Why does pressure equal density times mean squared speed?

[KatieKangaroo]

Equation 1: p = 1/3 d<c^2>
(p is pressure, d is density, <c^2> is mean squared speed)
The law of pressures states that for a fixed mass of an ideal gas at a constant volume, the pressure is proportional to the kelvin temperature. Explain qualitatively how this law follows from equation 1.

I know this may be pretty basic stuff but i keep going round in circles Any suggestions about how i should answer it?

 

[Doc Al]

How is temperature related to the speed of the molecules?

 

[KatieKangaroo]

1/2 m <c^2> = 3/2 KT ??
(for one molecule)

 

[Doc Al]

OK. That's all you need. P is proportional to <c^2> which is proportional to T; thus P is proportional to T.