The Student Room Group

Help with physics question

Hi
I really need help with the followign question I found on a past paper - after attempting to answer it, even the mark scheme didn't really explain it. This is the question:

The average kinetic energy of a molecule is directly proportional to the kelvin
temperature T, i.e. E = constant × T. The pressure p of an ideal gas is given by the equation

P = 1/3 &#961; <c^2>

Use this information to show that p is directly proportional to T for a fixed mass of gas at constant volume.

After looking at the mark scheme, it merely says this, which I don't understand:

"substitute for density in the pressure equation
½ m<c^2> = 3pV/2N
Equate this expression to constant xT"


Please help
Reply 1
P = 1/3 &#961; <c^2>
K.E=½ m<c^2>

&#961;=m/v
so
P = 1/3 m/v <c^2>
Pv= 1/3 m<c^2>

Pv= 1/3 m<c^2> times by 3/2=
3/2Pv= 1/2 m<c^2>

so 3/2Pv is proportional to kinetic energy
Reply 2
and PV is proportional to T (K).
Reply 3
Ah thanks, I understand now :smile: