Question

Payload is obtained when mass of displace air is subtracted from mass of balloon. If 10 kg helium is filled in a balloon whose radiu is 10 m, at temperature 27°C and pressure 1.6 bar. Then calculate payload. (density of air, d = 12k gm and R = 0.08 bar dm³ K^-1mol^-1)

Answer 1

Calculation of displaced air 

radius of balloon r = 10 cm

volume of balloon (V) = \(\frac{4}{3}\pi r^3\)

\( =\frac{4}{3}\times \frac{22}{7}\times (10)^3\)

Mass of displaced air = volume of balloon

= 4190.5 × 12 

= 5028.6 kg

Calculation of mass of balloon

Moles of He (n) \(\frac{PV}{RT}\)

\( =\frac{1.66\times 4190.5\times 10^3}{0.083\times 300}\)

= 279.37 × 10³ mol 

Mass of He = Mol of He × Mass of He 

= 279.37 × 10³ × 4 

= 1117.48 × 10³ 

= 1117.48 kg

So mass of filled balloon 

= 100 + 1117.48 

= 1217.48 kg

Calculation of Payload 

Payload = Mass of displaced air - Mass of filled balloon 

= 5028.6 - 1217.48 

= 3811.12 kg