General equation of an ideal gas

One of the basic features of gas is its property to exert pressure on the walls of the vessel in which it is contained. Let us determine this pressure for a state of ideal gas. On the way, we shall obtain a number of other important equations, hi spite of the fact that we will be using a considerably simplified model, we will obtain results conterminous to our exact consideration. 

In addition to those simplifications that we have aheady made when introducing the ideal gas model, we will also make some additional assumptions that will help us to simplify our calculations in order not to lose generality. In particular, we will (1) count all molecules as identical, spherically symmetric and moving at the same speeds (let this speed be the average root square velocity (2) consider that all mole- 

Taking into account the fact that the actual speeds of all the molecules vary, we should take the average values of the speed squared. 

Therefore, the pressure acquired by the ideal gas on the vessel s walls is equal to 2/3 of the volumetric density of the translational kinetic energy of the molecules. 

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