Question

A balloon of diameter $20m$ weighs $100kg$. Calculate its paylod if it is filled with helium at $1.0atm$ and ${27}^{\circ }C$. Density of air is $1.2kg{m}^{-3}$.
$(R=0.082d{m}^{3}atm{K}^{-1}mo{l}^{-1})$.

Answer 1

Volume of balloon $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (10{)}^3=4190.47m^3$

Mass of the air displaced $=4190.47\times 1.2=5028.56kg$

No. of moles of helium in the balloon $=\frac{PV}{RT}$ $=\frac{1\times 4190.47\times {10}^3}{0.082\times 300}=170344$

Mass of helium $=4\times 170.344\times {10}^{3}g=681.376kg$

Mass of filled balloon $=681.376+100=781.376kg$

Payload = Mass of air displaced $-$ Mass of filled balloon $=5028.56-781.376=4247.184kg$.