http://www.bioticregulation.ru/pump/pump4.phpFeel the Pump Physics
Biotic pump of atmospheric moisture functions like this. Water vapor from the forest canopy undergoes condensation in the atmosphere and disappears from the gas phase. For this reason, the air rarifies and its pressure drops. In the result, air is sucked from below to compensate for this pressure drop. This, in its turn, leads to the drop of pressure at the surface, so that surface air is drawn from the neighboring areas to the area of the upwelling. If there is ocean in the neighborhood, then the air which is drawn to the continent will be enriched by evaporated moisture.
Pump physics is simple. One needs to have an idea of what ideal gas is, what diffusion is and how it differs from the dynamic flow of gases and, finally, how water vapor pressure depends on temperature (Clausius-Clapeyron law). All these phenomena can be vividly illustrated with use of interactive Flash models. You can change and monitor gas pressure, make water evaporate, make gas mixtures diffuse or flow dynamically. You can also get an idea of the major components of atmospheric circulation over forests, clear-cuts or deserts, by switching the circulation on and off yourself. All models were created for our website by S.K. Buruchenko.
Ideal gas
If you have problems with viewing the Flash object, click here for free installation of the latest version of Flash Player.
If a slide starts moving in an uncontrolled fashion, click on it, this will bring it to order.
Scene I. Ideal gas equation of state
Suggested parameters to set: Na = 19; Nb = 19; Rb = 1; Ta = 20 K; Tb = 20 K.
Gas pressure p depends on (1) how often and (2) how energetically gas molecules collide with each other (or with the partition). In its turn, the frequency of collisions apparently depends on two factors: (1.1) number N of molecules in the considered area and (1.2) mean velocity v of their chaotic movement. The greater the number of molecules and the faster they move, the more frequently they will collide with each other. On the other hand, the "force" of collisions, or, more precisely, the momentum transferred, depends on (2.1) mass of the molecule m and, again, (2.2) on its velocity v. The more massive molecules are and the faster they move, the more heavily they will bombard each other during collisons. We thus conclude that gas pressure p is proportional to the product Nvmv or Nmv2.
The precise expression is p = N(2/3)mv2/2, where it is taken into account that (a) when a molecule hits the partition, the imparted momentum is 2mv (e.g., the molecule has been moving to the left having velocity v before the collision, then, after collision, it starts moving to the right with the same velocity, so velocity change is 2v) (multiplier 2), (b) only one half of all molecules on average move towards the considered plane (partition), the other half move away from it (multiplier 1/2), and (c) molecules move in the three-dimensional space, so only one third of the velocity square corresponds to movement in a given direction (multiplier 1/3).
The product mv2/2 gives kinetic energy of the molecule. Gas absolute temperature is T proportional to kinetic energy of molecules. It is defined as mv2/2 = 3/2 kT. Here Boltzmann's constant k = 1.38 × 10−23 J/degree Kelvin/molecule is the proportionality coefficient. It is equal to two thirds of the kinetic energy of gas molecule, when the gas has temperature of one degree Kelvin. Now substituting the definition of temperature into the expression for pressure, we obtain the equation of state for ideal gas: p = NkT. Ideal gas pressure is proportional to its concentration (number of molecules in a given volume) and to temperature.
Increase gas temperature, using the red regulator, in one of the parts of the vessel, and you will see how gas pressure will rise proportionally, as will be shown in the green horizontal pressure scale.
Scene II. Ideal gas pressure does not depend on the nature of molecules!
Suggested parameters to set: Na = 14; Nb = 14; Rb = 1.9; Ta = 101 K; Tb = 101 K.
This is a most important property of ideal gas: its pressure only depends on temperature and the number of molecules, but not on the type of molecules. For example, when water vapor undergoes condensation and disappears from the gas phase, the total air pressure drops.
If temperature in both parts of the vessel, a and b, is the same, this means that mean kinetic energy of molecules in both parts are equal, mava2/2 = mbvb2/2, where ma and va are mass and velocity of molecules in part a. Assuming that mass of molecules is proportional to the cube of their radius, we obtain that at constant temperature increasing the radius of molecules in part 2 by x times will decrease their velocity vb by x3/2 times. Although molecules in part b will move more slowly and hit the partition less frequently than do molecules in part a, they will every time hit the partition more heavily than do molecules in part a.
Therefore, when the number of molecules in these equal parts of the vessels is the same and their temperature is the same, gas pressure will be the same in both parts of the vessel irrespective of the size of molecules in part b. You can check it yourself setting various values of the relative radius Rb (Rb is the ratio of molecular radii in the right and left parts of the vessel).
If you have any questions, you are welcome to ask them here.
These slides regulate the number of molecules in the two parts of the vessel.
Move the slides down to the utmost, then click on the star
to the right of the copyright. There will be many molecules. You can set different numbers of molecules in the right and left parts
of the vessel. Current numbers of molecules are shown on the yellow scales.
These slides regulate temperature, which can vary from 1 to 101 degrees Kelvin, i.e. from −272 to −172 degress Celsius.
Red scales can be used to monitor the difference in gas temperature between the two parts of the vessel.
This slide sets the relative radius of molecules in the right part of the vessel as related
to the radius of molecules in the left part of the vessel. Move it down to the utmost,
then click on the star to the right of the copyright. Molecules will conspicuously
grow in size. To make them move more rapidly, increase the temperature.
These scales indicate gas pressure. They can be used to monitor the difference in gas pressure between the two parts of the vessel.
Top