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

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!