Calculating pressure inside a nebula
Hi, I'd appreciate it if I could get some help on this question, I'm unsure what I'm doing wrong.
"The Lagoon Nebula is a cloud of hydrogen gas located 3900 light years from the earth. The cloud is about 45 light years in diameter and glows because of its high temperature of 7500K. The cloud is also very thin; there are only 80 molecules per cubic centimeter. Find the gas pressure (in atmospheres) in the Lagoon Nebula."
What I did:
Model the nebula as a sphere
1 light year = 9.46*10^15m
Radius of the sphere is 22.5 light years or 2.1285*10^17m
Therefore volume is 4/3*pi*(2.1285*10^17)^3 = 4.04*10^52m^3
There are 80 molecules per cm^3, therefore 8*10^-5 molecules per m^3
Therefore in the sphere are there (8x10^-5)*(2.1285x10^17) = 3.232*10^48 molecules.
Converting this into moles gives 5.37*10^24 moles
Rearranging PV=nRT to give P=nRT/V
P=(5.37*10^24*8.31*7500)/4.04*10^52 = 8.28*10^-24Pa or 8.28*10^-29atm.
However, the answer gives an answer of 8.2*10^-17atm
"The Lagoon Nebula is a cloud of hydrogen gas located 3900 light years from the earth. The cloud is about 45 light years in diameter and glows because of its high temperature of 7500K. The cloud is also very thin; there are only 80 molecules per cubic centimeter. Find the gas pressure (in atmospheres) in the Lagoon Nebula."
What I did:
Model the nebula as a sphere
1 light year = 9.46*10^15m
Radius of the sphere is 22.5 light years or 2.1285*10^17m
Therefore volume is 4/3*pi*(2.1285*10^17)^3 = 4.04*10^52m^3
There are 80 molecules per cm^3, therefore 8*10^-5 molecules per m^3
Therefore in the sphere are there (8x10^-5)*(2.1285x10^17) = 3.232*10^48 molecules.
Converting this into moles gives 5.37*10^24 moles
Rearranging PV=nRT to give P=nRT/V
P=(5.37*10^24*8.31*7500)/4.04*10^52 = 8.28*10^-24Pa or 8.28*10^-29atm.
However, the answer gives an answer of 8.2*10^-17atm
Original post by Aiden223
Hi, I'd appreciate it if I could get some help on this question, I'm unsure what I'm doing wrong.
"The Lagoon Nebula is a cloud of hydrogen gas located 3900 light years from the earth. The cloud is about 45 light years in diameter and glows because of its high temperature of 7500K. The cloud is also very thin; there are only 80 molecules per cubic centimeter. Find the gas pressure (in atmospheres) in the Lagoon Nebula."
What I did:
Model the nebula as a sphere
1 light year = 9.46*10^15m
Radius of the sphere is 22.5 light years or 2.1285*10^17m
Therefore volume is 4/3*pi*(2.1285*10^17)^3 = 4.04*10^52m^3
There are 80 molecules per cm^3, therefore 8*10^-5 molecules per m^3
Therefore in the sphere are there (8x10^-5)*(2.1285x10^17) = 3.232*10^48 molecules.
Converting this into moles gives 5.37*10^24 moles
Rearranging PV=nRT to give P=nRT/V
P=(5.37*10^24*8.31*7500)/4.04*10^52 = 8.28*10^-24Pa or 8.28*10^-29atm.
However, the answer gives an answer of 8.2*10^-17atm
"The Lagoon Nebula is a cloud of hydrogen gas located 3900 light years from the earth. The cloud is about 45 light years in diameter and glows because of its high temperature of 7500K. The cloud is also very thin; there are only 80 molecules per cubic centimeter. Find the gas pressure (in atmospheres) in the Lagoon Nebula."
What I did:
Model the nebula as a sphere
1 light year = 9.46*10^15m
Radius of the sphere is 22.5 light years or 2.1285*10^17m
Therefore volume is 4/3*pi*(2.1285*10^17)^3 = 4.04*10^52m^3
There are 80 molecules per cm^3, therefore 8*10^-5 molecules per m^3
Therefore in the sphere are there (8x10^-5)*(2.1285x10^17) = 3.232*10^48 molecules.
Converting this into moles gives 5.37*10^24 moles
Rearranging PV=nRT to give P=nRT/V
P=(5.37*10^24*8.31*7500)/4.04*10^52 = 8.28*10^-24Pa or 8.28*10^-29atm.
However, the answer gives an answer of 8.2*10^-17atm
If you have 80 molecules per cubic centimeter, you have 80 million per cubic meter. You seem to be assuming the space around this cubic centimeter is empty. Secondly, the number of molecules in the sphere will be the number of molecules per cubic meter multiplied by the volume of the sphere (in cubic meters), not the radius.
The result will fall out fine if you follow the above.
It however would be easier to start from:
Where
Leading to:
Here represents the volume number density, or, number of molecules per unit volume. Here the unit volume is .
(edited 9 years ago)
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