Calculating Average Temperature in a Hot Air Balloon | Homework Guide

[zezima1]

Homework Statement

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 m_p is 500kg.

Homework Equations

Archimedes principle, ideal gas law ...

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) F_up = m_pg + ρ_hot-airVg

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

m_pg + ρ_hot-airVg=ρ_airVg
\Leftrightarrow
m_p + ρ_hot-airV=ρ_airV

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

 

[Spinnor]

You wrote,

"Fup = mpg + ρhot-airVg"

I think this might be more accurate?

Fup = - mpg + (ρ_air - ρ_hot-air)Vg