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Really hard balloon question!!!!!

Can someone help me with this question:

A hot air balloon of mass is carrying 5 people each of mass . The total volume of the balloon is . The balloon flies horizontally in dry air above sea level. The atmospheric pressure at this altitude is and the surrounding temperature is . Given that the molar mass of dry air is , work out the temperature of the heated air inside the balloon. (You can take gas constant and you may assume that air behaves as an ideal gas)


I don't understand this part...
since the mass of the balloon is 700kg, the mass of the air inside the balloon must be 700kg less than the air would be if it was at atmospheric pressure. (Mass)atm - (Mass)balloon = 700kg ????
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Avatar for justthatboy
justthatboy
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is anyone able to do it
Original post by justthatboy
is anyone able to do it


It's simply Archimides law: upthrust is equal to the displaced mass. Since the balloon is floating the upthrust acting on the balloon must be equal to the total mass of the balloon, heated air and passengers.

So the displaced volume of cold air must equal that total mass in order for it to float.

You need to work out the pressure difference that would displace the total mass and then work out the temperature required to generate that internal hot air pressure.
(edited 8 years ago)
Reply 3
Avatar for justthatboy
justthatboy
OP
4
Im still confused
why is it

(Mass)atm - (Mass)balloon = 700kg ????
(edited 8 years ago)
Original post by justthatboy
Im still confused
why is it

(Mass)atm - (Mass)balloon = 700kg ????
As I said, the upthust must be equal to the total mass in order for the balloon to float.

The equation you stated can be rearranged:

Atm(cold displaced air) - 700kg(hot air at same pressure) = balloon(mass)

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