Gas Laws -- An astronaut breathing presurized air

[haruspex]

because the pressure is lower at higher altitudes,

Not quite that directly - that's a popular misunderstanding.
First, it is not always true that it's colder at higher altitude. Temperature 'inversions' can occur. The primary reason it's colder is because the atmosphere is heated from the bottom by the insolation of the Earth's surface, and loses heat into space at the top. So with no convection it would be much colder at higher altitudes. But heated air expands and becomes less dense, so rises. This convection tends to spread the heat evenly up through the atmosphere (at least, as far as the tropopause). As against this, as a given parcel of warm air rises it expands further because of the lower pressure, and in expanding it 'does work', pushing aside other air. The energy for that work comes from the heat in it, so it cools. (This is an example of adiabatic expansion.) Thus convection can only occur when the temperature gradient is steep enough.

For the present problem, the key part in all that is the bit about air cooling as it is allowed to expand.

 

[Robyn Gibson]

ok so as the air expands, it will be converting its heat energy into work and therefore cool down, meaning temperature decreases and so the volume of oxygen in his tank will too?

 

[BvU]

0.075m^3

I was afraid of that. Based on 5 x 15 = 1 x 75. However, once the pressure in the tank is down to 1 bar (10⁵ Pa - one atmosphere is 1.01325 Bar !), don't you think the flow of oxygen stops ?

 

[BvU]

ok so as the air expands, it will be converting its heat energy into work and therefore cool down, meaning temperature decreases and so the volume of oxygen in his tank will too?

And no, the volume of the tank remains 15 liter. So guess what decreases ?

 

[Robyn Gibson]

And no, the volume of the tank remains 15 liter. So guess what decreases ?

pressure??

I was afraid of that. Based on 5 x 15 = 1 x 75. However, once the pressure in the tank is down to 1 bar (10⁵ Pa - one atmosphere is 1.01325 Bar !), don't you think the flow of oxygen stops ?

sorry, that's just how we've been taught, plus it's in an unrealistic sense, as assumptions have also been made

 

[Robyn Gibson]

And no, the volume of the tank remains 15 liter. So guess what decreases ?

the tank's volume remains the same but the question asks why he would have a lower volume of oxygen than calculated.

 

[Robyn Gibson]

Not quite that directly - that's a popular misunderstanding.
First, it is not always true that it's colder at higher altitude. Temperature 'inversions' can occur. The primary reason it's colder is because the atmosphere is heated from the bottom by the insolation of the Earth's surface, and loses heat into space at the top. So with no convection it would be much colder at higher altitudes. But heated air expands and becomes less dense, so rises. This convection tends to spread the heat evenly up through the atmosphere (at least, as far as the tropopause). As against this, as a given parcel of warm air rises it expands further because of the lower pressure, and in expanding it 'does work', pushing aside other air. The energy for that work comes from the heat in it, so it cools. (This is an example of adiabatic expansion.) Thus convection can only occur when the temperature gradient is steep enough.

For the present problem, the key part in all that is the bit about air cooling as it is allowed to expand.

sorry if this is a stupid question, but why would the air in the tank be heated? Is it the bit about the atmosphere's heat that you mentioned?

 

[BvU]

What you'vev been taught is just fine. I just want to point out that maybe not all of these 75 liters are available for the poor astronaut, even in an ideal case.

And yes, the temperature decreases: the gas has to do some work to expand, which cools it down. If there's nothing to maintan the temperature, the 1 Bar is reached before the 15 liter has expanded to 75 liters

 

[Robyn Gibson]

What you'vev been taught is just fine. I just want to point out that maybe not all of these 75 liters are available for the poor astronaut, even in an ideal case.

And yes, the temperature decreases: the gas has to do some work to expand, which cools it down. If there's nothing to maintan the temperature, the 1 Bar is reached before the 15 liter has expanded to 75 liters

ah ok, i considered that earlier but the other guy disagreed?

so because the pressure has decreased, the oxygen becomes less dense and expands, this makes it lose heat energy to work, therefore it cools down and is already at the lower pressure without being able to expand fully to the maximum volume?

 

[mfb]

I was afraid of that. Based on 5 x 15 = 1 x 75. However, once the pressure in the tank is down to 1 bar (10⁵ Pa - one atmosphere is 1.01325 Bar !), don't you think the flow of oxygen stops ?

We have that weird notion of a pump in the problem statement, so we don't know.

so because the pressure has decreased, the oxygen becomes less dense and expands, this makes it lose heat energy to work, therefore it cools down and is already at the lower pressure without being able to expand fully to the maximum volume?

I think this is the expected answer.
The problem statement is so unrealistic that it is hard to guess which part should be assumed to be realistic.

 

[haruspex]

the tank's volume remains the same but the question asks why he would have a lower volume of oxygen than calculated.

There are two different volumes here. There's the volume of the tank, which does not change, and there's the volume of gas as presented to the astronaut. The gas is originally at tank volume and the given pressure, but all ends up (eventually) at 1 atm. You calculated the total volume as breathed from the original volume by considering the change in pressure. But that simple calculation assumed constant temperature. The discussion now concerns why the temperature may change.
It is a bit complicated because while the tank is at greater than 1 atm the gas does work in expanding, so cools the tank. Once the pressure is below 1 atm the pump kicks in. I'm not well enough versed in thermodynamics to say what happens to the temperature then.

 

[haruspex]

ah ok, i considered that earlier but the other guy disagreed?

BvU is overlooking the mention of a pump.

 

[BvU]

Haru: Sure, they mention a pump. For the last 15 liter only ? They mention 1 Bar, too. In a zero pressure environment. They don't mention CO₂ (http://spaceflight.nasa.gov/shuttle/reference/faq/eva.html does; apparently they work at 1/3 Bar). I figured the 15 liter would be a nice and simple booby trap in the exercise, which (post #40) is grossly unrealistic. Didactically rather unsatisfactory. My impression is that pV = nRT is all the students are supposed to carry when doing this exercise.

 

[Robyn Gibson]

There are two different volumes here. There's the volume of the tank, which does not change, and there's the volume of gas as presented to the astronaut. The gas is originally at tank volume and the given pressure, but all ends up (eventually) at 1 atm. You calculated the total volume as breathed from the original volume by considering the change in pressure. But that simple calculation assumed constant temperature. The discussion now concerns why the temperature may change.
It is a bit complicated because while the tank is at greater than 1 atm the gas does work in expanding, so cools the tank. Once the pressure is below 1 atm the pump kicks in. I'm not well enough versed in thermodynamics to say what happens to the temperature then.

ah ok, thank you

 

[Robyn Gibson]

ok so i'll write about how pressure ch

We have that weird notion of a pump in the problem statement, so we don't know.
I think this is the expected answer.
The problem statement is so unrealistic that it is hard to guess which part should be assumed to be realistic.

ok, thanks a lot everyone:)