# Hot air balloon

1. Feb 7, 2012

### zezima1

1. The problem statement, all variables and given/known data
Estimate the average temperature inside a hot-air balloon. Assume that the total mass of the unfilled balloon and payload, which we will all call mp is 500kg.

2. Relevant equations
Archimedes principle, ideal gas law ...

3. The attempt at a solution
Okay I'm not really sure how to understand the question, but my guess is that they want the temperature of a balloon which is hanging in the air. In this case it it clear that the upwards force equals the downwards force, i.e.:

(1) Fup = mpg + ρhot-airVg

here V is the volume of the balloon which we would have to estimate ourselves and ρhot-air the density of the hot air.
From archimedes principle we know that the upwards force equals:
(2) FupairVg
So equating (1) and (2) gives:

mpg + ρhot-airVg=ρairVg
$\Leftrightarrow$
mp + ρhot-airV=ρairV

Now what can I do from here? I tried applying the ideal gas law, as it gives us a connection between V and T, which we want. However that failed, since I'd then have to know the pressure. Is this approach even right?

Kind regards

2. Feb 7, 2012

### Spinnor

You wrote,

"Fup = mpg + ρhot-airVg"

I think this might be more accurate?

Fup = - mpg + (ρ_air - ρ_hot-air)Vg