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Question

A balloon of diameter $$21\:meter$$ weight $$100 kg$$. Calculate its pay-load, if it is filled with $$He$$ at $$1.0\: atm$$ and $$27 ^\circ C$$. Density of air is $$1.2\: kg m^{-3}$$. (Given: $$R = 0.082\: L\: atm\: K^{-1} mol^{-1}$$)



A
4952.42 kg
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B
4932.42 kg
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C
493.242 kg
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D
None of these
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Solution

The correct option is B 4932.42 kg
Weight of balloon$$=100\:kg=10 \times 10^{4}\:g$$.

Volume of balloon$$= \displaystyle \frac{4}{3} \pi r^{3}$$.

$$= \displaystyle \frac{4}{3} \times  \displaystyle \frac{22}{7} \times ( \displaystyle \frac{21}{2} )^{3}$$

$$=4851 m^{3}=4851 \times 10^{3} \:L$$

Weight of gas $$(He)$$ in balloon$$= \displaystyle \frac{PVM}{RT}$$

$$= \displaystyle \frac{1 \times 4851 \times 10^{3} \times 4}{0.082 \times 300} =78.878 \times 10^{4}$$


$$\therefore$$ Total weight of gas and balloon 
$$=78.878 \times 10^{4}+10 \times 10^{4}$$

$$=88.878 \times 10^{4}g$$ or $$888.78\:kg$$

Weight of air displaced$$=1.2 \times 4851$$
$$=5821.2\:kg$$

$$\therefore$$ Pay load=wt. of air displaced-wt. of (balloon+gas)
$$\therefore$$ Pay load$$=5821.2-888.78=4932.42\:kg$$.

Chemistry

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