The picture to the right shows the potential energy between two xenon (Xe) atoms

Question

The picture to the right shows the potential energy between two xenon (Xe) atoms (Xe is inert like helium, neon, and argon). Solid Xe melts at 161 K and liquid Xe boils at 165 K. Suppose we put a one mole piece of solid Xe at T = loo K into a large container, seal it so the Xe cannot escape, and place the container in the room (T room = 300 K) and wait for thermal equilibrium between the Xe and the room. Explain how you would estimate the amount of heat that was transferred by the air in the room to the Xe in order to bring them to equilibrium at 300 K. You don?t need to do the final calculation but you do need to give your estimated values for all the physical quantities you need and explain how those physical quantities are to be used in finding the total heat transferred.

Explanation / Answer

We know that the distance between Xe atoms will be increased due the heat transfer to the Xe. If the amount of heat transfered is enough, Xe will be first melted and then vaporized. As Xe reachs themal equilibrium with the room we know that, in fact, it will be vaporized. You need to know the mean distance between Xe atoms when it is in solid, liquid and gas phase, then you can read from the figure the energy per atom required for the Xe to change its phase (if r1 is the mean distance in solid phase and r2 is that in liquid phase then PE2-PE1 is the energy required to melt the Xe. The same for boiling process). Since you know how many atoms there are in a mol, you can estimate the amount of heat transfered.

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