A hot air balloon has a radius of 8 meters and a total mass, not including the a

Question

A hot air balloon has a radius of 8 meters and a total mass, not including the air inside, of 300 kg. When the balloon is inflated with air, the air is heated and some of it leaves the balloon through the bottom opening.

A.) The thermal expansion coefficient for air is 3.2*10-3/K. Starting with the balloon full of air at 293K, calculate the volume it would occupy at 450K and determine the fraction of the original gas remaining in the balloon.

B.) Calculate the buoyant force acting on the balloon when the gas inside is at 450K. the density of air is 1.2 kg/m3 at 293K.

C.) Calculate the work done by the expansion of the original gas in the balloon. Simplify the calculation by thinking of the gas pushing aside the air around it without mixing. The pressure is 1.01*105 Pa.

D.) Using CP=1.00 kJ/Kg*K for air, calculate the heat absorbed by the original gas in the balloon, using the same simplification as in (c). (This ignores the heat lost to the surroundings.)

E.) The operator of the balloon tells you that it takes a long time to initially inflate the balloon since his fan only blows 10 cubic meters per minute. The actual inflation time was 30 minutes with the fan located 2 meters from the balloon opening. Calculate the time needed to inflate the balloon at a fill rate of 10 m3/min and explain the difference in time.

Explanation / Answer

Hydrogen is 1/16 th the weight of air. Helium is twice as heavy so it is 1/8 th the weight of air.

Air weighs about 1.29 kg per cubic meter, so helium will lift about 7/8ths of 1.2 m^3 or about 1.1 kg per cubic meter.

And the buoyant mass for one m^3 of helium in air is:

Helium = 0.178 kg/m3
0.178 kg * (1 ? (1.292 / 0.178) ) = 1.11 kg lift per m^3

Hot air balloons are usually around 210F so it doesn't melt the envelope using a density of 0.95 kg/m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.