Mass of the atmosphere

The average radius of the Earth is 6,374kilometres.
The volume of a sphere is 4/3phi r3
Pressure at the surface is 760mm of mercury.
The density of mercury is 13.5
Please calculate the weight of the Earth's atmosphere and compare
answers
Nelson

Nelson wrote:
The average radius of the Earth is 6,374kilometres.
The volume of a sphere is 4/3phi r3
Pressure at the surface is 760mm of mercury.
The density of mercury is 13.5
Please calculate the weight of the Earth's atmosphere and compare
answers
Nelson

Why??

Sjouke Burry wrote:
Nelson wrote:
The average radius of the Earth is 6,374kilometres.
The volume of a sphere is 4/3phi r3
Pressure at the surface is 760mm of mercury.
The density of mercury is 13.5
Please calculate the weight of the Earth's atmosphere and compare
answers
Nelson

Why??

So that Nelson can get an A on his homework.


Tim

First, convert your figures to SI units and scientific notation:

average radius = 6.374e6 m
average surface pressure = 0.76 mm Hg where density of Hg = 1.35e4 kg/sq.m

Second, calculate surface area (not volume):

area at surface = 4.pi.r^2 = 4.pi.(6.374e6)^2 = 5.1054494709e14 sq.m

Thirdly, convert presure from mm Hg to kg/sq.m :

pressure = 0.76 x 1.35e4 = 1.0264e4 kg/sq.m

Finally, get the weight:

weight = pressure x area = 1.0264e4 x 5.1054494709e14 =5.24023333693e18 kg

or 5,240,233,336,930,000 tonnes (5.24 quadrillion, using the American
idiom)

Published estimates range from 4.99 to 5.23 so this figure appears slightly
high. Your turn to discuss.

Either way, it is only about a millionth of the Earth's total mass.


"Nelson" wrote in message
oups.com...
The average radius of the Earth is 6,374kilometres.
The volume of a sphere is 4/3phi r3
Pressure at the surface is 760mm of mercury.
The density of mercury is 13.5
Please calculate the weight of the Earth's atmosphere and compare
answers
Nelson

Tim Auton wrote:
Sjouke Burry wrote:
Nelson wrote:
The average radius of the Earth is 6,374kilometres.
The volume of a sphere is 4/3phi r3
Pressure at the surface is 760mm of mercury.
The density of mercury is 13.5
Please calculate the weight of the Earth's atmosphere and compare
answers

Why??

So that Nelson can get an A on his homework.

But why Mercury?

" wrote in message
ps.com...
But why Mercury?

Millimetres of mercury as in a manometer tube. It is a somewhat outdated
measure of atmospheric pressure. The 'inches of water gauge' was also used.
Now we're still using 1013.25 milliBars, although more correctly it should
be 1.01325 Pascals (average at sea level). The SI (Système International
d'Unités) is a much abused bitch.

Typo correction: Line 3 should read:

average surface pressure = 0.76 m Hg where density of Hg = 1.35e4 kg/sq.m

Maybe not relevant to the original question, but out of geeky interest ...

Using Mosteller's formula for estimating the surface area of the human body:
area (sq.m) = SQRT { height (cm) x weight (kg) / 3600 }

I'm quite a big chap and that yields 2.95 sq.m in my case. That means that
the total 'weight' acting on my body due to atmospheric pressure is
approaching 30 tonnes. Of course, there is an inate equal and opposite
pressure inside the body which neatly counterbalances it so that we don't
notice it. It is also presumably the reason that I would tend to explode
rather messily if I were thrown out into the near vacuum of outer space.

Now who is going to tell us the weight of the world's seas and oceans?

TeaTime wrote:

Of course, there is an inate equal and opposite
pressure inside the body which neatly counterbalances it so that we don't
notice it.

Is that so? We have a counter pressure of -1 bar (0 bar abs. pressure)
inside? And a diver at 10 meters below surface have an inside pressure of
-2 bar (-1 bar abs. pressure)?

"Iordani" wrote in message
...
TeaTime wrote:

Of course, there is an inate equal and opposite
pressure inside the body which neatly counterbalances it so that we don't
notice it.

Is that so? We have a counter pressure of -1 bar (0 bar abs. pressure)
inside? And a diver at 10 meters below surface have an inside pressure of
-2 bar (-1 bar abs. pressure)?

Actually, the absolute pressure both inside and outside our body is
typically 1.01325 Bar at sea level. One can say that is 0 Bar pressure
relative to sea level. (Absolute pressure is pressure above a pure vacuum).

When a diver reaches a depth with a pressure of 1 Bar higher than
atmospheric, the absolute pressures inside and outside his body both become
2 Bars. One can say that is 1 Bar relative pressure.