Ideal gas law problem in outer space

AI Thread Summary
The discussion revolves around calculating the average speed and pressure of hydrogen atoms in outer space, given specific conditions of density and temperature. The average speed of hydrogen atoms is calculated to be approximately 300 m/s using the ideal gas law. However, there is confusion regarding the pressure calculation, with the initial result being incorrectly stated as 5 X 10^-24 atm instead of the correct 5 X 10^-22 atm. Participants clarify that there are indeed 100 cubic centimeters in a cubic meter, which impacts the calculations. The conversation highlights the importance of unit conversions in solving physics problems accurately.
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Homework Statement



In outer space, the density of matter is about one atom per cm^3, mainly hydrogen atoms, and the temperature is about 3.4K. Calculate the average speed of the hydrogen atoms, and the pressure (in atmospheres)


M_H = 1.0079au = 1.67 X 10^-27 Kg
1 Hydrogen atom per cm^3 = 100 hydrogen atoms per m^3
K (Boltzmann's constant) = 1.381 X 10^-23
T = 3.4K

Homework Equations


m\bar{}v^2 /2 = 3kT/2
PV = Nm\bar{}v^2 /3



The Attempt at a Solution



part 1:
m\bar{}v^2 /2 = 3kT/2
\bar{}v = \sqrt{}3(1.381 X 10^-23)(3.4)/(1.67 X 10^-27)
\bar{}v \approx 300m/s

part 2:
Consider V = 1m^3

PV = Nm\bar{}v^2 /3
P =Nm\bar{}v^2 /3V
=(100)(1.67 X 10^-25)(300)^2/3(1)
P \approx 5X 10^-19 N/m^2 \approx 5 X10^-24 atm

As usual, I get the first part of the question right, but the answer to the second part is 5 X 10^-22 not ^-24. Anyone know what I'm doing wrong?
 
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How many cc in a cubic metre?

Hint 1 cc = sugar cube, 1m^3 = refridgerator
 
Isn't there 100 cubic centimetres in a cubic metre? I'll be really embarrassed if that's where my mistake is. If there is 100 cc in 1m^3, then my "1 Hydrogen atom per cm^3 = 100 hydrogen atoms per m^3" is correct, is it not?
 
Freye said:
Isn't there 100 cubic centimetres in a cubic metre? I'll be really embarrassed if that's where my mistake is. If there is 100 cc in 1m^3, then my "1 Hydrogen atom per cm^3 = 100 hydrogen atoms per m^3" is correct, is it not?

1 cubic centimeter = 1.0 × 10-6 cubic meters.
When you use a million, you should get: 5.01E-17 Pa, when converted, you end up with 4.8546E-22 atm.
 
Freye said:
Isn't there 100 cubic centimetres in a cubic metre? I'll be really embarrassed if that's where my mistake is.

A cubic metre is a 100cm on one side, 100cm on the width and 100cm on the height.

As I said, picture it
1 cc is a sugar cube, 100 sugar cubes would be the size of your hand , 1000 sugar cubes would be 10x10x10cm the size of a saucepan.
 
Oh gawd, now I am embarrassed, lol. Thanks guys, that clears that up.
 
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