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

Given the outside air temperature (which is 283.15 K), we can compute the air density:
P=p/RT=101325/287.00*283.15 =1.24686kg/m^3
This gives us-
L=mg=pVg (delta T/T + delta T)
Plugging in the numbers this gives us 780*9.81 (Delta T/T+Delta T) = 0.368

Using this ratio and t=283.15K, we find that Delta T= 165 K, so T+Delta T= 175 degrees Celsius

Hope this helped!