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Kinetic Theory — Physics STD 11 Science — Question

Gujarat 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 $5.34 \times 10^{-26}kg$ (Boltzmann constant $k = 1.38 \times 10^{-23} Joule/K)$.
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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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