# Homework Help: Hydrogen in space

1. May 11, 2008

### fredrick08

1. The problem statement, all variables and given/known data
in space far from stars is filled with a very low density of hydrogen atoms, the number density is about 1atom/cm^3 and T is about 3degreeK

a. estimate the pressure in space, answer in Pa and atm.
b. what is the rms speed of the atoms
c. what is the edge length L of an LxLxL cube of gas with 1J of thermal energy
k=1.38x106-23
1atm=101.3kPa
atomic mass of hydrogen=1.67x10^-27kg
2. Relevant equations
N/V=n
vrms=sqrt(3kT/m)
N/V*M=m
PV=NkT

3. The attempt at a solution
a. P=(N/V)kT=(1/1x10-6)*1.38x10^-23*3=4.14x10^-17Pa=4x10^-22atm?
b.m=(N/V)M=(1/1x10^-6)1.67x10^-27=1.67x10^-22kg
so vrms=sqrt(9*1.38x10^-23/1.67x10^-22)=.86m/s????

and c. i have no idea, plz someone help, this micro macro stuff is stupid.... im not sure about the vrms formula is correct, since in the book it says its for molecules, but i cant find anything on atoms... im pretty sure i have done something wrong for the number density, as i dont know, coz its in atoms/cm^3.... and im just stuck plz some help me...

2. May 12, 2008

### fredrick08

ok well i think m is just atomic mass so vrms=sqrt(9*1.38x106-23/1.67x10^-27)=273m/s i think
plz can anyone tell me if i am doing this right?????

3. May 12, 2008

### alphysicist

Hi fredrick08,

What is the average kinetic energy of one atom? And so how many atoms would you need to give 1 J of energy? Once you have that, how is the number of atoms related to the volume they occupy?

4. May 12, 2008

### sirzerp

How about just converting to moles per volume? A gas is 22.4 liters per mole at STP. Just use the gas laws from chemistry.

5. May 12, 2008

### alphysicist

Hi sirzerp,

Perhaps I'm not understanding your train of thought; how will converting to moles and calculating volumes at STP help find the volume containing 1 J of energy at 3K?

6. May 12, 2008

### Redbelly98

Staff Emeritus
(a) looks good to me

(b)
Right idea, but one of the numbers is incorrect here.

7. May 12, 2008

### sirzerp

We know the number of moles per volume and temp. Just treat it as an ideal gas right?

Once you know pressure, is not pressure a direct energy unit?

Last edited: May 12, 2008
8. May 12, 2008

### alphysicist

Hi Redbelly98,

There is a 6 where a ^ should be; but I think other than that the numbers are correct. Are you seeing something that I am overlooking?

9. May 12, 2008

### alphysicist

Yes, so you could use

$$P =\frac{2}{3}\frac{U}{V}$$

and solve for V; but I don't think you need to convert to moles or calculate things at STP.

-------------------

My original suggestion also gave the volume in two step from the given data. The number of molecules giving an energy U is:

$$U=\frac{3}{2} N k T$$

and since the density is (1 atom/cm^3) then number for N is the volume (in cm^3).

10. May 12, 2008

### Redbelly98

Staff Emeritus
Oops, I was looking at the first factor of 9, thinking it should be a 3. But he had already multiplied 3 with the T=3K.

Sorry!

(b) looks good to me now!

11. May 12, 2008

### fredrick08

ok ty heaps, srry i was away, just got up lol, ok it makes sense now, srry for also confusing anyone, unfortunately ive never done chemistry before, so i dont really know the chem formulas just the ones in my physics book...

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