Question

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 mand R=0.083 bar dm³ K-¹ mol-¹)​

Answer 1

➮ AnSwer :-

The pay load of the balloon is 3811.1kg

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Explaination :-

Given,

Radius of the balloon, r = 10m

we have to find,

$\sf volume \: of \: the \: ballon = \dfrac{4}{3} \pi {r}^{3}$

$\sf = \dfrac{4}{3} \times \dfrac{22}{7} \times {10}^{3}$

$\sf = 4190.5 {m}^{3} \: \: \: \: \: (approx)$

Thus, the volume of the displaced air is 4190.5m³

Now,

Density of air = 1.2 kg$^{-1}$ [Given]

Then, mass of displaced air = 4190.5 × 1.2 kg = 5028.6kg.

Now, mass of helium (m) inside the balloon is given by,

$\sf m = \dfrac{MpV}{RT}$

Here,

• M = 4 × 10$^{-3}$kg mol$^{-1}$
• p = 1.66 bar
• V = Volume of the balloon= 4190.5m³
• R = 0.083 bar dm3 K$^{-1}$mol$^{-1}$
• T = 27°C = 300K

Then,

$\sf m = \dfrac{4 \times {10}^{ - 3} \times 1.66 \times 4190.5 \times {10}^{3} }{0.083 \times 300}$

$\sf = 1117.5 \: kg \: \: \: \: (approx)$

Now, Total mass of the balloon filled with helium

= (199 + 1117.5) kg = 1217.5 kg

Hence, pay load = mass of displaced air - Total mass of the balloon filled with helium

= (5028.6 - 1217.5) kg = 3811.1 kg

Thus, the pay load of the balloon is 3811.1kg