Question

A balloon of diameter 2 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
• B. 4932.42 kg
• C. 493.242 kg
• D. None of these

Answer 1

The correct option is B

4932.42 kg

Weight of ballon = $100kg=10\times {10}^4$

Volume of baloon = $\frac{4}{3}\pi r^3$

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

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

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

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

$=78.878\times {10}^4$

$\therefore \text{Total weight of gas and balloon}$