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^@C. (Density of air= 1.2 kg m^-3 and R=0.083 bar dm^3K^-1mol^-1)

Pay load is defined as the difference between the mass of displaced ai

1.	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^@C. (Density of air= 1.2 kg m^-3 and R=0.083 bar dm^3K^-1mol^-1)
Answer» Solution :Volume of balloon (V) `4/3 pi r^3 = 4/3 xx 22/7 xx 10^(3)` `= 4190.50 m^3` `= 4190.5 xx 10^(3) DM^(3)` MASS of displaced air = volume of air `xx` density of air `= 4190.5 xx 1.2 = 5028.6 kg` Mass of He in balloon = `(PVM)/(RT) = (1.66 xx 4190.5 xx 10^3 xx 4)/(0.083 xx 300)` `= 1117 xx 10^(3) g = 1117 kg` Mass of filled balloon =`100 + 1117 = 1217 kg` Pay load = mass of displaced air - mass of balloon `= 5028.6 - 1217 = 3811.6 kg`