Bottom line:
There are roughly 3 + 5 + 4 = 12 billion constantly-heat-generating
'room-space-heater equivalents' on Planet Earth --- working hard every day,
24/7 --- according to usage data from recent years (about 2014 to 2019).
That is about 1.5 times the number of humans on Earth ---
giving each human about 1.5 room-space-heaters --- running
24 hours per day, every day --- even in summers.
It can be said that humans have already 'over-populated' Earth --- with
themselves and their machines & comfort-devices
(vehicles, furnaces, ovens, heaters, etc).
It has been noted on a
Calculation-of-Temperature-Rise-from-Fossil-Fuels page (of this site) that the Earth
is surrounded by a very thin atmosphere --- on the order of 5-miles thin ---
versus an Earth that is 8,000 miles in diameter. So the thickness (or thin-ness)
of Earth's atmosphere is about 6-hundredths of one-percent of Earth's diameter.
The question arises:
How many 'standard-sized rooms' will fit into
that thin spherical shell of air?
And:
How does the atmospheric-volume --- measured in units of the volume of
'standard-sized-rooms' --- compare to our 12-billion fossil-fueled
'room-space-heaters'?
Is there one of those heaters for every one of those atmospheric-rooms?
The typical room that will be heated by our 1500 watt 'room-space heater'
is anywhere from about 10-by-10 feet to 20-by-20 feet. Let us say
our 'standard-sized room' is 15-by-15 feet --- and 8 feet high.
So the volume of our standard-sized room is 15x15x8 = 1800 cubic feet
--- or about 51 cubic-meters.
Now we need the volume of the air around the Earth --- but that
gets somewhat complicated by the fact that the density of the air gets
smaller as we go higher. In fact, about 5 miles above the Earth (such
as on top of Mount Everest) the air is so thin, humans need oxygen
masks to survive.
But let us imagine compressing the air down until the air is a
spherical shell around the Earth with the same density as the
density of air at sea level --- which is about
1.225 Kg/cubic-meter (Wikipedia link).
The 'Calculation-of-Temperature-Rise' page (link above) pointed out
that the mass of air around Earth has been determined to be about
5.1480 x 10^18 kg (Wikipedia link).
Now we can divide that mass (in kilograms) by air-density-at-sea-level
(in kilograms per cubic meter) to give us the volume of air
around Earth --- if the air were compressed down to be the density
of air at sea level, uniformly throughout that volume.
The volume of that uniformly-dense air around Earth is
(5.148 x 10^18 kg) / (1.225 kg/m^3)
=
4.20 x 10^18 cubic meters
We can divide this volume by the volume of our 'standard-sized-room'
( 51 cubic-meters ) to get the volume of that uniformly-dense air
around Earth in units of 'stardard-sized-rooms':
(4,200 x 10^15 m^3) / (51 m^3/standard-sized-room)
=
82.3 x 10^15 standard-sized-room-volumes
This is about 6.8 x 10^6 (6.8 million) times more rooms than
our 12 billion (= 12 x 10^9) fossil-fueled space heaters.
So each of our 12 billion fossil-fueled 'room-space-heaters' is
effectively spreading its heat over about 6.8 million room-volumes
--- that are piled up over the surface of the Earth.
But that heat is building up over time, because the kinetic energy
in all those N2-and-O2 molecules --- unlike solar radiation, which
can be reflected & radiated away from Earth --- has nowhere to go
but Earth. In other words: Because the Earth's atmosphere is surrounded by
empty space, there is nothing 'off-Earth' to absorb excess energy in
those N2-and-O2 molecules.
At a future date, there may be calculations here that indicate
roughly how many years it will take to heat up the entire Earth's
atmosphere by several degrees (Centigrade, say) --- due to those
12 billion constantly-running 'room-space-heaters'.
Actually, this has been done, on this site, using the
specific-heat-capacity of air.
The calculations of the
Calculation-of-Temperature-Rise-from-Fossil-Fuels page indicate
that the Earth's air temperature will rise between 0.02 and 0.1
degrees-Centigrade per year. The 0.02 figure is near the current rate
--- one-fifth of a tenth-of-a-degree Centigrade per year.
But, as the snow-and-ice of the Arctic-Greenland-Antarctica melt off
--- and as the sea & land masses heat up, the rate of temperature
rise will come much closer to the 0.1 deg-C/year rate.
NOTE:
A question arises due to the fact that some of those
heated-up N2-and-O2 molecules may reach
'escape velocity' --- about 25,000 miles/hour or 40,000 km/hour.
In that case, some of those molecules may be slowly 'boiling off' of
the Earth --- into outer space. Many of them may be captured by the
gravitational attraction of the Moon. So it would be interesting
to put instruments on the Moon to measure whether there is a
slow accumulation of N2-and-O2 molecules around the surface of
the Moon. In other words: Is the Moon slowly accumulating an
atmosphere of N2-and-O2 molecules?? --- due to N2-and-O2 molecules
being 'boiled off' from the Earth's atmosphere.
An area-question (an alternative to the volume-question above):
How many 'standard-sized rooms' will fit onto the
surface area of the Earth? --- in particular, onto the land-area of the Earth,
which is about one-third of the Earth's surface.
And:
How does the land-area --- measured in units of area of
'standard-sized-rooms' --- compare to our 12-billion fossil-fueled
'room-space-heaters'?
Is there one of those heaters for every one of those room-areas on the
land area of the Earth?
The floor-area of our typical room (defined above) is 15-by-15 feet.
So the surface area covered by our standard-sized room is
15x15 = 125 square feet --- or about 11.6 square-meters.
The surface area of our near-spherical Earth is given by the well-known
formula
4 x pi x R x R, where R is the radius of the spherical Earth ---
and the radius of the Earth is about 6336 kilometers --- or
6.336 x 10^6 meters = 6.336 million meters.
So the surface area of the Earth is about
4 x 3.14159 x 6.336 x 6.336 x 10^12 = 504.5 x 10^12 square meters
The land-area of Earth is about one-third of that --- so land-area
is about
168 x 10^12 square meters
To convert that area in square-meters to our standard-sized-room-areas,
we divide by 11.6 square meters (per standard-room) giving
14.5 x 10^12 standard-sized-room-areas
So each of the 12 billion ( = 12 x 10^9 ) fossil-fueled 'room-space-heaters'
is spreading its heat over about 14.5 x 10^12 standard-sized-room-areas.
The following division
(14.5 x 10^12 standard-room-areas) / (12x 10^9 'room-space-heaters')
tells us that there is the equivalent of about
1.2 x 10^3 = 1,200 standard-room-areas per fossil-fueled space-heater
over the land-area of the Earth.
As we noted above, the heat from those space heaters is not escaping from
the Earth, so that heat from each space heater (into about 1,200 'room areas'
on the land-surface of the Earth) is accumulating --- and is causing the
temperature of the Earth's air to rise at the rate indicated above --- about 0.02
degrees-Centigrade per year --- but trending toward 0.1 deg-C/year ---
about one degree Centigrade every 10 years -- about 7 degrees Centigrade
in a person's lifetime. ( If that isn't a wake-up call, find a better one! )
