Climate crisis - plenty of energy

Jul 17 2021

The calculations originally appeared in this post here, but had my .NET NMeasure library as the focus. I wanted to extract the calculations into its own post to have it readily available.

You may have heard about the global warming summit and that scientists have basically agreed with each other that we should try really hard to avoid the atmosphere to heat up an additional 2 degrees on average. It doesn’t sound much, but I was curious what this number means in terms of additional energy that the atmosphere would contain.

The calculation has been kept pretty straightforward:

We take the volume of the low atmosphere
We look up the specific heat of air in the proper temperature range (assuming today’s average temperature of 14°C) with constant volume.
We multiply it all through and get a number.

Let’s start with the constants we’re using

r_e = 6371km

Radius of Earth

r_a = 6373km

Radius of upper boundary of the air layer we will consider

\rho_a = 1.225\frac{kg}{m^3}

Density of air

CV_a = 718\frac{J}{kgK}

Specific heat of air

The volume of the considered air layer is:

V_a = \frac{4}{3}\pi(r_a^2-r_e^2)

Getting the surplus Joules by increasing the temperature of that air layer by 2 degrees gives us:

E = V_a \times \rho_a \times CV_a \times 2K

Gives us a number in Gigajoules of

1.795 \times 10^{12} GJ

Sounds quite a lot, and it is. If we compare this to the World’s energy production we see that in order to make this amount of energy available, our current worldwide energy production would have to run for almost 19 years.

So, this is very roughly the amount of additional energy we’re pumping into our lower athmosphere. Leave it to climate experts to figure out what exactly we can expect from that, but do you really think our climate will soak this amount of energy up and do, like, nothing?