat our blocks and get the same or an even better result ?
Are there other shapes which would be even better for this purpose.
Does more mass means more consumption?

Answer 1

Is a corrolation between the mass/surface/watt and heating efficiency???

Now what do you think ? ...
As a 'mind' exercise, consider what would happen if you took extream cases .. for example, mass = 1 gram, mass = 1 tonne ? .. surface area = like a sheet of paper or like a golf ball ? .. heat input from a candle or from a flame thrower ?

NOTE - this 'take extream cases' is a VERY GOOD way of working out if things are 'linked' in Science ..

The only thing that might not be obvious is that heat LOSSES are proportional to surface area - so (for a given heat input) a flat sheet will take longer to reach an even temprature compared to a solid ball.

Can we heat our blocks and get the same or an even better result ?

You have approx double the MASS and double the heat input. So the instinctive answer is 'yes' = the blocks shoud reach the same temprature in the same time. However the final temprature reached will depend on the LOSSES (assuming you don't turn off the heaters)


Are there other shapes which would be even better for this purpose.

It's unclear to me what is the function of the granit blocks ... I would expect better results if you use the heaters to directly heat up whatever container is used to hold the food you are cooking.

If the blocks are acting as a cooking "plate", then the ideal shape for heat up time and easy of use is 'as thin as possible' and 'no wider or longer than necessary to contain the food' ..

However for maximium efficiency I would suggest you need to heat minimise losses - so this suggest enclosing the heaters together with the food in a air tight container (to eliminate convection losse) enclosed in a vacumn bottle (eliminate conduction losses) painted silver on the inside (to minimise radiation losses)...


Does more mass means more consumption?

You mean total power consumption ?
Yes, of course (think about it - how much power needed to heat up a penny ? how much to heat up a frying pan ?)

If you want to reach the same temp. in the same time, then you need to put heat in "faster" (so more instantaneous power i.e. more Watts will be needed).

If you are willing to wait longer to reach a given temp. (and the losses are the same in both cases) then you don't need 'faster' power (watts) but you use it for a lot longer (so the total amount you use is more)

Answer 2

Your granite slabs are too thick (0.35m) compared to the other slabs of 0.03m (just 3 cm). So, you will not be able to achieve anywhere near the heat efficiency or temperature what the commercial heater can provide. You need to get your slabs sliced very thin carefully.

Yes, more mass means more consumption of energy and slower heat transfer.