The difference between the mass of displaced air and mass of balloon is called pay load. Find the value of pay load when a balloon of radius 8 m, mass 90 kg is filled with helium at 1.5 bar at 27∘CR=0.083 bar dm3Kmol density of air=1.2kgm−3).

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answer is 1967.7.

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Detailed Solution

P=1.5 bar, T=27+273=300 K,R=0.083×10−3 bar m3K−mol−r=8m;V= Volume =43πr3=43×227×(8m)3=2145.5m3PV=n RT ;n=PVRT=1.5bar×2145.5m3×1030.083barm3K−mol−×300K=129.24×103mol(ii) Mol. wt. of He=4gmol−∴ Mass of 1 mol of He=4gMass of 129.24×103molHe=129.24×103×4g=516960g=516960g×1kg1000g=516.90kgMass of filled balloon=90kg+516.9kg=606.9kg∴ Pay load = (Mass of displaced air - Mass of balloon)Mass of displaced air = volume x density=2145.5m3×1.2kgm−3=2574.6kg.∴ Pay load =2574.6kg−606.9kg=1967.7kg

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