What is the relationship between kinetic theory and the gas laws?

[luigihs]

Can someone explain me this theory ? and how to use the equation please

I have this in my notes but I don't understand :(

Average (translational) Kinetic Energy per molecule is

E= 3/2kT


The same, per mole, is U = 3/2 * R* T

 

[sophiecentaur]

Hi
The basics of deriving this involve quite a long string of steps and comes under the heading of 'bookwork'. I think you should just sit down with the book and follow it through. Else you can just accept it.
If you don't have 'a book' then Wiki would be a way forward. Start with Boltzmann Distribution

 

[technician]

Do you recognise the experimental equation for the gas laws in the form
PV = nRT ? where n = number of moles
So for 1 mole the experimental law is PV = RT

The kinetic theory leads to an expression PV = (N/3) x mc^2 where N is the number of molecules.
If this equation is written as 2(N/3) x 0.5mc^2 it makes no difference but it does highlight a combination 0.5mc^2 which is average KE of molecules.
Putting the experimental equation and the theoretical equations together leads to

RT = 2(N/3) x 0.5mc^2 or 0.5mc^2 = (3/2)TR/N

so average KE = (3/2)TR/N
R is the gas constant and N is the number of molecules in 1 mole (Avagadros number)
The combination R/N of these constants is known as Boltzmanns constant, symbol k

Therefore average KE = (3/2)kT

Hope this helps