Pay load is defined as the difference between the mass of displaced aiir and the mass of the balloon. Calculate the pay load when a balloon of radius 10m, mass 100 kg is filled with helium at 1.66 bar at `27^(@)C`. (R=0.083 bar`*dm^(3)*K^(-1)*mol^(-1)` and density of air `=1.2kg*m^(-3)`)

Explanation

Volume (V) of the balloon`=(4)/(3)pir^(3)=(4)/(3)pixx(10)^(3)m^(3)`
`=4186.66m^(3)=4186.66xx10^(3)dm^(3)`
to calculte the number of moles of He gas enclosed in the balloon, we apply ideal gas equation, PV=nRT
Given: `P=1.66` bar, `T=(273+27)K=300K`
So, according to the equation, PV=nRT,
`n=(PV)/(RT)=(1.66xx4186.66xx10^(3)" bar "*dm^(3))/(0.083"bar "*dm^(3)*mol^(-1)*K^(-1)xx300K)`
`=279.11xxx10^(3)` mol
Hence, the mass of he gas enclosed in the balloon
`=4xx279.11xx10^(3)g=1.116xx10^(6)g=1116kg`
Therefore, the mass of the balloon filled in with He gas
=(100+1116)kg=1216 kg
Volume of air displaced by the balloon=Volume of the balloon=4186.66`xx10^(3)dm^(3)`
Density of air`=1.2kg*m^(-3)=1.2xx10^(-3)kg*dm^(-3)`
`therefore`Mass of the air displaced by the balloon
`=4186.66xx10^(3)xx1.2xx10^(-3)kg=5024kg`
Hence, pay load=the mass of displaced air-the mass of the balloon=(5024-1216)kg=3808 kg.