An adult human requires an energy input that dissipates about 100 W, so we’re told that 8,400 kilojoules or about 4,200 (kilo)calories is needed to keep us alive. About 1 kg worth of fat (and associated interstitial water) in physiological terms. About 1,000 W of sunlight pours down on every square metre of Earth in broad daylight, varying with time of day and season, which is used by plant life at about 0.1% efficiency to make carbohydrates out of carbon dioxide and water. Per mole of carbon, about 480 kilojoules of energy is stored. Roughly 40% of that dry organic matter is carbon, thus about 20-16 MJ/kg is the stored energy density of dry biomass. Though the grade of energy density varies with the material. Oils/fats hold more, while sugars hold less.
According to the International Energy Agency, 7.45 billion humans used about 13 trillion joules of non-food energy every second in 2018 [here] – i.e. 13 terawatts. Day/night, 24/7, on average. Thanks to COVID-19, 2020 hasn’t been much higher. Of course, there are peaks and troughs to the demand. To supply it via the Sun, alone, some 13 billion square metres equivalent of collection area is required, with some multiplier based on the efficiency with which it’s turned into useful energy. That’s 13,000 square kilometres, minimum. Earth’s dry land surface area is about 150 million square kilometres so there’s plenty of collection space. However some areas are better placed than others. And for a significant fraction of the diurnal cycle there’s no Sun at all. Thus energy, to be available on demand, needs to be storable.
But let’s pause for a moment. There’s about 7.8 billion people alive today. At 100 watts each, that’s 780 billion watts of bioenergy being produced by all those bodies. Thus we use, from non-bioenergy sources, the equivalent of 17 ‘people’ in energy to power our modern life-styles. This varies from country to country significantly – some average 2 or 3, others maybe 100 People Equivalent Units (PEUs). If the World Population flattens out at 9 billion people and they all get ‘rich’ enough to use 100 PEUs, then the global demand will be 90 trillion watts. That’s about 22,000 tonnes of oil, or a kilogram of uranium, or 150 grams of deuterium. Every second. 31,557,600 seconds per average Julian year. The down-sides of oil and uranium are well known, and we’re still working on how to efficiently fuse deuterium for energy.
So what if we use solar? We can’t capture that energy via biomass. At 0.001 efficiency, we’d be using 90 million square kilometres of land. We could use 90,000 square kilometres of land to collect it at 100% efficiency, but there’s a few problems to circumvent. Firstly, the Sun’s maximum output received on the ground is available at most about 40% of the time in the very best locations – those near the Equator. Atmospheric attenuation and the diurnal cycle conspire against Solar. Away from the Equator and the percentage is lower. Some parts of the world receive the equivalent of 1/5-1/12 of the best maximum Solar input. So what do we do?
Imagine the 10 kW is supplied by solar. 24 hours in a day, but sunlight at maximum quality for 10-2 hours a day. So we use “storage” which means either batteries or chemical energy. One option is fuel cells powered by hydrogen/oxygen produced by electrolysis of water. With an electrolysis efficiency of 90% and a fuel-cell efficiency of 60%, then the total installed solar needed is between 4.6 to 22 times the maximum supplied. Batteries get charging efficiencies of ~95% and discharge efficiencies of 95%, giving a total of 90% cycle efficiency. Thus the solar power installed needs to be ~2.78 to 13.3 times the solar average. And batteries themselves cost money – Tesla is aiming at $50/kW.h price, thus a price of ~$33,400 to $160,000 in installed storage for the 10 kW super-users of some energy rich countries. Over a 30 year system life-cycle that’s a cost of ~$0.13-$0.60 per hour. Of course that’s spread through-out all the kinds of energy usage we pay for in our every day lives, so don’t think of it as an up-front fee.
But what if solar can be available more than the best case 3,500 hours a year of top quality sunlight? What if it can be supplied 8,765 hours a year?