Determining pressure in Interstellar space

AI Thread Summary
The discussion focuses on estimating the pressure in interstellar space, which is characterized by a low density of hydrogen atoms at approximately 1 atom/cm³ and a temperature of 3 K. The initial calculation for pressure using the ideal gas law yielded a value of about 4.14 x 10^-17 Pa. Participants confirmed the correct approach using the formula pV = nRT and discussed the calculation of root mean square (Vrms) velocity, which initially produced an incorrect value. The final consensus suggests that the correct Vrms should be around 2 m/s, aligning with expectations for atomic motion in such a low-density environment. The conversation emphasizes the importance of careful unit management and verification of calculations in physics problems.
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Homework Statement


Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H2). The number density is about 1atom / cm3 and the temperature is about 3 K. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.


Homework Equations


Average translational kinetic energy per molecule: Eavg = 1.5KbT = .5mv2
p = F/A = (1/3)(N/V)mVrms2
Eth = 1.5nRT
pV = nRT

The Attempt at a Solution


V = 10-6 m3
T = 3K
m = 1u = 1.66x10-27
n = 1.66x10-24 (not sure if this is right?)

pV = nRT --> p = 4.14x10-17
Where am I going wrong, or is this correct?

Thank you for any help/advice!
 
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Different approach, I get the same number:

<br /> \frac{10^6 \, \text{atom}} {\text{m}^3} \cdot<br /> \frac{1 \, \text{mole}} {6.0221415 \times 10^{23} \, \text{atom}} \cdot<br /> 8.3144621 \, \text{J}/\text{K}/\text{mole} \cdot<br /> 3 \, \mbox{K} \approx 4.142 \times 10^{-17} \, \text{pascal}<br />
 
The only formula you need is PV = nRT
 
That is exactly one of the formulae that pdonovan, Spinnor.
 
Thank you very much, that was the correct answer.

Now, how would I got about finding Vrms?

I know p = (1/3)(N/V)mVrms2
So, p = 4.14x10-17
N = 1
V = 10-6
m = 1u = 1.66x10-27
And found Vrms = .86m/s, but this is incorrect. I think my m or v might be incorrect.
 
Your value for m is correct (assuming units of kilograms; always carry units around). Your math is wrong somewhere. Show your work.
 
Now I have...

4.14x10-17pa = (1/3)(1/10-6)mVrms2

1.242x10-22 = mVrms2

74819.28 = Vrms2
Vrms = 275.64m/s

So something is definitely wrong, because the atom should be moving very slowly.
 
Yeah, your answer is too large. About 2 m/s too large. sqrt(74819.28) is about 273.53.

As a sanity check, you can always compute sqrt((3 * boltzmann's constant * 3 kelvin) / (1 amu)). You will get the same answer.
 
Then which values are wrong in the Vrms = sqrt(3KbT / m) formula? I have T = 3 and if m = 1, then Vrms = 1.11 x 10 ^ -11 which is wrong. And if m =1660x10^-27g it is too big (around 8.6).
 
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