In this clip I will present a brief overview of atmospheric pressure and explain why it decreases as we move upward through the atmosphere.
Atmospheric pressure is caused by the mass of the atmosphere that is being pulled towards the earth's surface by gravity.
Just like any other physical object an air consists of molecules and thus has a certain mass this mass is subject to Earth's gravity it is pulled down and rests on the surface of the earth resulting in a force per unit area which is referred to as atmospheric pressure.
On a molecular scale this pressure is caused by the collisions of air molecules against a surface.
If we move upwards through the atmosphere the amount of mass that is above us decreases and therefore the atmospheric pressure acting upon us also decreases.
At the top of the atmosphere the atmosphere pressure is equal to zero to understand why this decrease in pressure occurs let's look at the changes that take place when we pile different masses on top of each other.
Imagine a slab of material with mass M. one lying on the surface of the earth to make things easy we will assume that there is no atmosphere gravity pulls this mass downwards and therefore it exerts a force F. on the surface called the weight which is indicated here with the blue arrow.
According to Newton's second law this force equals am one multiplied by G. where G. is the Excel aeration of gravity. Pressure is defined as the force per unit area here the area on which the mass rests is indicated by a green line.
The pressure can be calculated as the weight as divided by the area.
Let's make a graph of the change in pressure with height the vertical axis indicated here with a Z. represents the height above the surface the value of the pressure P. is plotted along the horizontal axis.
The pressure at the surface P. with subscript S for surface is where the height equals zero.
At the top of the mass the pressure is equal to zero since there is no additional mass located above this height.
The difference in pressure is indicated by delta P.
The formula here shows that delta P. equals the mass M. one multiplied by G. divided by the area and.
Considering that both A and G. or constants we arrive at are first important conclusion. The pressure difference between two vertical heights or levels is directly proportional to the mass located between these two levels.
Next let's pile the mass M. two which happens to be larger than M. one on top of M. one. The total force exerted on the surface now increases and is proportional to the sum of the two masses we can see that the surface pressure increases accordingly. From our result we see that the pressure difference between two levels is proportional to the mass between these two levels thus we can create a similar graph of pressure versus height.
Although the surface pressure has increased the pressure difference delta P. between the lowest two layers remains the same because the mass between these two layers has not changed.
The pressure difference between the top two layers is larger because the mass M. two between these two layers is larger.
The pressure difference between the surface and the top is now proportional to the sum of the two masses and one plus M two.
If we continue piling masses on top of one another the surface pressure will increase thus the surface pressure can be written as G. over a multiplied by the sum of all the individual masses M one to M. N..
If we let the individual mass elements approach zero then we need an infinite number of these mass elements in mathematical terms this sum then becomes an integral over D M. D M equals density row multiplied by volume D V. From the last two e questions we can see that the surface pressure equals the acceleration of gravity multiplied by the total mass of a vertical column extending from the surface to infinity Please note that the surface pressure only remains finite if either the density decreases with height or if the upper limit of the integration is finite and not infinity.
Let's look at two examples. In the first example we assume that density has a constant value this means that the medium cannot be compressed a good example of this is water which almost always keeps its density constant even under extremely high pressures such as those found at the bottom of deep oceans the density curve shows a constant value at all levels pressure however decreases linearly with height it appears. That there is no relation between pressure and density one remains constant and the other decreases using the equation from the previous slide and keeping density constant we arrive at the following expression for pressure at the surface it now appears that pressure at a certain height Z. decreases linearly from the surface value to zero at the top.
In the second example we assume that density is not a constant anymore this means that the medium can be compressed this is the case for any gas including air the space between gas molecules is so large that compression is possible in the graph the density curve shows a decrease with height which is similar to the pressure curve it means that there is a strong relationship between pressure and density This is because if air is compressed both the density and the pressure increase the density increases because the same volume now contains a larger number of molecules the pressure increases because the large number of molecules means a larger number of collisions. Now if we want to create an expression for pressure as a function of height. We have to realize that we need an expression for the density as a function of height as well otherwise the integral cannot be solved for now we will assume that both density and pressure show a simple exponential decrease with height these two expressions show that the decrease of density and pressure are similar both are exponential and at height age only one over it e multiplied by the surface value remain. Age is called the scale height of the atmosphere if we substitute the expression for density in our formula it is easy to derive the following formula for H. so at a height of eight point five kilometers which is almost the height of Mount Everest the pressure is one over or just thirty seven percent of the value at sea level.
In this graph where the horizontal axis now is logarithmic the close relationship between pressure and density is visible once again the red line and the green dashed line almost coincide.