Calculate the energy in a sauna hot stone

[lkgilbert]

Hello, I have a physics question about saunas and hot stone technology which I hope someone can help me with.
I recently experimented by reconstructing a "sauna" found at a Bronze Age site in Scotland. We heated stones (sandstone) in fire pits and transferred them to the circular 'sauna' structure we had build from stone, wood and turf. The effect when pouring water over the hot stones to produce steam was brilliant and the experiment has been deemed a great success providing insight to how Bronze Age people might have used these structures.

I want to be able to work out how much energy the stones held. I recorded temperatures from 500-900 dC with a thermal imaging camera and now want to work out what the equivalent energy is.

I then want to find something with comparable energy. To be able to say a line like; "these Bronze Age stones hold an equivalent amount of energy as 5 kettles boiling." a an example.

Is this sort of simplification possible? Is this sort of equation possible?

Any advice would be hugely welcomed.

Thanks, Louisa

 

[Merlin3189]

Yes you certainly can do that.
What you need is the specific heat capacity of the rocks.
I looked up a few, granite 790, marble 880, sandstone 710, slate 760, limestone 909 all in Joules per kilogram ^oC
Unfortunately I don't have a lot of confidence in these, since there were some puzzling values , eg. quartz 730, sandstone 710, sand(quartz) 830 J/kg ^oC
So I'd suggest getting some stones / rocks from your garden and measuring the values yourself. (Method to follow)

But if you used a figure around 800 J/kg ^oC, I think that would be near enough for your purposes.

Edit. OMG my units! I've just corrected them. (I'd misread K as Kelvin rather than kg)

 

[lkgilbert]

Thanks Merlin, it was Orkney sandstone we used.
But if you have the 800J/K dC what then to work out the rock's heat energy?

I am very new to this, sorry if this is an amateur query

 

[Merlin3189]

In case you're not familiar with these ideas, specific heat capacity tells us the amount of energy needed to heat a unit of material by 1 degree. So here, using J/kg ^oC, it's the energy to raise the temperature of 1kg of rock by 1^oC.

So the amount of heat stored by a rock = its mass x temperature rise x specific heat capacity
For eg. a 2kg lump of granite, cooling from 500 ^oC to 100^oC (ie. difference of 400^oC),
would store 2 x 400 x 790 J about 632kJ.

To compare this to water you need the specific heat capacity of water, which is 4182 J/kg ^oC, and the volume of your kettle (or the mass of water it holds, which, in kg, is the same as its volume in liters, near enough.)
Eg. to heat 2 litre of water to boiling to 100 ^oC (ie. 80^oC above ambient 20^oC) requires
2 x 80 x 4182 J =680 kJ, a bit more than your 2 kg rock cooling from 500 ^oC. to 100 ^oC

You can get a general idea by comparing the specific heat capacities of rock and water: granite is 790 J/kg ^oC and water is 4182 J/kg ^oC
so every kg of water takes 4182/790 = 5.3 times as much energy to heat as rock. For a given amount of energy, you can heat a similar mass of rock to 5x the temperature, or 5x the mass of rock to the same temperature as water.

 

[CWatters]

I think some types of rock are prone to shattering or even exploding when heated. I'm no expert but would sandstone have been used? Some websites say avoid porous stone.

 

[Merlin3189]

Good point. The porous rock sounds maybe a bit risky to me as well. I just gave data for any rocks I could find quickly. (I don't know the names of most rocks of course!)
I also wonder whether non-porous rock also shatters. For example, glass might shatter when put in a hot fire - probably due to uneven rapid expansion - obsidian?. But presumably this is less energetic than a gas explosion.

The heating in the fire expt is already done (by geologists, anthropologists, paleontologists, or whatever). We're just looking at the numbers here.(*)

My suggested method for measuring the specific heat capacity involves heating the rocks in boiling water, so i don't think explosion by superheated steam in rock pores (or just heated air/gas) is likely to be a problem.

(*) Just struck me that most of PF is just looking at numbers. Have physicists deserted experiment? As too dangerous, or too messy, or too much work, or just not as accurate as formulae?