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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^(3)K^(-1)mol^(-1)). |
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Answer» Solution :Calculation of balloon.s VOLUME : Radius of balloon r = 10 m Volume of balloon `= (4)/(3)pi r^(3)=(4)/(3)((22)/(7))(10 m)^(3)` `= 4190.48 m^(3)` Calculation of weight of displaced AIR : `THEREFORE` Volume of He gas in balloon = Volume of balloon `= 4190.48 m^(3)` `~~4190.5 m^(3) = V` `therefore (("The weight of air"),("displaced by balloon"))=(("Volume of"),("balloon (V)"))xx(("Air of "),("density"))` `=(4190.5 m^(3))(1.2 kg m^(-3))` `= 5028.6` kg air Calculation of weight (w) of He gas in balloon : where, Volume of Balloon (V) `= 4190.5 m^(3)=4190.5xx10^(3)` Pressure of `H_(2)` gas in `dm^(3)` in balloon (p) = 1.66 bar Temperature (T) of He in Balloon, `(T)=(27+273)=300K` Moles of He in Balloon `= ("Weight (w)")/("Molecular Mass (M)")` Gas Constant (R ) = 0.083 bar `dm^(3)K^(-1)mol^(-1)` Molecular mass (M) of He gas = 4.0 gm `mol^(-1)` `= 4.0xx10^(-3)kg mol^(-1)` `pV = nRT=(wRT)/(M)` `therefore w=(pVM)/(RT)` `therefore w=(("1.66 bar")(4190.5xx10^(3)dm^(3))(4.0xx10^(-3)kg mol^(-1)))/(("0.083 bar dm"^(3)K^(-1)mol^(-1))(300K))` `= 1117.47 kg ~~ 1117.5 kg` Total calculation of balloon and He : Total weight = (weight of balloon) + (weight of He) `= 100 kg + 1117.5 kg` `= 1217.5 kg` Calculation of pay LOAD : Pay load `= (("Mass of air"),("displaced"))-(("Total weight of"),("He nad balloon"))` `= 5028.6 kg - 1217.5 kg` = 3811.1 kg |
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