### Re: What is the heat of vaporization of Earth's crust?

Date: Wed Feb 27 22:55:04 2002
Posted By: John Christie, Faculty, School of Chemistry, La Trobe University, Bundoora, Victoria, Australia
Area of science: Earth Sciences
ID: 1014590302.Es
Message:
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The best I can do with this sort of question is an "order of magnitude"
calculation-- the answer I get might be out by a factor of 2, maybe even a
factor of 5. Too many of the quantities are not precisely known. Some of the
estimates and averaging are not particularly accurate (more detail would
take us beyond the scope of a simple calculation).

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The Earth's crust is made up of a lot of different types of mineral. Basalt
from volcanic rocks typically has a density of about 3.3 to 3.5 tonne/cubic
metre. Granite is rather less dense -- around 2.7 tonne/cubic metre. We will
have to start out with a guess to obtain a value for the average density of
crustal rock. You can probably find it in Geology texts if you look hard. I
will guess at 3.1 tonne/cubic metre.

To "actually vaporize" our 3.1 tonne of rock, we will have to heat it to
boiling point, and then provide the extra heat necessary to turn it from
solid to gas. But even our starting temperature is problematic. We know the
temperature of surface rocks, and that there is generally an increase with
depth. Where is our 3.1 tonne of rock coming from? Let's initially suppose
that it is coming from the surface, and that it has to be evaporated at an
external pressure of 1 atmosphere.

In the CRC Handbook for Chemistry & Physics, we can find if we look hard, a
value for the boiling point of quartz -- 2590°C (Ed 56 p. B137) and for the
specific heat capacity of granite at 400°C -- 0.258 kcal/kg/degree = 1.08 J/
g/K (Ed 56 p. E16). We can also note that specific heat capacity increases
significantly with increasing temperature (but we can not do much about it).
We are not likely to find a value for latent heat of vaporization of quartz
at its boiling point. The best option is to assume that it is much smaller
than the heat input needed to raise the temperature. So for a very rough
estimate, our surface rock might require

2570 K * 3 100 000 g * 1.08 J/g/K = 9 047 000 000 J, or 9.05 GJ.

That is likely to be an underestimate because of the increase of specific
heat with temperature, and because of the neglect of latent heat.
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What is the amount of heat required to actually vaporize a cubic meter of
the Earth's crust? Around 10 GJ

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I know it's not supposed to be very deep, in comparison to
Earth's diameter, but just how deep is that?

Average thickness of continental crust is around 35 km, of oceanic crust
around 8 km. (any geology textbook).

------------

71% of the Earth's surface is under water, 29% is land. But a significant
part of the "under water" is in shallow seas and continental margins. So we
will work with 2/3 oceanic crust and 1/3 continental crust.
The Earth's surface area is 4 * pi * (6371 km)^2 = 5.1 * 10^8 km^2
For the volume of crust we therefore get 1.7 * 10^8 * 35 + 3.4 * 10^8 * 8 =
8.67 * 10^9 km^3

Furthermore, how many cubic kilometers of crust does the Earth
actually have? About 9 (American) billion -- 9 * 10^9 km^3

------------

Overall, what would be the heat of vaporization of all that crust?
We could just multiply the 10 GJ estimate of what is required to vaporize 1
m^3 by the number of m^3 in the total crust. The answer would come to 9 *
10^28 J.

This is an overestimate, because we assumed that we were starting with
surface rock at 20 deg C, and most of the deeper crustal rock will be much
hotter than that before we start (and therefore need less heating). The true
answer would probably be something like half this value  -- say 5 * 10^28 J.

The total daily solar radiation intercepted by the Earth is 1.5 * 10^22 J
(Campbell, Energy & the Atmosphere, Wiley, 1977, p. 40), so the energy
needed is
- about the total amount of energy in ten thousand years of sunlight
intercepted over the whole of the Earth.
- about a hundred thousand times the energy released in the largest
earthquake of recent times (China 1976)
- about 250 000 times the total energy stored in our fossil fuel reserves.

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