Comment on How much earth would compress and expand if all of it was 50°C
XeroxCool@lemmy.world 2 days ago
67% of the Earth’s mass is comprised of silicates in the mantle. Solid silicates have very low thermal coefficients of expansion, meaning they change volume very little in comparison to other compounds. So if the mantle was cooled and solidified to 0, then heated to 50, it’d have very little effect. It’d grow something like 0.02% in volume.
Being that the mantle is generally liquid, you’ll see a much larger effect from the initial cooling. But how much? I don’t know. Liquid rock isn’t present in mere mortal online calculators and my ability to dive into the material properties and manually calculate it is long gone from my head.
But “much” larger may not be significant to the human experience, given that 0.02% would be imperceptible as a baseline. If you had a 1km long solid silicon ruler, heating it from 0 to 50C would make it just 20m longer. A circumferential ruler reaching around the Earth along the equator would go from ~40,000km to 40,008km.
GreyEyedGhost@piefed.ca 1 day ago
Given the quaint physics of circles, the expansion of a ring of silicate around the earth would be quite noticeable. C = 2×pi×r, which can be converted to r = C/(2×pi). Plugging in those two values gives us
40000/(2×pi) = 6366.1977 km
40008/(2×pi) = 6367.4710 km
So, taking this ring from 0° to 50° would cause it to rise 1.2 km into the air, assuming it kept its integrity.
A simpler way to write this is
(40008 - 40000)/(2×pi) or 4×pi.
A tiny difference, relatively speaking, but a quite notable difference given the context.
XeroxCool@lemmy.world 20 hours ago
Yes, that would be one way to make it noticeable. If all land/sea floor lifted, gradually, 1.2km into the air, we wouldn’t see it. I also Flubbed the per-km increase of the ruler and edited it to correct the increase down to 20cm per km. So as far as our ability to tell things are 0.02% further, no mere mortal would recognize it. But with a lap band around the Earth, we’d definitely notice the new halo floating above us instead of being a tripping hazard.
That reminds me of a fun fact about how the increase in circumference does not care what your starting values are. If you wanted to wrap a rope around a soccer ball, then make the rope lift 1m above the surface of the ball all around, you’d do probably do the pid math like (pid2)-(pi*d1) :
3.140.022m=0.069m of rope around the ball
3.14(0.022+1+1)=6.349m of rope to float 1m above the ball
6.349-0.069=6.28m of extra rope
Then do it for the planet.
3.1440,000,000m=125,600,000. 00m of rope around the planet
3.14(40,000,000+1+1)=125,600,006.28m of rope to float 1m above the ground 125,600,006.28-125, 600,000= 6.28m of extra rope.
1m above, or 2m greater diameter, can just be fed directly into pid as derived from pi(d2-d1) since we know it’s a basic request to lift it 1m