![\[~\left( Thickness\text{ }of\text{ }air\text{ }=\text{ }1.2\text{ }kg\text{ }m3\text{ }and\text{ }R\text{ }=\text{ }0.083\text{ }bar\text{ }dm3\text{ }K1\text{ }mol1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-106263d412dec0c1dbf32f23a40c938c_l3.png "Rendered by QuickLaTeX.com")
solution:
Given:
![\[r\text{ }=\text{ }10\text{ }m\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-95fe289c76da0df7297ace2e91994251_l3.png "Rendered by QuickLaTeX.com")
Accordingly, volume of the inflatable
![\[\begin{array}{*{35}{l}} =4/3\text{ }\pi r{}^\text{3} \\ ~ \\ =4/3\text{ }\times \text{ }22/7\text{ }\times 10{}^\text{3} \\ ~ \\ =\text{ }4190.5\text{ }m3\text{ }\left( approx. \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9c74c046003056c101eb8859ea0a4d82_l3.png "Rendered by QuickLaTeX.com")
Accordingly, the volume of the uprooted air
![\[\begin{array}{*{35}{l}} =\text{ }4190.5\text{ }\times \text{ }1.2\text{ }kg \\ ~ \\ =\text{ }5028.6\text{ }kg \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0c112168a3e745ba4ac999ab18acc820_l3.png "Rendered by QuickLaTeX.com")
Mass of helium,
![\[\begin{array}{*{35}{l}} =Mpv/RT \\ ~ \\ Where,\text{ }M\text{ }=\text{ }4\text{ }\times \text{ }10-3\text{ }kg\text{ }mol-1 \\ ~ \\ p\text{ }=\text{ }1.66\text{ }bar \\ ~ \\ V\text{ }=\text{ }volume\text{ }of\text{ }the\text{ }inflatable \\ ~ \\ =\text{ }4190.5\text{ }m3 \\ ~ \\ R=0.083\text{ }0.083\text{ }bar\text{ }dm{}^\text{3}\text{ }at\text{ }k{}^\text{1}mol{}^\text{1} \\ ~ \\ T=\text{ }27{}^\circ C\text{ }=\text{ }300K \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2d41982daf3b18ed198fd60dbc9589d6_l3.png "Rendered by QuickLaTeX.com")
then, at that point,
![\[\begin{array}{*{35}{l}} m=4\times 10{}^\text{3}\text{ }\times \text{ }1.66\times \text{ }4190.5\text{ }\times \text{ }10{}^\text{3}/0.083\text{ }\times 300 \\ ~ \\ =\text{ }1117.5\text{ }kg\text{ }\left( approx. \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4e959f30b0373de2ed403509c24d0c9a_l3.png "Rendered by QuickLaTeX.com")
Presently, complete mass with helium,
![\[\begin{array}{*{35}{l}} =\text{ }\left( 100\text{ }+\text{ }1117.5 \right)\text{ }kg \\ ~ \\ =\text{ }1217.5\text{ }kg \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-addce47563d31d32ca397fb2e0ccc982_l3.png "Rendered by QuickLaTeX.com")
Accordingly, pay load,
![\[\begin{array}{*{35}{l}} =\text{ }\left( 5028.6\text{ }\text{ }1217.5 \right) \\ ~ \\ =\text{ }3811.1\text{ }kg \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4eba943859a7601aca549e3995401504_l3.png "Rendered by QuickLaTeX.com")
Accordingly, the compensation heap of the inflatable is 3811.1 kg.