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Question

If nitrogen gas molecule goes straight up with its rms speed at $$0^o$$C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of:


A
18 km
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B
15 km
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C
12.38 km
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D
8 km
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Solution

The correct option is C $$12.38$$ km
Molecular mass of Nitrogen molecule=$$14$$ g/mol
As nitrogen exists as $${N}_{2}$$=28 g/mol=$$0.028$$ kg/mol
Also we know $${ v }_{ rms }=\sqrt { \dfrac { 3RT }{ M }  } $$  where R= gas constant=8.31 bar/(K mol)=8.31$$\times{10}^{5}$$ Pa/(K mol)
T= temperature=$${0}^{0}$$ C=273 K
Also height $$=\dfrac{{V}^{2}_{rms}}{2g}$$

$$=\dfrac { 3\times 8.31\times { 10 }^{ 5 }\times 273 }{ 2\times 9.81\times 0.028 } \\ =12388\quad m=12.38\quad km$$

Physics

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