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 air=1.2 kg m^-3and R=0.083 bar dm³K^-1mol^-1)

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Solution

The payload of the ballon = mass of the displaced air – mass of the ballon
The radius of the ballon, r = 10 m, Mass of the ballon, m = 100kg
Volume of the ballon = $\frac{4}{3} π r^{3} = \frac{4}{3} \times 3.14 \times 10^{3} = 4186.7 m^{3}$
Now volume of the displaced air = 4186.7 $m^{3}$
Given, Density of air = 1.2 kg $m^{- 3}$ ,
Therefore, the mass of the displaced air = density $\times$ volume = $4186.7 \times 1.2$ = 5024.04 kg
M, Molar mass of He is 4, Temperature, T = 27+273 K = 300K
Let w be the mass of helium gas filled into the ballon.
We know that PV = n RT
here n = $\frac{g i v e n m a s s o f s u b s t a n c e (w)}{m o l e c u l a r m a s s o f s u b s t a n c e (M)}$
so $P V = \frac{w R T}{M}$
$w = \frac{P V M}{R T}$
$w = \frac{1.66 \times 4186.7 \times 10^{3} \times 4}{0.083 \times 300}$
= 1116.4 Kg
The mass of filled balloon is the sum of the mass of the empty ballon and the mass of He. It is 100+1116.4=1216.4 kg.
Pay load = mass of displaced air − mass of balloon =5024.04−1216.44=3807.6 kg

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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 air=1.2 kg m-3 and R=0.083 bar dm3 K-1 mol-1)

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 air=1.2 kg m^-3and R=0.083 bar dm³K^-1mol^-1)