(a) If it has enough kinetic energy, a molecule at the surface of the Earth can
ID: 1397976 • Letter: #
Question
(a) If it has enough kinetic energy, a molecule at the surface of the Earth can "escape the Earth's gravitation", in the sense that it can continue to move away from the Earth forever. Using the principle of conservation of energy, show that the minimum translation kinetic energy needed for "escape" is mgRE, where m is the mass of the molecule, g is the free-fall acceleration at the surface of the Earth, and RE is the radius of the Earth. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Calculate the temperature for which the minimum escape translation kinetic energy is 5 times the average translation kinetic energy of a nitrogen molecule.
Explanation / Answer
a)
Apply Energy conservation
Initial mechanical energy = final mechanical energy
PE1 + KE1 = PE2 + KE2
-G*Me*m/Re + KE1 = 0 + 0
KE1 = G*Me*m/Re
= (G*Me/Re^2)*m*Re
= g*m*Re (since, g = G*Me/re^2)
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