Embedded Files
Post date: Apr 12, 2015 8:48:5 PM
Recently I was delivering a mini-lesson for Yr7 students on: why does water boil at a lower temperature at a higher altitude? A good answer to this can be found all over the internet and particularly on youtube here. One concept I wanted to explain was why air pressure is lower at higher altitudes.
The air pressure around us is due to the weight of the atmosphere above us. At a higher altitude, there is a smaller weight of air above you, so you feel less pressure. This understanding also is the reason for the pressure in water increases as we go deeper (there is a greater weight of water above us) and can be very large (water weighs a lot!).
On a microscopic level, the air pressure comes from the gas particles colliding into things. For a balloon, air particles hitting the inside of a balloon give a force pushing out: this balances the inward forces of the air particles hitting the outside surface and tension of the balloon itself and keeps the balloon inflated. We call a force acting on an area: "pressure".
The arrows show the forces due to pressure from air molecules hitting the balloon surfaces. Not shown is the force due to the tension of the rubber.
Borrowing on some code from here (and correcting the gravity mistake in the original code), I adapted this to make nice animations of a vertical slice of atmosphere.
The physics put into this simulation are:
the balls collide elastically with one another (don't lose any kinetic energy when colliding which is true for an ideal gas.
the particles all have a weight that causes them to fall.
the particles collide elastically with the ground (this is another physically sensible approximation).
the particles collide elastically with the wall/ceiling. Although our atmosphere doesn't have these limits, they don't change the results of the calculation and this also makes the calculation much simpler.
With all the atoms bouncing around we can see that most fall to the bottom due to gravity. An object placed here (e.g. the green box) will feel lots of collisions and so the pressure is higher here.
At higher altitudes, an object (e.g. the red box) will experience fewer collisions from the particles and so the pressure will be lower.
Showing the pressure
The power of a simulation (rather than a simple animation) is that we can get useful physics from it. For example, we know that pressure comes from the particles hitting a surface, so we can look at how many particles hit surfaces at different heights and this will be correlated to the pressure.
The results show that
at high altitudes the pressure is very small. As we go to lower altitudes the pressure increases as we expect.
we also note that the dependence of pressure is not a straight line (linear) and instead looks exponential. This is correct (see earlier post) and is because gases (which is what we're simulating) can be compressed.
It's interesting to see that the pressure at low altitudes appears to change lots around an average value, whereas the pressure at high altitudes seems to be quite steady. This is an effect of statistics. As with all experiments it is important to make many measurements and repeat your results. In our case to get better statistics we could:
introduce more particles (this moves towards the real atmospheric conditions with many many particles) and stable pressure. This would take lots of computing power and would make any animation very slow.
instead of updating the pressure instantly, we could take an average value of the pressure which would smooth out the pressure fluctuations and give a more reliable pressure reading.
Page updated
Google Sites
Report abuse