4 ms·
The the ratio of area A to volume V for a sphere of radius R is 3/R. The larger the sphere, the less surface area to volume. A corollary of this is that a suf
by retrac 4y ago
The the ratio of area A to volume V for a sphere of radius R is 3/R. The larger the sphere, the less surface area to volume. A corollary of this is that a sufficiently large thermal tank has little in the way of heat loss to its surroundings in relation to its heat capacity.
At large enough scale, it's probably the most efficient way to store energy for general heating purposes. Simple water has significant thermal capacity. 1 tonne (roughly 1 kilolitre, 1000 litres) of water at 80 °C holds ~50 kWh of useful heat relative to normal indoor temperatures. Enough to heat a Canadian home overnight on a bad winter day and then some. 1 tonne of water isn't really that big; a typical car's interior volume would hold several tonnes of water. Home hot water storage, for heating over several days or a week, is quite viable with a large basement tank, and commercially available. Used with intermittent heat sources, and sometimes to save money when heat costs more at different times, like with electric time of use.
A standard Olympic swimming pool holds several thousand tonnes, the largest indoor swimming pools tens of thousands of tonnes. 20,000 tonnes of water at 80 °C = about 1 gigawatt-hour of usable energy storage. Assuming no losses, That could heat many dozens of typical Canadian suburban homes all winter. What about bigger? Some lakes are so large their thermal capacity causes their temperature to significantly lag behind the seasonal changes, moderating the local climate. The largest fully artificial reservoirs are measured in cubic kilometres. That's billions of tonnes. 1 cubic kilometre of hot water would have 30 terawatt-hours or so. That's in the range of the yearly energy consumption of small cities. And at that scale, even a lightly insulated tank would lose an insignificant fraction of its heat, even over a timescale of months.
Getting into less conventional territory, with much higher temperatures (perhaps a molten metal instead of water) and some real big tankers, it might be feasible to literally ship heat. This rarely made sense in the past except in some edge cases like using industrial waste heat. Fossil fuels were almost always the source of the heat to begin with. Just ship the fossil fuels. Far more energy dense and no conversion losses. But the economics are changing.
(As an aside, the effect of the ratio of area to volume is just not intuitive to me, for some reason. But it's a very powerful scaling force in nature. It is why a bucket of water takes days to evaporate while tiny droplets of mist take seconds. Area for evaporation relative to volume. It even limits the maximum size of a terrestrial animal. Elephants push that limit. About a kilowatt just for base metabolism. In a thickly-walled airtight tank. A really big tank. They'd cook from the inside out without active cooling in a matter of hours. Their hearts are heat pumps and their ears are radiators.)
- bjourne 4y ago> Assuming no losses, That could heat many dozens of typical Canadian suburban homes all winter. This honestly seem incredibly optimistic to me. Even a high-end thermos will lose its heat in less than a day. Faster in a cold environment. And afaik, temperature loss is proportional to temperature difference, so the hotter the liquid the faster it cools.
- pfdietz 4y agoThe thermal time constant for a sphere scales as radius squared (one factor of r due to volume/surface area, and one factor due to the temperature gradient scaling as 1/r). Your thermos is quite small.
- retrac 4y agoWhile literally zero loss is a violation of thermodynamics, with a really large tank and good insulation, it gets to self-discharge rates lower than most battery chemistries. A few percent per month. There's a small district heating system in Alberta driven with solar thermal power. It uses a large insulated soil heatsink. Most of the energy input is in the summer and it took four years to fully charge up to operating temperature. It holds enough heat to provide all required heating through the winter for ~50 large houses.