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).

Question

Philoid · Accepted Answer

Given

Radius of the balloon, r = 10 m

∴ Volume of the balloon = 4/3 x πr³

= 4/3 x 22/7 x 10³

= 4190.5 m³

Thus, the volume of the displaced air is 4190.5 m³.

Also, given that

Density of air = 1.2 kg m^-3

Then, mass of displaced air = 4190.5 × 1.2 kg

= 5028.6 kg

From ideal gas equation we know that: -

PV = nRT

⇒ PV = m/M x RT

Where, P = pressure = 1.66bar

V= volume = 4190.5 m³

R = universal gas constant = 0.083 bar dm³ K^–1 mol^–1

T= temperature = 27 + 273 = 300K

m = mass of helium inside the balloon

M = molar mass of helium = g

∴

=1117.5kg

Now, total mass of the balloon filled with helium:

= (100 +1117.5) kg

= 1217.5 kg

Hence, pay load = (5028.6 – 1217.5) kg = 3811.1 kg

∴The pay load of the balloon is 3811.1 kg.

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).