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Kinetic Theory — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsKinetic Theory3 Marks
Question
At what temperature will the average velocity of oxygen molecules be sufficient so as to escape from the earth? Escape velocity from the earth is 11.0km/sec and the mass of one molecule of oxygen is 5.34 × 10-26kg (Boltzmann constant k = 1.38 × 10-23 Joule/K).
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Answer

We know $\frac{1}2{}\text{mv}^2=\frac{3}{2}\text{kT}$ or $\text{T}=\frac{\text{mv}^2}{3\text{k}}$

Here, $\text{m}=5.34\times10^{-26}\text{kg}$

$\text{v}=11.0\text{km/s}=11\times10^3\text{ms}^{-1}$

$\text{k}=1.38\times10^{-23}\text{Jk}^{-1}$

$\therefore\text{T}=\frac{5.34\times10^{-26}\times(11\times10^3)^2}{3\times1.38\times10^{-23}}$

$=1.56\times10^5\text{K}$

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