Early this morning I spent a bit over an hour heating the basement. I'm no athlete, but my morning exercise session has about an hour of rowing with the target of an average of 150 watts of power. A real athlete could do much better - 400 watts for a cyclist is certainly possible, but 150 watts is what I can do and still function later in the day. A rower with a bit of training somewhere between 22 and 25% efficient, so my body is burning energy at the rate of about 700 watts. 600 watts for rowing and about 100 watts to keep the rest of me alive. That means I need to get rid of a lot of waste heat.
It is interesting to think about this in terms of power density - the power I use divided by the surface area of my body.1 Without exercise I need an average of about 100 watts of power from nutrition and my surface area is about 2 square meters, giving a power density of about 50 watts per square meter.2 Power density shoots up during exercise. Usain Bolt generates about 2000 watts of waste heat in his 100 meter trips - over 1000 watts per square meter. A problem is a body can't rid itself of heat that quickly, but that's another issue.
Most of the energy we use ultimately comes from the Sun. On average we get about 1366 watts per square meter at the top of the atmosphere. About 1,000 watts makes it to sea level on a clear day. Now through in the fact that the Earth is a rotating sphere, clouds, etc and the number drops to about 250 watts per square meter. More than a person.
Some of the sunlight is turned into carbohydrates by green plants. If the average efficiency of green plants was one percent (the real number is a few tenths of a percent), they would be average about 2 watts of power. If we could eat these high efficiency plants, about 50 square meters of garden would feed me. Real farmland needs are much greater - something like 0.5 hectares in the US and 0.08 in China.
Something like a 10,000th of the plants are turned into a stored fossil fuel over long periods of time. Coal production may only average a few tenths of a milliwatt per square meter, but the planet has stored it for millions of years. A little over a large area for a long time can add up.
Geothermal power sounds great at first glance. Some of it comes from heat leftover from the Earth's formation and some from radioactive decay within the Earth. On the scale of humans this amounts to a non-exhaustible power source. The interior of the Earth is hot, so why not let it heat up water to make power? We would have something rare - a non-intermittent renewable source of power. The problem is that of concentration. On average geothermal energy is diffuse working out to about 50 milliwatts per square meter - about a thousandth the power density of your body. On the other hand the Earth has a lot of surface area, so an estimate is in order to see if it is generally practical before considering its economics.
Unless you are in a location with active volcanoes or geysers, the diffuse heat from the ground only produces a tiny temperature difference at the surface. The efficiency of a machine that can extract power from a heat source depends on how hot the source of power is.3 The trick is to find some really hot water. Either find hotspots like those seem in Iceland, California, New Zealand and Japan or drill a deep hole to where it is hot.
On average drilling about 10,000 feet takes you to a hot enough area to get to give a 30% theoretical efficiency. 50 milliwatts per square meter is now down to about 17 milliwatts.4 We have to have a lot of surface area for the water to heat up, so fracking the rock is essential. A square kilometer would provide 17,000 watts. Now it is a question of asking your population density and looking at your needs. The average American household uses about 1,000 watts of electric power (twice that much if there is an electric car). Do the arithmetic, but this is not a global solution.
Geothermal can be great locally. Reykjavik gets almost all of its non-transportation power from hydro and geothermal and has the cleanest air of any world capital (assuming a volcano is erupting). A few other areas with very dense concentrations of very hot water have been exploited totaling about 11 gigawatts of electric power generation worldwide along with hot water for district heating and industrial use. The Western US is, at least in theory, economically exploitable using fracking, but some experiments have led to an increase in small earthquakes to prevent widespread use.
Iceland is so beautiful - unfortunately the weather gets a bit depressing over the long haul. Between the climate and language it seems likely the population should remain in check to allow them to get by with just hydro and geothermal power.
1 For historic reasons power density is usually power/area rather than power/volume although both are used. Confusing ... I'm sticking with power/area for now.
2 Direct measures of human surface area are difficult, but a few good approximations exist - fortunately as it is needed for dosing some medicines. My tables and formula handbook suggests one by Mosteller: body surface area (m2) = [height(cm) x weight(kg)]/3600]0.5. Mine comes out to 1.95m2 - close enough to 2 m2.
3 The theoretical efficiency limit is 1.0 - (ambient temperature)/(source temperature) where temperature is measured in degrees Kelvin. It is rare to find a geothermal source even one degree hotter than the ambient temperature. That would give about 0.3% maximum theoretical efficiency. A complete non-starter.
You can use this formula to find the maximum theoretical efficiency of an internal combustion engine. The temperature of the burning gas in a cylinder is about 1500°F - roughly 1100°K. So 1 - 300/1100 is a bit over .7 - 70% efficiency. Even the best engines are far below this. When you add the drivetrain about a quarter of the energy of the gas you buy goes towards moving you and your car. I like bicycles and electric vehicles:-)
4 Note there is enough heat to extract more than 17 wW/m2. The problem is you end up cooling the rock and need to move your well and fracture field. The 17 mW number represents the sustainable resource - its average replenishment rate. Hot spots have much larger power densities, which is why this technology is likely to be geographically limited.
It is now high tomato time and you should be celebrating. Here is an old recipe I've mentioned before, but with perfect tomatoes it is both simple and brilliant.
The format of this one is not standard, but rather from an email I sent to one of you a year ago. I won't translate as it seems better in the narrative form.
This is the time of year that excellent tomatoes begin to appear. If you find some with amazing flavor and want an equally amazing dinner the trick is to keep things simple. This is a tomato and pasta dish I dream about all Winter and Fall. If the ingredients are great it can be spectacular and it also happens to be amazingly simple
Simple Summer Pasta and Tomatoes
Some time ago I had a very simple tomato and pasta dish. The tomatoes were
in chucks and not really cooked. It would only work if they were perfect so
I gave it a try. Here is about what I did. This would be enough for two
hungry people or four people if served as a side course.
Two really amazingly blimpishly ripe tomatoes that are going to have great
flavor. I would go with an heirloom tomato as the new ones have so much
goodness bred out of them. My guess is I had maybe about one and a half
pounds of tomato. Chop these into half inch pieces and scape them into a
big enough bowl (how is that for precision?) be sure and get some of the
juice that is sitting on the cutting board.
Pour some good extra virgin olive oil on them. Maybe two glugs (another quality
measurement). Put a good amount of a good finishing salt (Malden is great) and freshly ground pepper on them stirring to mix. Let them sit.
Start some water boiling for the pasta and throw some salt in. Cheap salt
Now chop a strong red onion or some scallions into slivers. Maybe about a
Chop a handful of good arugula
Cook about a half pound of pasta and try to stay away from the marinating
Place the onions on top of the tomatoes spreading them out, then make a layer
of arugula choppings
Now dump the pasta on top of the layered mixture in the bowl and leave it
for a two or three minutes. To deal with the frustration grate some good
cheese for a topping and top it. The heat from the pasta is slightly cooking the ingredients beneath, but just barely.
Now mix it all up and serve.