Q.

A balloon of diameter 20 m weighs 100 kg. Calculate its pay-load, if it is filled with He at 1.00 atm and 27°C.Density of air is 1.2 kg m−3⋅R=0.082dm3atmK−1mol−1.

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answer is 4247.19.

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Detailed Solution

Diameter of balloon = 20 m Radius of balloon =202=10mVolume of balloon =43πr3=43×227(10m)3.                              =4190.47m3=4190.47×103LMass of displaced air  =  volume × density                                    =4190.47×1.2=5028.57kgWeight of He gas in balloon can be calculated by applying the gas equation,PV=nRT=mM⋅RT  or mHe=PVMHeRT = 1×4190.47×103×40.082×300.              =681.377×103g=681.377kgTotal weight of gas and balloon  =681.377+100=781.377kgPay load = Weight of air displaced - Weight of gas andballoon =5028.57−781.377=4247.193 kg.
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A balloon of diameter 20 m weighs 100 kg. Calculate its pay-load, if it is filled with He at 1.00 atm and 27°C.Density of air is 1.2 kg m−3⋅R=0.082dm3atmK−1mol−1.