KVPY Sample Paper KVPY Stream-SX Model Paper-16

Let's assume that our atmosphere consists only of nitrogen gas with molecular mass is nearly \[4.5\times {{10}^{-26}}\,kg.\] If mean temperature of earth is taken as \[27{}^\circ C,\] then height of our atmosphere is nearly

A) 15 km

B) 28 km

C) 40 km

D) 12 km

Correct Answer: B

Solution :

Kinetic energy of a molecule at temperature T is \[KE=\frac{1}{2}mv_{rms}^{2}=\frac{3}{2}{{K}_{B}}T\]

The molecule can rises until whole of its kinetic energy is changed to potential energy.

Let this height is h. Then, \[mgh=\frac{3}{2}{{K}_{B}}T\]

\[\Rightarrow \]\[h=\frac{3{{K}_{B}}T}{2mg}=\frac{3\times 1.38\times {{10}^{-\,23}}\times 300}{2\times 4.5\times {{10}^{-\,26}}\times 10}\]

\[=27.6\,km\approx 28\,km\]