# Balloon in Earth's atmosphere

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1. Oct 23, 2014

### cycrups

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

1. At an altitude of about 10 km, the temperature of the Earth’s atmosphere is roughly -50°C and the air pressure is around 16 kPa. (Assume ideal gas)
1. How many kilograms of hydrogen gas (H2, molecular mass 2g/mol) should be put in a balloon to fill it to 2000 m3?

2. What is the required mass of total ballast that the balloon will float at constant height (molecular mass of air 29 g/mol)?

2. Relevant equations
PV = nRT

3. The attempt at a solution

For 1. I used V = (P*A*N)/(R*T) = ( 2g/mol * 16000 Pa * 2000m^2 ) / (8.314 * 223K) = 34.51 Kg I don't know if it's correct way to do it or not

For the second part I have no idea how to even start.

2. Oct 23, 2014

### Orodruin

Staff Emeritus
Your numbers make sense, although the notation in your equation could be clearer. V is generally used to denote a volume, not a mass.

What must be fulfilled in order for the balloon not to accelerate either up or down?

3. Oct 23, 2014

### cycrups

certain weight?

4. Oct 23, 2014

### Orodruin

Staff Emeritus
Naturally, but what determines this weight? What determines whether any object is accelerating or not? Hint: There was this guy in the 17th century who got hit by an apple ...

5. Oct 24, 2014

### cycrups

Force. Hope it's correct.

6. Oct 24, 2014

### Orodruin

Staff Emeritus
Yes, so what must be true if the balloon is not supposed to accelerate?

7. Oct 24, 2014

### cycrups

The forces in both directions must equal the same.

8. Oct 24, 2014

### haruspex

I guess you mean M = (molecular mass)*n = (molecular mass)*PV/(RT)
Right. And without the ballast, what two forces do you have?

9. Oct 28, 2014

### cycrups

I'd say gravity and the force of the helium pushing up the balloon?

10. Oct 28, 2014

### haruspex

How does the helium push the balloon up? Does it have negative mass??

11. Oct 29, 2014

### cycrups

because Helium is lighter than air that's why it tends to push up

12. Oct 29, 2014

### Orodruin

Staff Emeritus
It would be more accurate to say that the surrounding air is pushing the helium up - with a force greater than the helium weight. If you block the helium from escaping, the surrounding air is providing the upward force on the balloon helium system.

To get back to the problem: What is the buoyancy force on the balloon + helium system? What forces act in the opposite direction? Does the weight of the system compensate for the buoyancy? If not, how much weight do you need to add?

13. Oct 29, 2014

### cycrups

Should I use this equation to get the Buoyant force F (b) = (air density)x(9.81 m/sec2)x(volume of the gas filled balloon) ?

14. Oct 29, 2014

### haruspex

Yes.

15. Oct 29, 2014

### cycrups

or should I use Fb= mass of air * g = P * Vb * g because I don't have air density OR do I get the air density from

density = P / R * T ?

16. Oct 29, 2014

### haruspex

mass = pressure * volume? Where does that come from?
Sort of. You know air density at standard surface temperature and pressure, right? So use that to figure out what it would be at the given temperature and pressure.

17. Oct 29, 2014

### cycrups

18. Oct 29, 2014

### cycrups

Okay so the density would be → density of air = 16000 Pa / 8.31 * 223 K = 8.63 Kg/m3

and then to find the Buoyant force Fb = 8.63 * 10 m/s3 * 2000 m3 = 172600

Is that correct, and if it is what's the next step? Do I equate Fb = Fg to get the Maximum altitude?

19. Oct 29, 2014

### haruspex

Sorry, I wasn't paying enough attention to exactly what data you are given.
Here's the easiest way:
- you have already calculated the mass of H2 for the given volume, temperature and pressure
- you know the molecular mass of H2 and the molecular mass of air
- how can you simply combine those facts to obtain the mass of air at the given volume, temperature and pressure?

20. Oct 30, 2014

### cycrups

I equate both of them together so the PV/nRT (of H2) = PV/nRT of air? I am sorry im really having a hard time solving this part.