Question

Some say that the hot air balloons with which the Montgolfier brothers performed their first flight had a volume of 1700 cubic metres and could lift 780 kilograms (that includes the balloon, basket and payload). Assume that the balloon took off on a day when the sea level pressure was 1013.25 hPa.

Given an outside temperature of 10.0 degrees Celsius, compute the temperature of the air (in degrees Celsius) in the balloon.

Answer 1

Using the given air pressure and outside air temperature (which is 283.15 K), we compute the air density to be:

ρ=pRT=101325287.00⋅283.15=1.24686kg/m3
This gives us:

L=mg=ρVg(ΔTT+ΔT)
780⋅9.81=1.24686⋅1700⋅9.81(ΔTT+ΔT)
(ΔTT+ΔT)=0.368
Using this ratio and T = 283.15 K, we find ΔT=165K, so T+ΔT=?

Answer 2

175.15

Answer 3

Only the dead men can see