Pressure and Volume of a Neutral Hydrogen Cloud

In summary, the conversation discusses a problem involving finding the pressure and volume of a hydrogen cloud with a given mass and temperature. There is a debate about whether to include gravity in the calculations and how to define the volume of the cloud. The issue of using the Ideal Gas Law for hydrogen atoms is also mentioned.
  • #1
Parzeevahl
6
0
Homework Statement
A diffuse cloud of neutral hydrogen atoms in space has a temperature of 50 K. Calculate the pressure (in Pa) and the volume (in cubic light-years) occupied by the cloud if its mass is 100 times the mass of the sun.
Relevant Equations
PV = NkT (k = Boltzmann constant)
Here's how I approached it. We know the total mass of the cloud, it is given. Let's call it 'M'. We can also find out the mass of a single hydrogen atom from its atomic weight. Let's call this 'm'. Then

N = M / m

is the total number of hydrogen atoms in the cloud. The temperature (T) is given - it is 50 K.

Then the gas equation becomes: PV = (M / m) * k * (50 K)

So, here are two unknown variables here that I have to find out - P and V. But I have only one equation (the gas equation above). How can I find out the other equation, since for two unknown variables we need two equations?
 
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  • #2
I don't know how you can solve this without more information. Such as the density of the cloud. This may be given as a certain number of atoms per cubic centimeter. Did they tell you any information such as this?
I was doing some searching when reading this problem, because I did not know if these atoms obey the Ideal Gas Law.

I didn't really find a definite answer to that, but it seems that they may. I did find this following article interesting, though:

https://www.britannica.com/science/hydrogen-cloud
 
  • #3
Yes, I also thought of the density and checked again, but the question didn't supply any such information.

Also, thanks for the article, I'll take a look :) !
 
  • #4
I suppose gravity would be the force that keeps the volume finite? Then the temperature would have to be an average value, I guess?
 
  • #5
DaveE said:
I suppose gravity would be the force that keeps the volume finite? Then the temperature would have to be an average value, I guess?
I agree that it makes sense to include gravity. But the temperature is given, so it doesn't need to be considered an average value. However, the pressure and density should vary with radial position.
 
  • #6
Chestermiller said:
I agree that it makes sense to include gravity. But the temperature is given, so it doesn't need to be considered an average value. However, the pressure and density should vary with radial position.
I am not convinced that this is the intended interpretation. But...

Suppose that we arbitrarily fix the density at the center of the [spherically symmetric] cloud. Now we should be able to obtain a differential equation for the density gradient at radius r in terms of r and the cumulative mass at or beneath radius r.

We solve the differential equation. If the limit as ##r \to \infty## is finite, we re-scale the initial density to obtain the desired 100 solar mass total and hope that the resulting density still qualifies as "sparse".

Unfortunately, even if this approach succeeds, we will not have obtained a volume. We might, I suppose, consider the pressure at the center as the "pressure" part of the answer and the hypothetical volume that would be required for 100 solar masses at that uniform pressure as the "volume".
 
  • #7
jbriggs444 said:
Unfortunately, even if this approach succeeds, we will not have obtained a volume.
Yes I find the volume issue problematic. I guess you have to pick a statistical definition, like "containing 99% of the atoms". For any volume chosen there could be an atom that has enough energy to leave that space.
 

FAQ: Pressure and Volume of a Neutral Hydrogen Cloud

1. What is the relationship between pressure and volume in a neutral hydrogen cloud?

The pressure and volume of a neutral hydrogen cloud are inversely proportional to each other. This means that as the volume of the cloud decreases, the pressure increases, and vice versa.

2. How does the pressure and volume of a neutral hydrogen cloud affect its stability?

The pressure and volume of a neutral hydrogen cloud play a crucial role in determining its stability. A higher pressure can counteract the gravitational force and prevent the cloud from collapsing, while a lower pressure can cause the cloud to fragment and form new stars.

3. What factors influence the pressure and volume of a neutral hydrogen cloud?

The pressure and volume of a neutral hydrogen cloud are affected by various factors such as the temperature, density, and composition of the cloud. Changes in these parameters can alter the balance between pressure and gravity and affect the overall dynamics of the cloud.

4. How do scientists measure the pressure and volume of a neutral hydrogen cloud?

Scientists use various techniques to measure the pressure and volume of a neutral hydrogen cloud, such as radio observations, spectroscopy, and numerical simulations. These methods provide valuable insights into the physical properties of the cloud and its evolution over time.

5. What is the significance of studying the pressure and volume of neutral hydrogen clouds?

Studying the pressure and volume of neutral hydrogen clouds is crucial for understanding the formation and evolution of galaxies. These clouds are the building blocks of galaxies and play a significant role in the formation of stars. By studying their physical properties, scientists can gain a better understanding of the universe's structure and evolution.

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