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Home » Payload is characterized as the contrast between the mass of uprooted air and the mass of the inflatable. Work out the payload when an inflatable of sweep 10 m, mass 100 kg is loaded up with helium at 1.66 bar at 27°C.    
Payload is characterized as the contrast between the mass of uprooted air and the mass of the inflatable. Work out the payload when an inflatable of sweep 10 m, mass 100 kg is loaded up with helium at 1.66 bar at 27°C.

    \[~\left( Thickness\text{ }of\text{ }air\text{ }=\text{ }1.2\text{ }kg\text{ }m3\text{ }and\text{ }R\text{ }=\text{ }0.083\text{ }bar\text{ }dm3\text{ }K1\text{ }mol1 \right)\]

CBSE | Chemistry | Class 11 | Exercise 1 | NCERT | States of Matter
Payload is characterized as the contrast between the mass of uprooted air and the mass of the inflatable. Work out the payload when an inflatable of sweep 10 m, mass 100 kg is loaded up with helium at 1.66 bar at 27°C.

    \[~\left( Thickness\text{ }of\text{ }air\text{ }=\text{ }1.2\text{ }kg\text{ }m3\text{ }and\text{ }R\text{ }=\text{ }0.083\text{ }bar\text{ }dm3\text{ }K1\text{ }mol1 \right)\]

solution:

 

Given:

 

    \[r\text{ }=\text{ }10\text{ }m\]

Accordingly, volume of the inflatable

 

    \[\begin{array}{*{35}{l}} =4/3\text{ }\pi r{}^\text{3} \\ ~ \\ =4/3\text{ }\times \text{ }22/7\text{ }\times 10{}^\text{3} \\ ~ \\ =\text{ }4190.5\text{ }m3\text{ }\left( approx. \right) \\ \end{array}\]

Accordingly, the volume of the uprooted air

 

    \[\begin{array}{*{35}{l}} =\text{ }4190.5\text{ }\times \text{ }1.2\text{ }kg \\ ~ \\ =\text{ }5028.6\text{ }kg \\ \end{array}\]

Mass of helium,

 

    \[\begin{array}{*{35}{l}} =Mpv/RT \\ ~ \\ Where,\text{ }M\text{ }=\text{ }4\text{ }\times \text{ }10-3\text{ }kg\text{ }mol-1 \\ ~ \\ p\text{ }=\text{ }1.66\text{ }bar \\ ~ \\ V\text{ }=\text{ }volume\text{ }of\text{ }the\text{ }inflatable \\ ~ \\ =\text{ }4190.5\text{ }m3 \\ ~ \\ R=0.083\text{ }0.083\text{ }bar\text{ }dm{}^\text{3}\text{ }at\text{ }k{}^\text{1}mol{}^\text{1} \\ ~ \\ T=\text{ }27{}^\circ C\text{ }=\text{ }300K \\ \end{array}\]

then, at that point,

 

    \[\begin{array}{*{35}{l}} m=4\times 10{}^\text{3}\text{ }\times \text{ }1.66\times \text{ }4190.5\text{ }\times \text{ }10{}^\text{3}/0.083\text{ }\times 300 \\ ~ \\ =\text{ }1117.5\text{ }kg\text{ }\left( approx. \right) \\ \end{array}\]

Presently, complete mass with helium,

 

    \[\begin{array}{*{35}{l}} =\text{ }\left( 100\text{ }+\text{ }1117.5 \right)\text{ }kg \\ ~ \\ =\text{ }1217.5\text{ }kg \\ \end{array}\]

Accordingly, pay load,

 

    \[\begin{array}{*{35}{l}} =\text{ }\left( 5028.6\text{ }\text{ }1217.5 \right) \\ ~ \\ =\text{ }3811.1\text{ }kg \\ \end{array}\]

Accordingly, the compensation heap of the inflatable is 3811.1 kg.

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