A spherical balloon has a diameter of 30 cm. It is filled with He to a pressure

Question

A spherical balloon has a diameter of 30 cm. It is filled with He to a pressure of 110 kPa. Buoyancy force is equal to the weight of fluid displaced minus the weight of the displacing object. This is why ships float even though they are made of steel. In this case air is displaced by helium. If you neglect the weight of the balloon skin material, what is the lifting force if the air is at standard atmospheric pressure and temperature? Use values in Table A-16 at an altitude of zero meters for standard atmospheric conditions.

Explanation / Answer

Lifting force =vdg - mg

Number of moles of He inside baloon = PV/RT = (110*4*pi*15*15*15)/(3*273.15*8314) = 0.685 moles

Weight of helium = 4*0.685 = 2.74gms

lifting force = (4*pi*15*15*15/3000)(1.225)(9.81)-(2.714*9.81/1000) N = 169.95-0.027 = 169.923 N

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