An oxygen molecule falls in a vacuum. From what height must it fall so that its

Question

An oxygen molecule falls in a vacuum. From what height must it fall so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 800 K? The mass of one O_2 molecule is 5.312 times 10^-26 kg. In the summer of 2010 a huge piece of ice roughly four times the size of Manhattan and 500 m thick caved off the Greenland mainland. How much heat would be required to melt this iceberg (assumed to be at 0 degree C) into liquid water at 0 degree C? The annual U.S. energy consumption is 1.2 times 10^20 J. If all the U.S.'s energy was used to melt the ice, how many days would it take to do so?

Explanation / Answer

1) Here, let the height it falls is h

Now, for the kinetic energy at the bottom = decrease in potential energy

for the molecule , Kinetic energy at temperature T , = 2.5 * k * T

m * g * h = 5/2 * k * T

5.213 * 10^-26 * 9.81 * h = 5/2 * 1.38 *10^-23 * (800)

solving for h

h = 53970 m

the O2 molecule shall fall 53970 m for the same kinetic energy

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