(adsbygoogle = window.adsbygoogle || []).push({}); 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 m_{p}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) F_{up}= m_{p}g + ρ_{hot-air}Vg

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_{air}Vg

So equating (1) and (2) gives:

m_{p}g + ρ_{hot-air}Vg=ρ_{air}Vg

[itex]\Leftrightarrow[/itex]

m_{p}+ ρ_{hot-air}V=ρ_{air}V

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

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# Homework Help: Hot air balloon

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