Question

Question 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 dm3 K–1 mol–1).

Class XI States of Matter Page 153

Answer 1

concept :- To calculate the pay load, we have to require mass of displaced air , mass of balloon with He .
mass of displaced air = V × d
where, V is volume and d is density.
volume of balloon (V) = 4/3πr³
so, mass of air displaced = 4/3πr³.d

then, calculate mass of He filled in the balloon by using , PV = nRT
and now, pay load = mass of displaced air - mass of Balloon with He.
$here, r_{balloon}=10m\\\\V=\frac{4}{3}\pi.r^3\\\\=\frac{4}{3}\times\:\frac{22}{7}\times(10)^3=4190.476m^3\\\\V_{balloon}=V_{displaced\: air(by\: balloon}$
so, mass of displaced air (m) = volume of displaced air × density
= 4190.576 × 1.2 = 5028.57 Kg


now, mass of He fill in balloon ( M):
PV = nRT
PV = mRT/M [ here, m is mass of He filled and M is molar mass of He ]
m = PVM/RT
= 1.66 × 4190.476 × 4 × 10^-3 /0.083 × 300
= 1117.46 Kg

now, total mass filled in balloon = mass of balloon + mass of He filled
= 100 Kg + 1117.46 Kg = 1217.46 Kg

now, pay load = mass of displaced air - mass of balloon with He
= 5028.57 - 1217.46 = 3811.11 Kg