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JEE Main 2014 (19 Apr, Shift 1) · Pressure & Kinetic Energy of a Gas

Pressure & Kinetic Energy of a Gas question from JEE Main 2014 (19 Apr, Shift 1)

Q37JEE Main 2014 · 19 APR · SHIFT 1Medium

Pressure & Kinetic Energy of a Gas

A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0oC. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (kB is Boltzmann constant)

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Answer: (d)

KE at $0^\circ$ C ( $T = 273$ K) $= \frac{3}{2}k_B(273)$ .
All of this KE becomes potential energy at the top: $Mgh = \frac{3}{2}k_B \times 273$
$h = \frac{819k_B}{2Mg}$
So the answer is (d) $\frac{819k_B}{2Mg}$ .

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