51
More left Oregon than arrived last year, Census Bureau says, reversing decades of growth
(www.oregonlive.com)
this post was submitted on 14 Sep 2023
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I did some math. I’m assuming that humanity figures out how to get energy from something like fusion reactions, or else we will run out of energy from the sun before the population gets that high.
Currently, humans are using 1.8e13 watts of energy, and this is growing at 2% a year [1]. Therefore power use by humans over time can be represented by the function 1.8e13*g^t where t is time in seconds, and g is exp(ln(1.02)/31558149).
This means energy used is just the integral of this function from 0 to x: a*g^t-a where a = 18e13/ln(g) ≈ 2.9e22 joules.
The earth has 1.4*10^21 kg of water [2] at 15°C [3]. It takes 4184 joules of energy to heat a kg of water 1°C [4]. So we need 5.0e26 J of energy to bring the oceans to boiling point. This will happen in 1.55e10 seconds or 497 years.
To boil a kg of water, you need 2.25e6 Joules of energy [5]. So you need an additional 3.2e27 Joules to boil the ocean; 3.7e27 Joules total. We will get there in 1.87e10 seconds or 549 years.
I neglected the heat that can be absorbed by non water components of the earth surface. But Im guessing thats probably negligible since the earth surface is mostly water, rock is a bad conductor of heat so not that much rock mass matters, and the specific heat of water is greater than that of rock. I also neglected the energy necessary to melt the remaining ice on earth. That might add a few years to the estimate.
I guess there may be some bad effects of heating the earth less than the amount necessary to boil the oceans, but you would have to ask a sociologist about that.
edit: Most importantly, I neglected the fact that hotter objects radiate more heat. This will certainly slow the heating of the earth. It would be very difficult to add this to the model since you have to add in the greenhouse effect, which will get more severe as the oceans release CO2 and H2O, so not quite as much heat will be radiated out as you would expect from a black body.
I'll accept 549 years as a decent ballpark of how long it'd take us to literally boil the oceans at our current rate.
Although 'boil the oceans' is, for me, more of a way to refer to the collapse point of the current society model. I don't think humans would survive long enough at temperatures required to boil the oceans.