Is internal energy really decreasing in situation 2?

[Chestermiller]

So, internal energy would not change according to the thermodynamics equation you gave. Is that true?

Well, since the interface has no mass, it would have no internal energy (or internal energy change)..

 

[vcsharp2003]

You have two non-conservative forces in your situation 2: The applied force of 200 N and the friction force. As in section 8.5 of your link, you can start with the work-energy theorem: W_net = ΔKE. Thus,
W_app + W_fric + W_grav = ΔKE. You don't have any work done by gravity, but I included it for generality.

Note that the change in internal energy is due to the work done by friction: W_fric = -ΔU_int. The work done by gravity can be written as W_grav = -ΔU_g. So, you get

W_app = ΔKE + ΔU_g +ΔU_int

If you take the block, table, and Earth as the "system", then this says that the work done on the system by the applied force equals the change in the total energy of the system.

I just found that the link I pointed to (http://teacher.pas.rochester.edu/phy121/LectureNotes/Chapter08/Chapter8.html#Heading9) stated under section 8.6 that the system being considered should be an isolated system for W_fric = -ΔU_int else W_fric ≠-ΔU_int.

In situations 1 and 2, that would mean we take block + table + Earth as the system when applying first law of thermodynamics and in that case we could say with certainty that W_fric = -ΔU_int for block + table + Earth system. If we take only block then in realistic conditions there will be some heat transfers across the block boundary which would make the system a closed system and not an isolated system, and the same would be also true for block + table system.

 

[Chestermiller]

I just found that the link I pointed to (http://teacher.pas.rochester.edu/phy121/LectureNotes/Chapter08/Chapter8.html#Heading9) stated under section 8.6 that the system being considered should be an isolated system for W_fric = -ΔU_int else W_fric ≠-ΔU_int.

In situations 1 and 2, that would mean we take block + table + Earth as the system when applying first law of thermodynamics and in that case we could say with certainty that W_fric = -ΔU_int for block + table + Earth system. If we take only block then in realistic conditions there will be some heat transfers across the block boundary which would make the system a closed system and not an isolated system, and the same would be also true for block + table system.

This is all exactly the consequence of the frictional heat distribution equation I gave in post #29.