Temperature Change for N Gas in 5L Bulb in Space

[duvix]

Bulb with volume of 5 liters is filled with nitrogen n = 3 molls. The bulb is set in space, the bulb cracks and the gas starts to expand. The nitrogen is considered as a real gas. Find the change in temperature. Joseph van der Waals' constant equals 0.137.

 

[Shooting Star]

In van der Waal's eqn of state, there are two constants. Or am I going in the wrong direction?

 

[duvix]

Well that is how the problem is given.

 

[Shooting Star]

Do you know the answer?

 

[duvix]

Yes, its -6.6K.

 

[duvix]

Anybody, somebody...

 

[Danger]

All that I'm sure of is that if I cracked one in space after my traditional bacon & jalepeno breakfast sandwich, I could be half-way out of the solar system before I realized that I couldn't breathe.

 

[duvix]

Come on guys, think...

 

[wysard]

What was the temperature of the gas in the bulb before it cracked?

So you have ab out 74 grams of Nitrogen (assuming N2 gas) in a 5 litre space at a pressure of (oddly enough) about Avagadro's number of atmospheres. (22.3)

I got all that stuff.

I can do the standard: nRT=(V-nb)((P+(n*n*a)/(v*v)) versus the standard P=nRT given that you have supplied the "a", thanks, but can you give the temperature.

Juast as a SWAG I would guess and it is nothing more than that a difference on the order of about 0.45%

But I can't give you the final answer without knowing the starting temperature and where the object is. Is it in direct solar sunlight in space? In the shade? Or am I misreading your intent?

 

[duvix]

There is no information about the location of the bulb. Its mentioned that the bulb is made of some kind of highly melting metal.

 

[Shooting Star]

What is the unit of the constant you have mentioned?

In the table for van der Waals' constants, the values for nitrogen is not at all close for either a or b to 0.137.

 

[duvix]

Well as I checked it couple of tables in my books and on the internet 0.137 is quite reasonable number.

 

[Shooting Star]

For which one?

 

[duvix]

In my problem a = 0.137 Nm^4/mol^2

 

[duvix]

In my problem a = 0.137 Nm^4/moll^2

Considering that van-der Waals` formula is (P+a/V^2)(V-b)=RT for one moll of matter.

 

[Q_Goest]

Hi duvix,

Bulb with volume of 5 liters is filled with nitrogen n = 3 molls.

Do you know the thermodynamic state of the nitrogen given this information? Why not? What additional information would you need? (hint: you don't know the state from this info)

the bulb cracks and the gas starts to expand. The nitrogen is considered as a real gas.

Do you know anything about the final state of the gas from this? What do you need to determine final state?

Find the change in temperature.

If you don't know the initial state, don't know the final state, what can this mean? What are they asking for? Are there any simplifying assumptions you need to make and if so, what are they? (hint: regardless of initial and final states, is there a relationship between them?)

 

[duvix]

Actually the state is given as gaseous. After the bulb cracks, it expends as gas.

 

[Q_Goest]

By state, I don't mean solid, liquid or gas. Knowing something is a liquid or gas does not give us enough information to determine the pressure, temperature, internal energy, entropy, density, etc... We need to know two of these things to know its thermodynamic state. Pressure and temperature are the most common two. The question as posed doesn't provide sufficient information to determine its thermodynamic state.

The OP provides only enough information to determine density. We can assume there is some pressure and temperature, but those variables can be almost anything since there is no way to pin down any second piece of information about the state. Remember, you need 2 pieces of information to determine the state such as density and temperature. From that, you can calculate the pressure.

Similarly, you can't determine the final state. Nor can you determine any of the states the nitrogen may transit as the gas expands and leaves through the crack in the container.

So what is the OP really asking? You can't assign any values to any of it. The best you can do is write the equations which describe how the nitrogen transists the various states, and input the variables you do know. I don't think the OP is looking for a difinitive answer, it is asking only for you to demonstrate how to calculate the future state of a gas given some initial, but undefined conditions. The bit about the Joseph van der Waals' constant is a bit missleading, perhaps intentionally so since you are told the nitrogen behaves as an ideal gas, thus - no additional information would be needed to plug into the ideal gas equation.

 

[duvix]

Okay there is just one more fact. The bulb, is formed by pumping air into melted metal, cooled and only then moved into space and then happens what happens. By the way the teacher says that the problem is solvable.

 

[Q_Goest]

If you made an assumption about the pressure when the metal was molten (can you think of what that is?) then you can determine the state of the gas at that point. But if you then say, you cool it down, then you have to make an assumption about what temperature it is being cooled down to. Somewhere along the line, if you really want to put numbers to this, you will need to make some assumptions about the state.

 

[pervect]

My impression is that it is intended that the expansion of the gas be modeled as adiabatic (being in space, there's nothing to exchange energy with).

So you'll want to re-derive the adaibatic gas law, derived for ideal gases at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiabc.html#c1

for a non-ideal adiabatic gas.

 

[Privalov]

I believe van der Waals equation is inapplicable in this case. I believe the gas temperature will not change at all. Process will be adiabatic and isothermal.

Temperature is a measure of kinetic energy of gas particles. Decrease in temperature means decrease in kinetic energy. If you believe temperature decrease will be involved, where the kinetic energy will go?

Let’s imagine the 5 liters bulb in a huge (but finite) vacuum camera. Instantly release nitrogen – and the temperature will not change. Technically, the temperature will be converted into kinetic energy of gas particles, which is, in turn, temperature.

I don’t think 5 liters bulb in space is any different from 5 liters bulb in huge huge vacuum camera.

IMHO.

 

[Shooting Star]

The KE will get transformed into PE, much as a comet travels slowly when it's far away from the sun. There is no doubt about a real gas cooling down, in the vacuum camera or in space.

 

[Privalov]

The KE will get transformed into PE, much as a comet travels slowly when it's far away from the sun.

There is no potential energy involved.

Comet has gravitational potential energy. What kind of potential energy gas particles have in vacuum? Wikipedia lists the following types of potential energy:

1 Gravitational potential energy
2 Elastic potential energy
3 Chemical potential energy
4 Electrical potential energy
4.1 Electrostatic potential energy
4.2 Electrodynamic potential energy
4.3 Nuclear potential energy
5 Thermal potential energy
6 Rest mass energy

I believe none of that applies.

When gas is packed in a bulb, it has thermal potential energy and electrostatic potential energy. When it’s released, these types of energy are converted to kinetic energy of moving gas molecules, which is, in turn, thermal potential energy. You can say “thermal energy is being converted into thermal energy”. Temperature does not really change.

Quote: “Thermal energy of an object is simply a sum of average kinetic energy of random motion of particles …”
http://en.wikipedia.org/wiki/Potential_energy

There is no doubt about a real gas cooling down, in the vacuum camera or in space.

I have no doubt the real gas will not cool down in vacuum camera. That's a fact - I can prove it either by direct experiment or using computer model.

Then comes the tricky part: I believe there should be no difference in definition of temperature in lab vacuum or in space. Velocity of chaotic movement of molecules is, actually, temperature - in space or anywhere else. It's not fact, it's my personal opinion.

Here are some thoughts to support that personal opinion:

The search for "temperature of solar wind" in Google returns 23,100 results.

Quote: "The temperature of solar wind plasma around the Earth is about 150000°K."
http://www.windows.ucar.edu/tour/link=/sun/wind_character.html

The nitrogen molecules in our case will end up in exactly the same state, as solar wind: they will become just particles, moving in space with known velocity. It's hard to say if the word "temperature" applies to them, but if it does, the temperature of nitrogen will not change, when it leaves the bulb. At least 23,100 writers out there believe the word “temperature” can be applied in this case.

Another way to describe the situation is: velocity of nitrogen molecules will not change. In a bulb, velocity of molecules is temperature. In space, I can not say what the temperature is.

If we use classic definition of temperature, we end up with the conclusion the temperature will not change.

Quote: “On the microscopic scale, temperature is defined as simply the average energy of microscopic motions of a single particle in the system per degree of freedom.”
http://en.wikipedia.org/wiki/Temperature

 

[Shooting Star]

I believe van der Waals equation is inapplicable in this case. I believe the gas temperature will not change at all. Process will be adiabatic and isothermal.

Temperature is a measure of kinetic energy of gas particles. Decrease in temperature means decrease in kinetic energy. If you believe temperature decrease will be involved, where the kinetic energy will go?

What are the scientific reasons for your beliefs, both the first and the second?

From http://www.encyclopedia.com/doc/1E1-vandrWls.html (Just one random source from many.)
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Van der Waals was led to the hypothesis of the continuity of the gaseous and liquid states of matter by combining the kinetic theory of gases with Laplace's theory of capillarity. In his theory of corresponding states (1880) he presented an equation of state (now named for him) for homogeneous substances in terms of pressure, volume, and temperature (see gas laws ); unlike the ideal gas law, his equation contains constant factors (different for each real substance) to account for the fact that molecules are of finite size and experience weak forces of mutual attraction (now called van der Waals forces).
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There are various intermolecular forces in a gas, which are feeble but attractive when the distances between molecules become large. In order to overcome these forces while expanding, the molecules have to lose a part of their KE, and the gas cools down in the process.

The a/V^2 term in van der Waals’ eqn of state represents the attractive force, which reduces the observed pressure of a real gas, as compared to an ideal gas.

An ideal gas would not cool down while expanding in space.

A computer simulation does not prove anything, because it’ll depend on what laws are built into the programme.

There is no potential energy involved.

Comet has gravitational potential energy. What kind of potential energy gas particles have in vacuum? Wikipedia lists the following types of potential energy:

1 Gravitational potential energy
2 Elastic potential energy
3 Chemical potential energy
4 Electrical potential energy
4.1 Electrostatic potential energy
4.2 Electrodynamic potential energy
4.3 Nuclear potential energy
5 Thermal potential energy
6 Rest mass energy

Perhaps 4.2 would be best suited. Anyway, this is a matter of nomenclature. The Physics is well understood.

 

[Privalov]

You are right; I did not think about it.