Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar 27°C . (Density of air = $$1.2 kg m^{–3}$$And R = $$0.083\; bar\; dm^3 K^{–1} mol^{-1}$$ ).

Asked by Pragya Singh | 1 year ago |  68

##### Solution :-

Given:

r = 10 m

Therefore, volume of the balloon

$$\dfrac{4}{3}πr^3$$

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

= 4190.5 m3 (approx.)

Therefore, the volume of the displaced air

= 4190.5 × 1.2 kg

= 5028.6 kg

Mass of helium,

$$\dfrac{ MpV }{ RT }$$

Where, M = 4 × 10-3 kg mol-1

p = 1.66 bar

V = volume of the balloon

= 4190.5 m3

R =$$0.083 0.083 \;bar\; dm^{ 3 } at \;K^{-1} mol^{-1}$$

T = 27°C = 300 K

Then,

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

= 1117.5 kg (approx.)

Now, total mass with helium,

= (100 + 1117.5) kg

= 1217.5 kg

= (5028.6 – 1217.5)

= 3811.1 kg

Therefore, the pay load of the balloon is 3811.1 kg.

Answered by Pragya Singh | 1 year ago

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