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The kinetic theory of gases formula

We consider a gas to be a collection of molecules and made the following assumptions about these molecules:

1. molecules behave as if they were hard, smooth, elastic spheres
2. molecules are in continuous random motion;
3. the average kinetic energy of the molecules is proportional to the absolute temperature of the gas;
4. the molecules do not exert any appreciable attraction on each other
5. the volume of the molecules is infinitesimal when compared with the volume of the gas
6. the time spent in collisions is small compared with the time between collisions.


Pressure of the gas (P) = 1/3[m/V]Nc2 and so PV = 1/3[mNc2]

where c is the mean square velocity of the molecules, V the volume of the gas, m is the mass of one molecule and N is the number of gas molecules per cubic metre.

The total mass of the gas M = mN, and since the density of the gas r = M/V

Pressure of the gas (P) = 1/3[rc2]
 
 
 
© Keith Gibbs 2011