I can't remember if I saw the argument here or on Reddit, but this is my preferred platform so it's going here.
Summary of argument: a user should have been using water for their thermal battery, not sand, because water has better heat capacity (4.18 joules per unit of mass person unit heat - 4.18/gK). Sand's thermal capacity is significantly lower (0.835J/gK).
Looking at these numbers alone in the post I understood why someone would say that; it also made me question why so much research is being done on sand batteries. The user who argued against sand batteries missed a crucial factor: material density. Water has a density of 1000kg per m^3. Dry sand (regular not pure quartz sand) has a density of 1730 kg per m^3. I found no satisfactry response to the argument in that thread, but that thread is now lost to me. I have also been curious about how much better regular sand is for heat batteries than water.
When designing large batteries, the goal is usually energy per volume. Let's compare 1m^3 of each (roughly 3.3ft cube) and how much heat it can hold before the next state change (which matters a lot when managing the pressure from steam).
Total stored energy = mass (g) * thermal capacity (J/gK) * heat (kelvin).
Water: 1,000,000 * 4.18 * 373.15 = 1,559,767,000J Sand: 1,730,000 * 0.835 * 1996.15 = 2,883,538,482.5J
Over 1 billion more joules per m^3. I hope this makes it clearer why sand batteries are such an area of interest lately. It certainly did to me.
Disclaimer: I am not an expert, so there may be mistakes. All the numbers and relevant equations were found on the internet.
How are you getting your sand that hot?
There is a sand battery start up in Tampere (Finland) that is heating to 1k Celsius so by the OPs calculations that would still give it a small edge over water but with the added bonus of the intrinsic insulation - very handy in the cold winters. They have a pilot plant that is being developed to support the municipal heating network.
Curious what they're using for a transfer liquid. Are NaK or sodium systems pressurized to handle that?
It looks like their current generation of systems are electricity in, via resistive heating, then heat out via hot air. Efficient electricity out would appear to be an active research area for them, but it would also seem, that there are still a number of applications where on demand heat at several hundreds of degrees is still very valuable.
The easiest method is using sand as an electrical resistor allowing the resistance to heat the sand up. I've also wondered about other methods too, such as solar ovens or baking the sand in some way and dumping the hot sand into the battery.