Gas Laws -- An astronaut breathing presurized air

[Robyn Gibson]

Homework Statement

An Astronaut on a spacewalk has an oxygen tank strapped to his suit. The oxygen in it is pressurised to 5 atmospheres (5x10^5 Pa), and the volume of the tank is 15 litres.

a) The oxygen is pumped to his mouth at atmospheric pressure (1x10^5 Pa). What is the maximum volume of oxygen available to the astronaut at this pressure?

b) What assumptions are made about the gas that allow us to perform this calculation?

c) In reality, the astronaut would find that he had less oxygen available to him than calculated in part (a). Why would this be the case? (Problem Solving!)

Homework Equations

The Attempt at a Solution

Help with question (c) please, I've put in the rest of the question for context too.

I thought it may be that as he breathes more oxygen, the tank will become more space/air molecules than oxygen molecules and so there would be less oxygen, or that the cold temperature outside would could the tank and the gas, making the temperature decrease and therefore the volume decrease but I'm not sure after that?

 

[BvU]

Hello Robyn, and welcome to PF :)

If I understand things right, the assumptions under b) arent fully realistic in the perception of the problem writer. What assumptions did you find were necessary ?

 

[haruspex]

I thought it may be that as he breathes more oxygen, the tank will become more space/air molecules than oxygen molecules

Where would air molecules be coming from?

and so there would be less oxygen,

Where else can the oxygen molecules go?

or that the cold temperature outside would cool the tank and the gas, making the temperature decrease and therefore the volume decrease

You are right to think about temperature, but the temperature outside the tank has not changed, and presumably the tank started at the ambient temperature.
Note exactly what the question is asking - volume, not moles. Can the number of moles available change? The pressure is stated as constant at the mouthpiece. What else affects the volume there?

 

[Robyn Gibson]

Hello Robyn, and welcome to PF :)

If I understand things right, the assumptions under b) arent fully realistic in the perception of the problem writer. What assumptions did you find were necessary ?

I put that we assumed mass and temperature were constant

 

[haruspex]

I put that we assumed mass and temperature were constant

Is it unrealistic that total mass is constant?

 

[Robyn Gibson]

Where would air molecules be coming from?Where else can the oxygen molecules go?
You are right to think about temperature, but the temperature outside the tank has not changed, and presumably the tank started at the ambient temperature.
Note exactly what the question is asking - volume, not moles. Can the number of moles available change? The pressure is stated as constant at the mouthpiece. What else affects the volume there?

i figured the oxygen molecules he would be breathing in and so they would eventually become less until there isn't enough anymore? and I have no idea what moles are haha, we weren't taught that. And density and mass can affect volume?

 

[Robyn Gibson]

Is it unrealistic that total mass is constant?

what do you mean?

 

[haruspex]

i figured the oxygen molecules he would be breathing in and so they would eventually become less until there isn't enough anymore? and I have no idea what moles are haha, we weren't taught that.

A mole is just a certain (large) number of molecules of the molecular species in question. If the molecular mass of oxygen is 32 (say) then one mole would have a mass of 32 grams.
Yes, as he breathes there are fewer molecules left in the tank, but we are told that the gas is delivered to the astronaut at a constant pressure. So there is some pump which is scavenging nearly every molecule out of the tank until exhausted. (Maybe this is unrealistic when there's not much left.)

And density and mass can affect volume?

I was thinking of the gas laws (which you ought to have listed in Relevant Equations). Please post what you know about them.

what do you mean?

You wrote that the mass being constant was an unrealistic assumption. What exactly did you mean by that?

 

[Robyn Gibson]

A mole is just a certain (large) number of molecules of the molecular species in question. If the molecular mass of oxygen is 32 (say) then one mole would have a mass of 32 grams.
Yes, as he breathes there are fewer molecules left in the tank, but we are told that the gas is delivered to the astronaut at a constant pressure. So there is some pump which is scavenging nearly every molecule out of the tank until exhausted. (Maybe this is unrealistic when there's not much left.)

I was thinking of the gas laws (which you ought to have listed in Relevant Equations). Please post what you know about them.

You wrote that the mass being constant was an unrealistic assumption. What exactly did you mean by that?

Oh, I meant that I wrote for question b) that the assumptions made were that mass and temperature remained constant.

 

[Robyn Gibson]

Oh, I meant that I wrote for question b) that the assumptions made were that mass and temperature remained constant.

ah ok thanks. Ok that makes sense. Sorry, I figured you wouldn't need them for part c), I guess you do?

P1V1/T1 = P2V2/T2

P1V1 = P2V2

P1/T1 = P2/T2

V1/T1 = V2/T2

 

[haruspex]

Oh, I meant that I wrote for question b) that the assumptions made were that mass and temperature remained constant.

Yes, I know. So I'm asking what made you say that constancy of mass (of, presumably, the total amount of oxygen, remaining plus used) is an assumption (as opposed to a fact).

 

[Robyn Gibson]

Yes, I know. So I'm asking what made you say that constancy of mass (of, presumably, the total amount of oxygen, remaining plus used) is an assumption (as opposed to a fact).

oh because we're not told that mass remains the same

 

[haruspex]

ah ok thanks. Ok that makes sense. Sorry, I figured you wouldn't need them for part c), I guess you do?

P1V1/T1 = P2V2/T2

P1V1 = P2V2

P1/T1 = P2/T2

V1/T1 = V2/T2

OK, but those laws apply in certain conditions, which are not the same for each law.
The general one is the first, but it's usually written PV=nRT, where nR represents the total quantity of gas (as a count of molecules). Rewriting this as PV/T = nR, the right hand side being constant means PV/T is constant. From that you can deduce the first equation as you posted it. The other equations are derived from it by taking one additional variable to be constant: respectively, T, V, P.
At the mouthpiece, what are we told is constant? What variables does that leave?

 

[haruspex]

oh because we're not told that mass remains the same

The total mass of oxygen, used plus remaining? Why would it not be constant?

 

[Robyn Gibson]

OK, but those laws apply in certain conditions, which are not the same for each law.
The general one is the first, but it's usually written PV=nRT, where nR represents the total quantity of gas (as a count of molecules). Rewriting this as PV/T = nR, the right hand side being constant means PV/T is constant. From that you can deduce the first equation as you posted it. The other equations are derived from it by taking one additional variable to be constant: respectively, T, V, P.
At the mouthpiece, what are we told is constant? What variables does that leave?

we assume mass and temperature are constant? so that leaves pressure, which we're already told and volume which we can work out?

 

[Robyn Gibson]

The total mass of oxygen, used plus remaining? Why would it not be constant?

I agree, but we aren't specifically told in the question anything about it's mass, so we've been taught to write that we assume that

 

[haruspex]

we assume mass and temperature are constant?

Right, constancy of temperature is an assumption, and if it changes then the volume will change.
Why would the temperature change?

 

[Robyn Gibson]

Right, constancy of temperature is an assumption, and if it changes then the volume will change.
Why would the temperature change?

If the speed of the gas increased, temperature would increase? temperature inside the tank to outside of it?

 

[haruspex]

If the speed of the gas increased, temperature would increase? temperature inside the tank to outside of it?

No.
Let's apply the gas law PV=nRT to the tank itself. What is constant there?

 

[Robyn Gibson]

No.
Let's apply the gas law PV=nRT to the tank itself. What is constant there?

volume, temperature and mass

 

[haruspex]

volume, temperature and mass

How can the mass be constant in the tank?!
Of volume and temperature, which is surely constant and which merely an assumption?

 

[Robyn Gibson]

How can the mass be constant in the tank?!
Of volume and temperature, which is surely constant and which merely an assumption?

Sorry, I thought you meant the actual tank :/ volume is surely and temperature is an assumption

 

[Robyn Gibson]

How can the mass be constant in the tank?!
Of volume and temperature, which is surely constant and which merely an assumption?

ah wait, so would he have less because he won't be able to get the maximum volume as volume remains constant and there is less than the max volume of oxygen in the tank?

 

[haruspex]

ah wait, so would he have less because he won't be able to get the maximum volume as volume remains constant and there is less than the max volume of oxygen in the tank?

No.
Forget the astronaut for the moment. We have established that there is a question mark over whether the tank's temperature is constant. Concentrate on the tank. Of P, V and T, which can vary?

 

[Robyn Gibson]

No.
Forget the astronaut for the moment. We have established that there is a question mark over whether the tank's temperature is constant. Concentrate on the tank. Of P, V and T, which can vary?

P?

 

[haruspex]

P?

Yes, P is likely to vary, greatly. In this case nR is not constant because we are taking gas out. And we've said temperature might vary.
Can you think of a particular reason why temperature is likely to vary? Hint: why is it colder at higher altitudes?

 

[Robyn Gibson]

because the pressure is lower at higher altitudes, so if the pressure varies, the temperature will vary in the same way.

So when the pressure lowers from 5x10^5 Pa to 1x10^5 Pa, then the temperature will lower?

 

[Robyn Gibson]

because the pressure is lower at higher altitudes, so if the pressure varies, the temperature will vary in the same way.

So when the pressure lowers from 5x10^5 Pa to 1x10^5 Pa, then the temperature will lower? This will therefore decrease the volume available to him and so he will have less than calculated in (a)?

 

[BvU]

What, may I ask, did you answer under a) in this exercise ?

 

[Robyn Gibson]

0.075m^3

 

[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