A spherical hot air balloon is neutrally buoyant in air at an ambient temperatur

Question

A spherical hot air balloon is neutrally buoyant in air at an ambient temperature of 0 degrees Celsius with a load of 500 kg. The mass of the balloon and all connective gear is an additional 100 kg. The radius of the balloon is 10.0 m. What is the temperature of the air inside the balloon? For Your Information: The density of the air at 0 degrees Celsius and standard atmospheric pressure is 1.3 kg/m3. Assume that the density of the air is inversely proportional to the temperature on the absolute scale (in Kelvins). You will need to look up how to convert temperature from degrees Celsius to Kelvins.

Explanation / Answer

Given,

Ambient air temperature=0?=273K

Total mass of balloon=500+100=600kg

Volume of balloon=4*3.14*103/3=4188.8m3

Now, for neutrally buoyant:

Volume of balloon[density of air-density of balloon]=mass of balloon

4188.8*[1.3-p]=600

p=1.16 kg/m3

Now,

p1/p2=T2/T1

1.3/1.16=Tballoon/273

Tballoon=307 K=34 C

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