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
B
15 km
C
12.38 km
D
8 km

Solution

## The correct option is C $$12.38$$ kmMolecular mass of Nitrogen molecule=$$14$$ g/molAs nitrogen exists as $${N}_{2}$$=28 g/mol=$$0.028$$ kg/molAlso 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 KAlso 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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