Question

# Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $$10 m ,$$ mass $$100 kg$$ is filled with helium at $$1.66$$ bar at $$27^o C ($$ Density of air $$= 1.2 kg m^{-3}$$ and $$R = 0.83$$ bar $$dm^3 K^{-1} mol^{-1} ) .$$

A
1138.12 Kg
B
3811.12 Kg
C
1381.12 Kg
D
3112.38 kg

Solution

## The correct option is D $$3811.12$$ KgPayload of the ballon = mass of the displaced air- mass of the ballonRadius of the ballon, $$r=10m$$Mass of the ballon, $$m=100kg$$Therefore volume of the ballon $$=4.3nr^3=4/3\times 22/7\times (10)^3=4190.5\, m^3$$Now volume of the displaced air $$=4190.5\,m^3$$Given :Density of air $$=1.2\, kg\,m^{-3}$$Therefore, the mass of the displaced air $$=4190.5\times 1.2=5028.6\,kg$$Let $$w$$ be the mass of helium gas filled into the ballon, then $$PV=(w/m)RT$$OR $$w=PVM/RT$$$$=(1.66\times 4190.5\times 10^3\times 4)/(0.083\times 300)$$$$=1117\,kg$$ (approx)Total mass of the balloon filled with He $$=1117+100=1217\,kg$$Therefore payload of the balloon $$=5028.6-1217=3811.6\,kg$$Hence,m the pay load of the balloon is $$3811.6\,kg$$Therefore, the correct option is B.Chemistry

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