Built on Facts

There’s a little bit of buzz burbling around over Al Gore’s scientific goof during a Conan O’Brien interview. Discussing geothermal energy, he said the following:

It definitely is, and it’s a relatively new one. People think about geothermal energy — when they think about it at all — in terms of the hot water bubbling up in some places, but two kilometers or so down in most places there are these incredibly hot rocks, ’cause the interior of the earth is extremely hot, several million degrees, and the crust of the earth is hot …

Of course the interior of the earth is extremely hot, but not that hot. It’s several thousand degrees rather than several million. If the earth were several million degrees it would be a rapidly diffusing cloud of metallic vapor. Even the center of the sun is only perhaps 13 million degrees C.

But I’ll let him slide; pretty much everyone blanks out from time to time. And it gives us a chance to do a little thinking about just how much thermal energy is in the earth.

First of all, just because something is hot doesn’t mean you can squeeze energy out of it. You can only squeeze energy out of temperature gradients – you need something hot and something cold. This is why we can’t just set up a temperature-to-energy machine in the desert and have free energy. In your car, for instance, you need both the heat of the burning gasoline and the much cooler ambient temperature from the outside air via your radiator to turn the hot gasoline vapors into forward progress. Power plants frequently have large cooling towers for that very reason. It’s not the energy of the hot substance, it’s the process of moving that heat to a cooler place that creates useful work. Think of it in the same way as water flowing downhill can turn a paddlewheel – it won’t work unless the water starts off high and ends up low.

But that’s not a problem here. The interior of the earth is hot and the exterior is much colder. The difference in temperature is such that the efficiency of heat-to-work conversion could be near 100% in theory, though in practice it would be much lower. And we’re not likely to run out of geothermal heat any time soon. As a slightly wild Fermi calculation, assume that the earth is uniformly iron at 3000 C. The specific heat of liquid iron is about 611 J/kg K, so cooling the earth to room temperature this yields about 1.8 million joules of energy per kilogram. Multiply by the mass of the earth, and the total energy content might be in the neighborhood of 10^31 joules. The total energy consumption of the world’s human population is in the vicinity of 5e20 joules per year.

Divide out, the earth’s geothermal energy could support that consumption rate for about 21 billion years. We’re not likely to use it up.

So why isn’t it in widespread use? After all, every nation has domestic access to it – all you have to do is drill straight down. The main problem is that the temperature really doesn’t start getting ramped up until dozens of miles down. Drilling a hole that deep and pumping water (or whatever) down and up is technically unfeasible. Geothermal is at its best at those places which are close to geological activity that brings the heat closer to the surface. Volcanic and other geologically active locations often do very well with geothermal power. Iceland in particular produces vast quantities of usable energy from the internal heat of the earth. Most other places are much farther from the hot regions of the earth’s interior and geothermal is correspondingly much more difficult to get.

Sadly Al Gore’s hopes for geothermal as a major clean energy technology are probably futile until deep drilling develops into a much more mature form. It would be nice if that happened; the energy to be tapped is pretty close to inexhaustible.

Comments

#1 Ryan V
November 18, 2009

“In your car, for instance, you need both the heat of the burning gasoline and the much cooler ambient temperature from the outside air via your radiator to turn the hot gasoline vapors into forward progress.”

I’m pretty sure that cars don’t work like this. Cars don’t have a carnot engine built in, instead their energy comes from the expansion of reagents in the gas-air mixture after they ignite.

The radiator keeps the engine cool, since an engine that is too hot will cause the air-gas mixture to detonate at the wrong point in the cycle, but it has nothing to do with carnot efficiency or the ability to get work out of the engine.
#2 Charlie (Colorado)
November 18, 2009

Well, I’m inclined to agree on the “millions of degrees” thing, except that I’ve started to get a little cranky about what people can or can’t get away with in the press.

If Bush, or Sarah Palin, had said this, it would be the lead on HuffPo, Olbermann, and every MSNBC news show for a week.
#3 Ryan V
November 18, 2009

On thinking about it more, I see your point.

If the engine is too hot then the only source of work would be expansion due to the liquid->gas chemical reaction. At normal temperatures you probably get a fair amount of work from the expansion of it all due to the heat of reaction.

Although I am still not convinced either way, there are alot of factors in this example
#4 Matt Springer
November 18, 2009

A car engine more or less operates under the Otto cycle, which is of necessity less efficient than the Carnot efficiency for mathematical reasons. Carnot is just an upper bound. You’re entirely right about the proximate reasons for this, but not quite right about the implications. A car engine has to have a cold reservoir (the outside air) just like any other heat engine. If it didn’t, the exploding gasoline mixture wouldn’t move the cylinders because the equally-hot outside air would be pushing back with equal force.

Obviously a real engine will die at much lower temperatures than this thermodynamic limit! But the general point still works.
#5 marc
November 18, 2009

Energy for a car comes from a chemical reaction, the combustion of gasoline. When the gas is ignited by the spark plug, it burns, producing gases at a higher that push the piston.

http://www.howstuffworks.com/engine.htm

But I’ll let this slide; pretty much everyone blanks out from time to time.
#6 Chris Noble
November 18, 2009

The real question is whether Al Gore, when corrected by scientists, will agree that he made a mistake – or will he insist that thousands of scientists are wrong.

I’m pretty sure that I know the answer.
#7 Nathan Myers
November 18, 2009

… and I’m completely sure your answer is wrong.
#8 Art
November 19, 2009

I’m not sure that exhaustion of the heat energy of the earth’s core is the practical limit on use. I suspect that long before it is cooled to the same temperature of the crust that the molten core will be slowed in rotating. This then would weaken or disrupt the magnetic field around the planet that protects the atmosphere.

So you can’t afford to let that core solidify or viscosity thicken enough to let that happen. So it is something less than 21 billion years of energy.

On the other hand, as I understand it the sun is due to run out of fuel and expand to the point where earth is pretty much fried to a cinder in something like 10 billion years. So if we can get 10 billion years out of geothermal heat energy becomes somewhat less of a hot commodity on earth. What with it being pretty common and the reductions in populations to sell it to.

I’m also bothered a bit by the word “inexhaustible”. The North American continent was said to have more trees than could ever be used. The oceans were so large that they were thought to be inexhaustible as a dump site. It would never cause problems. Nuclear power was going to be inexhaustible and too cheap to meter. We seem to be perpetually overestimating resources and underestimating our ability to consume.

Maybe it is different in this case but it would be nice to see at least one case where we planned ahead and designed a sustainable use system from the start. I mean, it isn’t like it really has to last forever. Ten billion years of power will be quite enough thank-you. After that we, it, and anything else left of earth is gravy.
#9 Left_Wing_Fox
November 19, 2009

Actually, the geothermal trend in housing here in Canada (Perhaps fad, we’ll see) is based on ground source heat pumps. Not the same as true geothermal, since it still requires an external energy source, but still offsets external energy requirements.
#10 rob
November 19, 2009

“In your car, for instance, you need both the heat of the burning gasoline and the much cooler ambient temperature from the outside air via your radiator to turn the hot gasoline vapors into forward progress.”

the above quote is true. the details of internal combution engines and carnot versus otto blah blah blah have nothing to do with it.

basic thermodynamics shows if you somehow discovered a way to get a heat engine to operate without the necessity of a cold resevoir, it would be the same thing as perpetual motion.

you would be able to hook up your “magic” engine to a heat pump and get work for nothing.

entropy: not just a good idea, it’s the second law.
#11 Polyester Mather
November 19, 2009

I;m afraid the apologetics don’t wash- despite decades of continuous tuition by the good and great-, Al’s scientific ground state remains close to zero- six months ago he invited a Senate committee to accept the climate of Venus as representative of the fate of the earth, insisting CO2 has led to to surface temperatures “hotter than the boiling point of lead ”

There is also the small matter of innumeracy- remember the infinite rate of extinction cure that gracing a million or so copies of his 1990′s best seller ‘The Earth In The Balance ?

Instead of adding a note of explanation as to why we are not extinct- the curve went dead vertical in the year 2000, that spectacular gaff was redacted without comment from this century’s editions.
#12 nanoAl
November 19, 2009

Actually, the carnot cycle thermo-stuff does matter, thats why hybrids that run on the atkinson cycle are more efficient, the atikinson cycle uses less compression and comes closer to the carnot cycle. Wikipedia it

Geothermal heating/cooling is a booming business here in alberta. Once you dig down a little bit the temperature is constant and pretty comfortable at about 16 Celsius, colder than our ridiculous summers and warmer than our frozen winters. cool stuff
#13 Matthias
November 19, 2009

The 21 Gyr estimate is probably quite conservative, because some (IIRC about 50%) of the heat comes from natural radioactive, i.e. there is heat being produced in the Earth right now and for another few billion years.
#14 doug l
November 19, 2009

Apparently both the DOE and Google.org think the feasability is worth investigating.
Check out this:
http://www.potterdrilling.com/
and this:
http://www.altarockenergy.com/egs.html
#15 beautox
November 20, 2009

New Zealand (where I live) gets around 10% of it’s power from Geothermal ; see http://en.wikipedia.org/wiki/Geothermal_power_in_New_Zealand

In addition to this there is considerable use made of it in various places for heating, hot water, etc.

Incidentally, in total 65% of our power comes from so-called renewable resources, mainly hydro-power.
#16 William Wallace
November 20, 2009

But I’ll let him slide; pretty much everyone blanks out from time to time.

I don’t know about you, but this is not the type of compassion shown by most bloggers. Usually, they grab hold of any trivial mistake to avoid the better argument.

Next question, since you seem to have a decent grasp of thermodynamics. If we started heating water to do 5e20 joule-years of power, would that affect global warming? Or does Al Gore also need steam reclamation (steam scrubbing or clean geo-thermal) to be invented as well.

Lastly, Al Gore also claimed “it is a relatively new one.” He should check out the wikipedia article on The history of geothermal power. I suppose his defense here will be “relatively new one compared to the age of the universe”.
#17 rob
November 20, 2009

the details of the cycle (otto, atkinson etc) don’t matter with respect to answering comment #1.

Carnot showed that his results are independent of the internal operation of a heat engine: the Carnot cycle is the most efficient cycle, and the efficiency is a function of the hot and cold resevoirs tempertures only.

when you think about it, this is pretty cool. it doesn’t matter how clever your design is, how tricky you are, you cannot get more efficient than the Carnot cylce. never.

for any car engine operating on a comfortable day, the maximum efficiency is e=1-(293K/1073K)~ 70% where 293K is 20°C and 1073K is 800°C, the approximate engine operating temperature.

in reality, since car engines are not reversible, you do not get anywhere near 73% efficiency.
#18 Richard Hertz
November 21, 2009

Does anyone think it’s ironic that that same man who several years ago said: “The planet has a fever!” with his global warming tripe NOW wants to extract heat from the center of the earth and bring it up to the surface?
#19 CCPhysicist
November 21, 2009

ryan@1,3, mark@5 and rob@10 are wrong about how an automobile engine works, but ryan@1 did correctly identify your mistake. The radiator is there to remove heat that the Otto cycle wishes would not end up in the engine block, not as part of the Otto cycle itself. You get an “Al Gore” pass for that one.

The error made by those talking only about combustion is that they forget that a sequence of explosions will not drive an engine more than once unless there is an EXHAUST part to the cycle that connects to the cold reservoir, and the radiator is not part of the exhaust system. Indeed, there are Otto engines that run just fine without any radiator or cooling system at all. There is no need for cooling if you can travel that 1000′ in 4 seconds.

rob@17 is correct to point out that any engine that turns heat into work must be limited by what Carnot proved, but why bother with that calculation when the Otto cycle tells you that the efficiency is limited by the compression ratio and the adiabatic constant gamma for its working fluid, air? That limits ideal gasoline engines to the low 60s if you could ever engineer a perfect one.

On the other hand, your reference to the cooling tower in a power plant is closer to the mark. Although the cycle is over before the used steam enters the condenser, you can’t really afford to make purified water for an open loop and you need liquid water to get the most efficient heat transfer in the boiler, where superheated water flashes to steam. So in a power plant, the condenser and cooling tower are part of the “cold” side of that heat engine.
#20 Ned Wright
November 21, 2009

Geothermal power is limited to the 40 terawatts coming from the interior of the Earth, mostly from radioactive decay, but the half-lives are shorter than 21 Gyr anyway. Averaged over the surface of the Earth this is only about 0.1 W per square meter. Since solar power with 1367 W/sq.m is usually considered to be too diffuse for easy use, it is only the places where geothermal power is naturally concentrated that are useful for power production.

So the Earth has an internal luminosity that is 1E-13 of a solar luminosity, while Jupiter’s luminosity is 1E-9 L_sun, mainly from gravitational potential energy left over from the formation of the planet.
#21 Chris
November 22, 2009

A steam engine would be a better analogue than a gas engine for the point you were trying to make. Others have pointed out the radiator’s purpose and we must consider the huge number of gas engines with no radiator at all.
#22 Alonzo Riley
November 22, 2009

Does anyone think it’s ironic that that same man who several years ago said: “The planet has a fever!” with his global warming tripe NOW wants to extract heat from the center of the earth and bring it up to the surface?

I know that you’re probably not too interested in what Gore meant, since it’s all tripe, but your misunderstandings are so simplistic that it’s not too hard to try and enlighten you.

Global warming is more like putting on a coat that can’t come off while turning up the thermostat. Extracting heat from the center of the earth is just turning up the thermostat. See the difference? Anytime you put more co2 into the atmosphere you are adding more layers on that you can’t take off. Grabbing energy from the heat within the earth adds absolutely zero layers.

Tadaa! That wasn’t so hard, was it? So no, it’s not ironic. Go eat more of your stagnant tripe.
#23 Kaleberg
November 23, 2009

I had always heard that the energy of a car engine is related to the difference in the temperature of the air and fuel intakes and the temperature of the exhaust gas. You want the hottest exhaust gas you can get. I know this is the case for jet engines. They run much more efficiently in the stratosphere where the air temperature is usually minus something, F or C. It is probably also the case for rockets, and liquid fuel rockets get a little bonus boost from the liquid oxygen being so cold.
#24 Fourth Stooge
November 23, 2009

You don’t know how an internal combustion engine operates.

The larger point is that the man in charge of the global warming scheme has less of a clue about the geology and climate of the earth (a system in existence for millions upon millions of years) than you do about internal combustion (a system that has existed for over 100 years and any grease monkey could describe).
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