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When a block slips on a rough surface, the work done by the surface on block is negative, while the work done by block on surface is zero. While writing the first law of thermodynamics, I have considered the block as my system and surface as the surroundings.

Now here's the poblem: by the first law if thermodynamics, we have:

$$\Delta U=Q+W$$

The equation works for the block as a system ($Q=0$ and its energy goes down by $-W$), but does not seem to work-out for the table because positive work was done on it.

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    $\begingroup$ There is no convention, the work on a system has its own sign. The fact that sometimes the work on the system and the one on the external system are equal up to the sign is not matter of convention, when it is true. Here it is false. The correct equation is the second one, but the LHS should also include the kinetic energy of the block. $\endgroup$
    – Valter Moretti
    Commented Sep 4, 2021 at 6:50
  • $\begingroup$ Possible duplicate by OP: physics.stackexchange.com/q/664079/2451 $\endgroup$
    – Qmechanic ♦
    Commented Sep 4, 2021 at 7:55
  • $\begingroup$ Hi Anonymous. Welcome to Phys.SE. Please don't repost a closed question in a new entry. Instead, you are supposed to edit the original question within the original entry. $\endgroup$
    – Qmechanic ♦
    Commented Sep 4, 2021 at 7:56
  • $\begingroup$ You asked two questions actually. The sign convention took most of the space and was repeat. I answered both though so youre good $\endgroup$
    – Al Brown
    Commented Sep 4, 2021 at 8:11
  • $\begingroup$ In this version you accidentally had one if them say delta Un= Q, without a W. Thats why originally had thst in my answer $\endgroup$
    – Al Brown
    Commented Sep 4, 2021 at 8:20

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Good question.

The first law with those terms is just a subset (special case) of the law of conservation of energy (which technically is a special case of the law of conservation of energy-matter). If we assume matter is not being converted to or from energy, then energy is conserved, and matter is conserved.

Some laws can be broken by introducing things that aren’t included (things assumed during the law’s statement to be held constant, or even stuff that hadn’t been discovered when the law was first formulated). Also, the sign for work is sometimes a convention. Usually we have to just work-out which way the energy flows.

In the case of the block, it is losing kinetic energy and it is breaking bonds in the matter comprising the surface, bonds that hold negative energy, and also heating-up both block and surface. Like bending a bar takes work, and so it puts energy into the bar; the bar has more bond energy (sometimes called cold working) than before it was bent.

We tend to think of friction energy as just disappearing, but it does go somewhere, usually in bending or breaking and/or generating heat.

Same logic applies to conservation of momentum. The block loses momentum and it may seem like it disappeared, but the earth/table/block system still has the same total momentum. The earth (excluding the block) now has a drop more rotation and/or translation after stopping the block.

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