A NASA lander on Jupiter\'s moon Europa (see above picture) zaps the surface wat

Question

A NASA lander on Jupiter's moon Europa (see above picture) zaps the surface water ice with a laser at a wavelength of 3070 nm (3.07 microns). Each photon in the beam is converted to 6.63 times 10-20 J of kinetic energy for each water molecule. In this way, a cloud of water molecule is blasted off of the cold surface. What temperature will the cloud have? Assume that each photon is turned entirely into a water molecule's kinetic energy. Approximately 10,000 molecules of water are turned into the hot cloud in Part A. If they join a cloud of 100,000 molecules of water at a temperature of 300 K, what will the temperature be of the mixed gas? Assume that the molecules at 300 K are all moving at VRMS. What will the new VRMS be the mixed gas? For the temperature of the hot cloud, you may use either the temperature you got in Part A, or 1000 K

Explanation / Answer

A)

Every molecule has kinetic energy of 6.63E-20 Joules.
But we know that every molecule's Kinetic Energy can be written as 3KT/2.
Then the temperature is T=2K.E./(3K).
Here K=Boltzmann's constant = 1.38E-23 J/K ; K.E.= Kinetic Energy ; T=temperature to be found.

Then by putting in the values T=3202.8 Kelvin

B)

10,000 molecules from part A will have KE of 6.63E-20 x 10000 = 6.63xE-16 Joules

other 100,000 molecules are at temperature 300 Kelvin,
so their KE is 100,000 x 3KT/2 = 100,000 x 3 x 1.38E-23 x 300 / 2 = 6.21E-16 Joules.
Total KE = 6.21E-16 + 6.63xE-16 = 1.28E-15 Joules for 110,000 molecules.

Then the temperature of this mixed gas will be T=2K.E./(3NK) [N=number of molecules]
=> T = 2 x 1.28E-15/(3 x 110,000 x 1.38E-23) = 563.9 Kelvin

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Problem 2 is not visible (even in the link provided).

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