IDEAL GASES The kinetic energy of a molecule.
TEMPERATURE AND KINETIC ENERGY.
Comparing the equation of state, p V = n R T, with the pressure equation,
p = 1/3 ρ c2', we get p V = 1/3 M c2',
where M is the mass of the whole volume of gas. Dividing by N (the number of molecules) and shuffling, we get.
p V = 2/3 N ( 1/2m c2' )
where m is the mass of 1 molecule. Comparing this with the original equation of state,
p V = n R T
it can be seen that, the K.E. of the gas molecules, 1/2m c2' = 3/2 .
n R / N T or for a single molecule..
1/2m c2 = 3/2 .
R / N T
where N is avogadros number. This equation is often written as 1/2m c2 =
3/2 k T, k is the Boltzmann constant with a value of about 1.38 * 10-23 J K-1.
Notes
- T (the temperature of a gas) is shown to be proportional to its kinetic energy.
Rob Coles 11 April 1996 16:31:31