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.

Question

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