Class 11 Chemistry - Chapter States of Matter NCERT Solutions | Pay load is defined as the difference be

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Question 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 dm3 K–1 mol–1).

Answer

Payload of the ballon  = mass of the displaced air – mass of the ballon

Radius of the ballon, r  = 10 m

Mass of the ballon, m = 100kg

Therefore volume of the ballon = 4/3πr3 = 4/3 x 22/7 x (10)3 = 4190.5 m3

Now volume of the displaced air = 4190.5 m3

Given,

Density of air = 1.2 kg m–3

Therefore, the mass of the displaced air

= 4190.5 x 1.2  = 5028.6 kg

Let w be the mass of helium gas filled into the ballon,then

PV = (w/m)RT

OR w = PVM/RT

= (1.66 X 4190.5 X 103 X 4) / (0.083 X 300)

 = 1117 kg (approx)

Total mass of the balloon filled with He  = 1117 + 100 = 1217 kg

Therefore payload of the balloon  = 5028.6 – 1217 = 3811.6 kg

Hence, the pay load of the balloon is 3811.6 kg.

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