1st year physic help - hot air balloons

[bruceflea]

1st year physics help - hot air balloons...

see next post...

 

[bruceflea]

question:

The buoyancy force that pushes the balloon upward is proportional to the density of the cooler air outsider the balloon and the volume of the balloon, and can be expressed as

force buoyancy = denisty(ofcoolair)*g*volume(ofballoon)

where g is the gravitational constant.

Consider a 20-m-diameter hot-air balloon that, together with its cage, has a mass of 80 kg when empty. This balloon is hanging still in the air at a location where the atmospheric pressure and temperature are 90 kPa and 15 o C, respectively, while carrying three 65 kg people. Determine the average temperature of the air in the balloon.

this is what I have so far...

The buoyancy force required for the balloon to hang still in the air is equal to the force exerted downwards by the weight of the balloon so:

Force buoyancy, Fb = mass*gravity = 275*9.81 = 2697.75 N
Therefore:

denisty(ofcoolair)*g*volume(ofballoon) = 2697.75 N

volume(of balloon) = 4/3*pi*10^3 = 4188.79 m^3

density(ofcoolair) = 0.066 kg m^3

I know that for the balloon to be hanging still:

density(ofcoolair) = density(ofhotair)

Is it ok to assume that the pressure inside the balloon is the same as the outside (90kPa)? I'm also assuming that V1 = V2. Which would give me the expression:

T2/T1 = n1/n2

Am I heading in the right direction?

 

[quicknote]

Hot air balloons use the basic principles of buoyancy and the ideal gas law to operate. The balloon is filled with hot air, which is less dense than the surrounding cool air. This creates a buoyant force that allows the balloon to rise.

The ideal gas law, which states that pressure, volume, and temperature are all directly proportional, also plays a role in the operation of hot air balloons. As the air inside the balloon is heated, its volume increases, causing the pressure to increase as well. This increased pressure pushes against the fabric of the balloon, causing it to expand and rise.

To control the altitude of the balloon, the pilot can adjust the temperature of the air inside the balloon by using a burner to heat the air or a vent to release hot air. This allows for a controlled descent or ascent.

Hot air balloons also rely on wind currents to move horizontally. The pilot can control the direction of the balloon by ascending or descending to different wind currents at different altitudes.

Overall, hot air balloons are a fascinating example of how the principles of physics can be applied to create a mode of transportation.