Question

At what temperature is the rms speed of helium molecules half its value at STP (0 C, 1.0 atm})?(answer in K)

I think i need to use V_rms=sqrt3kT/m
k=1.38e^-23J/K
helium has 4g so i think helium molecule is 4/6.02e23
but i don't know how to proceed further

then i have to answer this also:
At what temperature is the rms speed of helium molecules twice its value at STP?(answer in K)
Thanks

Answer 1

There is an easier way to answer this problem.

Molecular speed is proportional to the square root of absolute T. To reduce speed by a factor ot 2, temperature must be reduced by a factor of 4, in this case to 273.2/4 = 68.3 K

You should be able to do the second question with the same method.

Answer 2

Your answer is correct, but i was wondering how can i use the formula to answer this question?

Answer 3

For the 2nd part i got around 1100k by playing around, but not sure if it is correct

Answer 4

The answer to the second part is 1093 K.

Since V = sqrt (3kT/m), and m and k do not change,
V2/V1 = sqrt (T2/T1, or
T2/T1 = (V2/V1)^2

There is a formula for you to use.