# Estimating Pressure, RMS Speed of Hydrogen in Space

• fredrick08
In summary, in space far from stars, the density of hydrogen atoms is approximately 1 atom/cm^3 and the temperature is 3 degrees Kelvin. Using gas laws and the given constants, the pressure is calculated to be 4.14x10^-17 Pa or 4x10^-22 atm. The root mean square speed of the atoms is calculated to be 0.86 m/s. To find the edge length of an LxLxL cube with 1 J of thermal energy, the number of atoms is calculated using the average kinetic energy per atom and the ideal gas law, resulting in a volume of 5.56x10^-25 cm^3. Alternatively, the number of molecules can be found using

## Homework Statement

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

N/V=n
vrms=sqrt(3kT/m)
N/V*M=m
PV=NkT

## 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, please someone help, this micro macro stuff is stupid... I am not sure about the vrms formula is correct, since in the book it says its for molecules, but i can't find anything on atoms... I am pretty sure i have done something wrong for the number density, as i don't know, coz its in atoms/cm^3... and I am just stuck please some help me...

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

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?

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.

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?

(a) looks good to me

(b)
vrms=sqrt(9*1.38x106-23/1.67x10^-27)

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

alphysicist said:
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?

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?

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Hi Redbelly98,

Redbelly98 said:
(a) looks good to me

(b)

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

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?

sirzerp said:
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?

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).

alphysicist said:
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?

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!

ok ty heaps, srry i was away, just got up lol, ok it makes sense now, srry for also confusing anyone, unfortunately I've never done chemistry before, so i don't really know the chem formulas just the ones in my physics book...