A hot air balloon carrying 3 passengers is found to have a total weight (basket,

Question

A hot air balloon carrying 3 passengers is found to have a total weight (basket, burner, fuel, envelope, passengers, and, of course, champagne) of 800 kg before the balloon is inflated. An envelope of 18 m in diameter is used to support this 3-passenger basket.

If the outside air temperature is 15?C, what temperature must the gas within the envelope be heated to lift the basket off of the ground?

In order to prevent premature degradation of the nylon envelope, the maximum temperature allowed within the balloon is 120?C. What is the maximum altitude that the balloon can reach?

You should consider the change in atmospheric pressure (density) with altitude, but can assume that the temperature is constant as the balloon rises.

Atmospheric pressure as a function of altitude can be calculated using the barometric formula:

Explanation / Answer

weight downwards = 800 x 9.8

bouyant force = weight of air displaced

balance the two forces for lifting of the balloon

volume = 4/3 pi r^3
r =9 m

bouyant force = x v x g

so

800 x 9.8 = x 4/3 pi r^3 x 9.8

800 = x 4/3 x3.14 x 9^3

= 0.26198 kg/m^3

the air has this density coressponding to 1050 degree C

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