Question

A balloon of diameter 21 metre weight 100 kg.
Calculate its pay-load, if it is filled with helium (He) at 1.0 atm and 27° C. Density of air is 1.2 $kg{m}^{-3}$.

(Given: R = $R=0.082\:L\:atm\:{K}^{-1}{mol}^{-1}$)


(a)4952.42 Kg

(b) 4932.42 Kg

(c) 493.242 Kg

(d) None of these

✔️✔️Proper solution needed✔️✔️​

Answer 1

Solution:-

Given:-

weight of balloon = 100 kg

Weight of Balloon = 10 × 10⁴ g.

volume of balloons = 4/3πr³

=> Vol. of Balloon= 4/3 × 22/7 × (20/2× 100)³

=> Vol. of Balloon = 4190× 10³ litre

=> weight of gas ( Helium) in balloon = Pvm / RT

=> Weight of Helium in Balloon= 1 × 4190 * 10³×4 /0.0821× 300

=> Weightof Helium in Balloon= 68.13 × 10⁴g.

Now,

Total weight of balloon = 68.13 × 10⁴ + 10× 10⁴

= 78.13× 10⁴g

weight of displaced air = 1.2 × 4190 × 106/10³

=> Weight of Displaced Air = 502.8× 10⁴g

=>Pay load = (weight of air displaced) - ( weight of balloon + weight of gas )

=> Pay load = 502× 10⁴ = 424.67 × 10⁴g.

Hence ,

Correct Option is D. None of These.