Calculate Pressure of Interstellar Hydrogen Gas at 3K

[hasan_researc]

Homework Statement

Some regions of interstellar space is made of lone hydrogen atoms with a density of 1 particle / cm³, at a temperature of around 3 K. Calculate the pressure due to these particles.

Homework Equations

P = nk_bT, where P is the pressure, n is the number density and T is the temp.

The Attempt at a Solution

n = 10^-6
T = 3
So, P = 4.14 X 10^-29 Pa.

The gas is not contained in a container, so are we assuming an imaginary surface within which lies a certain quantity of hydrogen atoms and then calculating the pressure exerted on that imaginary surface by the atoms? This interpretation seems to make sense to me because the volume of the surface is independent of the pressure, as seen from the original equation.

What does everyone think?

 

[graphene]

Our sun is mainly hydrogen. But, the gas in not enclosed by a container. Gravity keeps the gas together. This is true with the gas planets, other stars, ...

 

[hasan_researc]

But in order for pressure to have physical meaning, should the gas be not imagined to exist in a container, be it real or imaginary?

 

[ehild]

The formula for the pressure of ideal gases was derived by assuming the gas confined in a container. The molecules are in random motion, collide to the wall and transfer momentum to it. During two subsequent collisions, there is an average force on the wall, and so on. At the end you get a formula that the pressure is proportional to the average translational kinetic energy of the particles and their number density. Using the Equipartition Principle, the average translational kinetic energy of a particle is 3/2 kbT and you get the relation in the form

P=nk_bT

where n is the number density. This equation does not contain the volume, so you can apply it even in free space. This pressure would be experienced with any wall placed into the gas. There is no difference if you place an imaginary container or a simple wall: the wall experiences the pressure given by the formula. The molecules are in random motion, as they collide not only with the walls of a container, but with each other, too. The number of the molecules arriving at a single wall is the same either in the presence of other walls confining a big enough closed volume or without them.

ehild

 

[rwisz]

I would first clarify the assumptions and limitations of the problem. It seems that we are assuming a uniform distribution of lone hydrogen atoms in interstellar space, and that there is no external pressure acting on this gas. I would also confirm the units for the number density and temperature, as they may need to be converted to a more appropriate scale for this problem.

Assuming these assumptions are correct, the calculation for pressure using the ideal gas law seems reasonable. However, it is important to note that this pressure is extremely low, as expected for a gas at such a low density and temperature. It is also important to consider that this gas may not behave as an ideal gas due to the low temperature and potential interactions between particles.

In terms of the interpretation of the pressure, it is correct to think of an imaginary surface within which the gas particles are contained. However, it is important to note that this pressure is not exerted on the surface by the particles themselves, but rather is a measure of the force per unit area exerted by the particles as they collide with the surface.

Overall, the calculation seems reasonable, but it is important to consider the assumptions and limitations of the problem and to interpret the pressure correctly.