Equipartition Theorem Question

[ashworcp]

Homework Statement

Assuming that pressure remains constant, at what temperature is the root-mean square speed of a helium atom equal to the root-mean-square speed of an air molecule at STP? Express your answer to 3 significant figures in Kelvin.

The Attempt at a Solution

the root mean square speed is given by vrms = Sqrt[3 kT/m]

where T is the temperature and m is the mass of one molecule (k is the Boltzmann constant)

so if we take ratios, we get

vrms(He)/vrms(O2) = Sqrt[T(he)/T(O2)] Sqrt[m(O2)/m(He)]

I am using oxygen since air is a mixture and there is no such thing as a molecule of air. If you need to compare an ensemble of He atoms to an ensemble of air molecules, use molecular weight = 28.97

so we have

vrms(He)/vrms(O2) = Sqrt[T(He)/273][Sqrt[32/4]

for vrms(He) = vrms()2), then

1 = (T/273)(8) => T=273/8 solve for T

So you get 34.125 C? Then going to Kevlin it would be 307.125 and rounding to 3 significant figures is 307?

Is this right??

 

[ehild]

T is the absolute temperature in K.

ehild

 

[ashworcp]

So it is 34.1 rounding to 3 significant figures?