The place I saw this most clearly described was in Standard Thermal's concept, which will store the heat in huge piles of dirt heated to 600 C. The thermal time constant of such piles can be many years.
If we assume the delta of 550 degrees (600 down to 50), you'll need: 7.913×10^10 J / (550K * 1000Jkg^-1K^-1) = 143,872,727 kg of material in your pile. This is a ridiculously stupid number. And I don't see any obvious mistakes?
I use units(1), which also helps me avoid dimensional errors (dividing when I should have multiplied, etc.):
You have: 7.913e10 J / 550K / (1J/g/K)
You want: kg
* 143872.73
/ 6.9505876e-06
maxerickson says, "Still big number," and 144 tonnes would typically be an unwieldy quantity of material if you had to buy it. But Standard Thermal's intention is not to buy dirt, just pile up already-on-site dirt with a bulldozer or excavator. If we assume 1.3 tonnes/m³, that's 110m³, or, in medieval units, 144 cubic yards. https://www.eaglepowerandequipment.com/blog/2022/03/how-much... tells us:
> An excavator could be used to dig anywhere from 350 to 1,000 cubic yards per day, depending on a number of factors including bucket capacity, type of ground, operator skill and efficiency level, and more. (...)
> One of the biggest factors that impact how much an excavator can dig in one day is the unit’s bucket size, which typically ranges from 0.5 to 1.5 cubic yards of bucket capacity. Most common regular-size excavators have a 1 cubic yard bucket capacity, and mini excavators are closer to the 0.5 cubic yard capacity.
So, with this number, we're talking about a few hours of work for a "mini excavator". https://www.bigrentz.com/rental-locations/pennsylvania/pitts... tells us that a "4,000 lb. mini excavator" rents for US$197 per day. So the expense of moving the dirt is not really significant, compared to other household projects such as replacing the roof, insulating the walls, or repainting the exterior.
Standard Thermal mentions that they are in effect firing the clay in the ground, that they've had significant trouble with resistance-heater reliability, and that their objective is to power steam-turbine power stations with the stored heat. These three facts lead me to believe that they're targeting a temperature closer to 1000° than to 600°.
600 C is about what a coal fired power plant would use. And 600 C is around the maximum that you want if you're using cheap steel for the pipes. Much beyond that and creep becomes a problem. So I don't think 1000 C is their target.
The surface will always be only slightly hot. Heat will be stored inside, insulated by overlying dirt. Dirt isn't the best insulator by thickness, but it's a very good insulator by $.
A typical house in Midwest needs around 22,000kWh (7.913×10^10 J) over the winter (75 million BTU - https://www.eia.gov/todayinenergy/detail.php?id=57321 ).
If we assume the delta of 550 degrees (600 down to 50), you'll need: 7.913×10^10 J / (550K * 1000Jkg^-1K^-1) = 143,872,727 kg of material in your pile. This is a ridiculously stupid number. And I don't see any obvious mistakes?