A balloon of diameter 20m weighs 100 kg. Calculate it's payload if it is filled with He at 1 atm and 300K. Density of air is 1.2 kg/(m^3).

weight of ballon = 100 Kg displayed air by this ballon = density of air*volume of ballon = 1.2 kg/(m^3) * 4/3 * Pi * 10^3 = 5026.55 Kg Byuoncy Force = 5026.55 * g (upward direction) weight of gas inside ballon = molecular weight of He * (PV)/(RT) = 4*10^(-3)*(1*4/3 * Pi * 10^3)/(.082*300)Kg =681.10*10^(-3) Kg total upward force = total downside force Byuoncy Force= payload+force of weight of ballon's gas+force of weight of ballon 5026.55*g = payload(N) + 681.10*10^(-3) g + 100 g 681.10*10^(-3) g is very small quantity so we can neglect this ==> 5026.55 * g = payload(N) + 100 * g ==> payload(N) = 5026.55 * g - 100 *g =4926 * g payload(Kg)= 4926.55 Kg Ans

Weight of balloon=100kgVolume of balloon=4/3*pie r cube =4/3*22/7*(20/2*100) =the whole cube =4190*10 raise to 3 litreWeight of gas (He) in balloon=PVM/RT=1*4190*10raise to 3*4/0.082*300=68.13*10 raise to 4 gramsTherefore total weight of gas and balloon=68.13*10raise to 4+10*10raise to 4=78.13*10raise to 4 gramsWeight of air displaced=1.2*4190*10raise to 6/10raise to 3=502.8*10raise to 4gramsTherefore payload=weight of air displaced -(weight of balloon + weight of gas)Payload=502.8*10 raise to 4-78.13*10raise to 4=424.67*10raise to 4 grams