# What quantity of basalt would power NYC with power for a day?

Some companies are refitting steam power stations to hot basalt, where many tons of rocks are heated to 750°C by wind power and the thermal energy is used to generate steam in power stations.

How much basalt can supply 11,000 megawatt-hours, enough to power New York City for a day, given a total process efficiency rate of 55%?

• What's the specific heat capacity of basalt? Then you can work it out.
– Transistor
Jun 5 at 12:05
• "... given a total process efficiency rate of 75%?" Where does this number come from? As far as I know 45% would be considered good for a steam plant on its own, never mind the additional losses with hot rock.
– Transistor
Jun 5 at 12:16
• Couldn't we just build cities on big basalt blocks? ;-)
– Scott Seidman
Jun 5 at 12:49
• endmemo.com/chem/specificheatsearch.php?q=Basalt%20Rock and "The average density of basalt is 2.9 g/cm3" from wikipedia.
– ErikR
Jun 5 at 12:57
• Reason you can't find a spec has to do with there being a fairly wide variety in composition. To make it more annoying, you probably shouldn't just consider composition by mass since there are vesicles which can be air pockets of varying sizes (probably part of why you're considering it in the first place - insulation built in)
– Abel
Jun 5 at 13:14

Engineering Toolbox gives the specific heat capacity of rock as 0.84 kJ/kg.K.

Let's work with 40 TJ = 4 × 1013 J = 4 × 1010 kJ.

Let's say we could operate with rock starting at 600°C and ending at 200°C so a ΔT of 400°C through the heat extraction cycle.

From the SHC we can calculate

At 3 T/m3 that gives a volume of

That's a cube of 34 m side.

• That confidence is what i required!!! cheers! compare that to fossil fuels it's a lot less quantity through the year.
– DeltaEnfieldWaid
Jun 5 at 13:21
• Just for comparison, the total amount of gold mined in human history is about a 19 m cube.
– Transistor
Jun 5 at 13:25
• Just one gold mine can dig >150 m cube of rocks though. the total value of the gold is \$7.5 trillion, and the same volume of basalt is priced at a competitive \$4 million. I think it's amazing that it would take only 4 million's worth of basalt battery to keep NYC running every day for a year. perhaps its'the future? google.com/search?q=gold+mine
– DeltaEnfieldWaid
Jun 5 at 13:51
• Ask Iceland if they have any going cheap. They can supply you a load already pre-heated.
– Transistor
Jun 5 at 13:53
• @DeltaEnfieldWaid be aware that the basalt will be nowhere the most expensive part of such an operation. It may as well go into "others" category in the Big Table Of Expenses.
– fraxinus
Jun 5 at 20:25

I'll try to figure it out:

11,000 MWh = 39,600,000,000 kJ

Basalt specific heat: 0.84 kJ/kg kelvin

if we were using 1 kelvin of the basalt we would need 39,000,000,000 kg / 0.84 = ~47,000,000,000 kg of basalt

Using 600° C of usable thermal storage: 47,000,000,000/600 = ~ 78,000,000 kg of basalt, 78 thousand tonnes,

basalt is about 3 tonnes per m3, NYC needs 26,000 m3 of basalt

say 50,000 m3 of basalt given an efficiency of 50%, that's cube of 36m L-w-h

A giant shipping container is 78m3, it's only 649 shipping containers, it's about 5% the capacity of the biggest shipping container boat in the world.

5% of this boat:

• I'd say there are more than 200 containers visible above deck on the first row of that ship.
– Transistor
Jun 5 at 13:23

A few hints...

Basalt has a specific heat capacity of 603 joules per kg per °C. This means that to warm 1 kg basalt up by 750°C you need to imbibe it with 603 x 750 joules of heat energy. That's 0.452 MJ. It's the same story when extracting heat from the warmed-up basalt but, you only want to cool it a small fraction of what it has been "charged" to so that the conversion to steam process is not compromised. Bear this in mind.

Also note that 11,000 MWh in joules is 11,000 MJ x 3600 = 39,600 GJ.

The next part calls for a judgement to be made on how much energy you can take from the Basalt without cooling it too much. You don't want to cool it too much else the steam process is going to sag a little. But, maybe you can allow it to cool by 100°C with a bit of hand-waving.

So now, you have to work out how much mass of Basalt will cool by 100°C when 39,600 GJ is taken from it.

• Hey Andy, I tried to figure it out using 600'C of usable temperature, i.e. from 150 to 750'C. Perhaps the range is 750'C, from 200'C to 950?
– DeltaEnfieldWaid
Jun 5 at 13:19
• At 150C the steam plant efficiency will be hopelessly low.
– user_1818839
Jun 5 at 17:14