A sealed container of 0.10 m3 holds a sample of 3.0x1024 atoms of helium gas in equilibrium. The distribution of speeds of the helium atoms shows a peak at 1100 m s-1.
Take the mass of a helium atom to be 4.0 amu.
I, calculate the temperature and pressure of the helium gas.
ii, what is the average kinetic energy of the helium atoms?
iii, what is the position of the maximum in the energy distribution?
,<E> = (3/2)KT
delta vsd = sqrt(<v2> - <v>2) (?)
PV = NKT
f(v) = Bv2e-mv^2 / 2KT
<v> = sqrt((8KT) / (pi m))
vmp = sqrt((2KT) / m)
The Attempt at a Solution
I believe that the peak in the Maxwell-Boltzmann speed distribution corresponds to the most probable speed (vmp), hence I think the temperature can be found by rearranging the equation for vmp to T = (vmp2 * m) / (2K) and then finding pressure from P = NKT / V. One thing i'm not clear on is whether the mass needed is that of one atom, or all of them.
Part ii, seems reasonably straight forward once temperature is known (ie just plugging values in to the equation).
I do not know the definition of the maximum in this context but assume it is the highest energy of any of the helium molecules. I understand that the speed and energy distributions are linked somehow but I cant understand how you obtain information about one from the other. im wondering whether standard deviation of molecular speeds has something to do with it or even the square root rule for averages? I am very unsure of this one.
Thanks in advance guys, any help would be hugely appreciated!