It seems that pretty much all the wood stoves that work by heating up a large mass in order to slowly radiate heat between burns use various forms of masonry to store and gradually release that heat, not water, with the marginal exception of outdoor water stoves. I'm wondering whether masonry or water can practically hold more heat by volume or by mass. As I understand it, there's a lot more heat (something roughly like 5 times as much by mass, maybe roughly half that much by volume if my very uncertain math and understanding of the science is correct) released as a given mass of water cools off a given number of degrees compared to the same mass of masonry, but water can only be heated up to the boiling point, whereas masonry can be heated to much higher temperatures. Practically speaking, in an average eastern European style masonry heater how hot is that? And if we're comparing a given mass of masonry to the same mass of water, how do masonry and water compare in terms of practically holding heat? If water can practically be heated up close but not too close to boiling (say 190 degrees?) and 120 degrees (just throwing out my best guess) is the lower limit of a heating cycle, then masonry would have to be heated (averaging the external and internal temperatures of the entire mass of masonry) to approximately 5 times whatever that differences is, so perhaps 470 degrees (190-120=70 degrees, 70x5=350 degrees, 120 plus 350=470 degrees) to equal the heat storing capacity of water. Is it reasonable to expect to heat a masonry stove to an average temperature of 470 degrees (with much higher internal temperatures and much lower surface temperatures)?
storing heat -- masonry versus water
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Some thoughts. No recommendation 
The heat capacity (amount of energy stored to raise 1 kg by 1 deg C) for water is 4182 J/(kg C). For masonry it is 922 J/(kg C).
That is a factor of 4.5 difference in heat stored per kg of material.
So, to store the same amount of heat in the same weight, the masonry should be 4.5 times hotter (assuming the heat capacity does not change with temperature).
I'm not sure you would want a 90*4.5 = 405 C = 761 F piece of masonry in your home. Of course the hottest part will be inside the masonry where the fire was, not the outside.
Moving the heat with water is easier.
Masonry slowly diffuse the heat to the outside. But it'll only be warming the room it is in.
And that is what folks in e.g. Russia are doing: small home, big masonry heater in the center, heating the rooms adjacent to that heater (only). So you have to *design* your home for a masonry heater to work really well, if you want to heat your home rather than a room.
Holding the heat only depends on the insulation, i.e. the resistance for the heat to move outside of the holding mass. That does not depend on the type of mass (water or masonry).
So it depends on what you want; masonry can be really nice and slow. But it also remains localized. Water can be pumped around, and the rate of heat release can be more controlled.
There is something to say for masonry heaters - the tradition, the "identity" of the presence of such a heater in the home - versus having water piped everywhere.
The heat capacity (amount of energy stored to raise 1 kg by 1 deg C) for water is 4182 J/(kg C). For masonry it is 922 J/(kg C).
That is a factor of 4.5 difference in heat stored per kg of material.
So, to store the same amount of heat in the same weight, the masonry should be 4.5 times hotter (assuming the heat capacity does not change with temperature).
I'm not sure you would want a 90*4.5 = 405 C = 761 F piece of masonry in your home. Of course the hottest part will be inside the masonry where the fire was, not the outside.
Moving the heat with water is easier.
Masonry slowly diffuse the heat to the outside. But it'll only be warming the room it is in.
And that is what folks in e.g. Russia are doing: small home, big masonry heater in the center, heating the rooms adjacent to that heater (only). So you have to *design* your home for a masonry heater to work really well, if you want to heat your home rather than a room.
Holding the heat only depends on the insulation, i.e. the resistance for the heat to move outside of the holding mass. That does not depend on the type of mass (water or masonry).
So it depends on what you want; masonry can be really nice and slow. But it also remains localized. Water can be pumped around, and the rate of heat release can be more controlled.
There is something to say for masonry heaters - the tradition, the "identity" of the presence of such a heater in the home - versus having water piped everywhere.
Water undergoes a phase change at a pretty low temperature, which means that using it safely as a passive system isn't really possible - you need release valves at a minimum, and probably need pumps and a storage tank, and possibly a heat exchanger. If you build all of that, you have basically a wood fired boiler running baseboard heaters, which isn't uncommon.
For masonry, it's much simpler, but becomes a point source heat - you create a very long flue, surround it with a ton (or 3) of masonry, and burn a really hot fire once or twice a day to charge up the thermal battery. Because you can get the central masonry very hot without getting a steam explosion or having an 800 degree surface in the actual house, you can safely store all the heat in one spot and release it slowly.
If you want something located in your living space, the plumbing needed for a boiler setup is usually impractical, so things marketed as stoves specifically lean towards masonry as a thermal heat sink, but both boilers and masonry heaters are reasonable options.
For masonry, it's much simpler, but becomes a point source heat - you create a very long flue, surround it with a ton (or 3) of masonry, and burn a really hot fire once or twice a day to charge up the thermal battery. Because you can get the central masonry very hot without getting a steam explosion or having an 800 degree surface in the actual house, you can safely store all the heat in one spot and release it slowly.
If you want something located in your living space, the plumbing needed for a boiler setup is usually impractical, so things marketed as stoves specifically lean towards masonry as a thermal heat sink, but both boilers and masonry heaters are reasonable options.
Yes, a big issue is pressure. Masonry heating does not create pressure hazards. Water does. And when it goes wrong, you have a steam explosion.
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