For an atmospheric physics class, we are given this problem that I and a classmate have been struggling with for days. Reaching out here for some help.
Full Problem statement in the image attached.
We have a balloon at 293 K and 101,300 Pa. How much fuel is needed to raise the balloon to a pressure of 90,000 Pa if the fuel gives 5*107 J/kg. The Balloon expands adiabatically while rising.
That's all the information we're given accept that the answer should be about 5 kg (or 2.5 * 108 J)
Perhaps the adiabatic work condition? But that involves volume.
cp*m*ΔT = Q but I can't see how to solve for the air mass
The Attempt at a Solution
I have tried everything I can think of. My professor's only response has been to say I should solve for the final temperature first, which he says should be about 360 K. I can't get this value. But even if I take it as a given I can only solve the final density, not the actual mass and therefore not an amount of energy.
Every route I try hits a wall where I need a volume or an air mass to obtain an energy value.
Can anyone suggest a way to solve for the energy required without knowing the mass or at least the volume of the balloon? Going kind of crazy with this problem. It's due in two days and there are midterms to study for. Any help is appreciated.
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