# Gas Laws -- An astronaut breathing presurized air

1. Oct 26, 2014

### Robyn Gibson

1. The problem statement, all variables and given/known data
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!)

2. Relevant equations

3. 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?

Last edited: Oct 26, 2014
2. Oct 26, 2014

### 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 ?

3. Oct 26, 2014

### haruspex

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?

4. Oct 26, 2014

### Robyn Gibson

I put that we assumed mass and temperature were constant

5. Oct 26, 2014

### haruspex

Is it unrealistic that total mass is constant?

6. Oct 26, 2014

### Robyn Gibson

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?

7. Oct 26, 2014

### Robyn Gibson

what do you mean?

8. Oct 26, 2014

### haruspex

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?

9. Oct 26, 2014

### Robyn Gibson

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

10. Oct 26, 2014

### Robyn Gibson

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

11. Oct 26, 2014

### haruspex

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).

12. Oct 26, 2014

### Robyn Gibson

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

13. Oct 26, 2014

### haruspex

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?

14. Oct 26, 2014

### haruspex

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

15. Oct 26, 2014

### Robyn Gibson

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

16. Oct 26, 2014

### Robyn Gibson

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

17. Oct 26, 2014

### haruspex

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

18. Oct 26, 2014

### Robyn Gibson

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

19. Oct 26, 2014

### haruspex

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

20. Oct 26, 2014

### Robyn Gibson

volume, temperature and mass