On a sunny morning in a field, the atmospheric pressure is 10^5N/m^2 and the tem
ID: 1836810 • Letter: O
Question
On a sunny morning in a field, the atmospheric pressure is 10^5N/m^2 and the temperature is 279 K. The film crew has filled a balloon with 1000m3 of preheated air at atmospheric pressure and a temperature of 300 K. The mass of the empty balloon and its load is 240 Kg. Under these conditions, the balloon rises above its burden, but the airship remains grounded. To begin the ascent, the air within the balloon is brought to a higher temperature. It expands but remains at the pressure of 10^5N/m^2. No air enters or leaves the balloon. How much heat must be added to the air in the balloon to initiate the flight?Explanation / Answer
Since hot air balloons fly by changing the temperature inside the balloon with heat, it stands to reason that outside air temperature is going to affect balloon flights, and it does! When the air in the balloon is heated, it becomes hotter and thus less dense than the surrounding outside air. This hotter air is "lighter" and the balloon will float upward. The more heat, the higher up you go. A balloon will fly when its temperature is around 140 degrees above the outside air temperature (generally). So, the colder it is outside, the less heat it takes to fly and conversely, the hotter it is outside, the more heat it will take to fly. Can't wrap your head around this? Here is an example:
Outside Air Temperature + Heat it Takes to Fly (140 F) = Temperature Inside the Balloon
HERE 279K =42.5300F
SO 43.5300F+140F =182.53F
182.53 Fahrenheit = 356.78 Kelvin
so you have to apply 356.78K heat