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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.

5.16     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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The payload can be defined as:

(Mass of the displaced air - Mass of the balloon)

Given the radius of the balloon, r = 10 m.

Mass of the balloon, m = 100 kg.

Therefore, the volume of the balloon will be:

$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\times\frac{22}{7}\times10^3 = 4190.5\ m^3$

Now, the volume of the air displaced:

$V_{d} = 4190.5\ m^3$

The mass of the air displaced :

$m_{d} = density \times V_{d} = 1.2kgm^{-3}\times 4190.5\ m^3$

$= 5028.6kg$

Let $W$ be the mass of helium gas filled into the balloon, then

$PV=(\frac{W}{m})rt$

Or, $W = \frac{PVM}{RT}$

$= \frac{1.66\times4190.5\times10^3\times4}{0.083\times300} = 1117\ kg$ approximately.

The balloon is filled with He with total mass of $= 1117+100= 1217kg$

$\therefore$ The payload of the balloon will be:

$= 5028.6 -1217 = 3811.6kg$

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