# For how long can we make an air balloon stay flying via remotely controlled heat system?

I wonder how a function $$f=f(h, m_{\mathrm empty}, V_{max}, T_{h}),$$ with the top height $h$, the empty mass $m$, the maximum volume $V_{max}$, and the temperature of the heater $T_{h}$ would look like for a balloon with a remote controlled heating element and desired top height?

(bolune=balloon=helium balloon)

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Hi user1078642, and welcome to Physics Stack Exchange! This question isn't very clear as it is; in particular, how exactly does the heating element work? What is the nature of the gas leak? Basically, you would need to define more precisely the model you are having us use to figure this out. –  David Z Apr 4 '12 at 15:45