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

Welcome to the NCERT Solutions for Class 11th Chemistry - Chapter States of Matter. This page offers a step-by-step solution to the specific question from Exercise 1, Question 16: pay load is defined as the difference between the....
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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