We have 6 observations :: On heating, what happens to ...
1) A metal ring,
2) a metal disk,
3) A metal disk with a hole,
4) an expandable tube (toroid) filled with gas.
5) A metal wire.
6) A tight lid of fruit-jam or pickle bottle
7) Heating then cooling, to "fit" a metal ring/annular/lid "tightly onto" something without a weld.
There must be a single logic that gives the answer to each question. Here are 3 propositions,
1) 1st one says "the molecules need space for vibrating, so they move apart to REDUCE CONGESTION". By the proposition P1, 1.1)disk expands, ring expands, the disk with hole expands, hole increases & diameter of ring also increases, as particles wouldnt come closer, increasing the congestion..... forget the expandable toroid, P1 can answer all other cases.
1.2) but it fails to explain "if the metal is heated strongly, it will melt and the molten metal would flow to reduce the hole, just like when a ring of ice is melted or a disk of ice with a hole is melted, the water would fill the hole", in what context P1 holds? That is, "if its heated", then "how much has it been heated?", no conditions are given, its airy-fairy...
2) "the molecules need space for vibrating, so they move apart IF THEY CAN, ie. if no force constraints their motion",
2.1) this explains how the lid of jam/pickle bottle becomes loose, as the lid is tightened on the bottle which is made of glass, glass is hard enough to stop metal molecules from "vibrating inward" hence they only "move outward" and loosen their grip over the bottle.
2.2) also explains "Consider two pieces of copper wire of length L, when heated say they both double in length, so both wires double in length, they both expand L/2 in both ends. total length now = 4L. Now consider a single wire of length 2L, on heating this will also double, the new length is 4L, but wait a second, if we consider this 2L wire to be made of two wires of length L fused together, we see that they both expanded on only one of their ends by L each. This is explained as the individual wires wanted to expand L/2 in both, but since they were fused at junction, "their expanding forces cancelled, and they had no choice but to expand another L/2 on the other end due to 3rd law"
2.3) According to logic L2 and 3rd law "The two imaginary wires wanted to expand by L/2, the heat caused a force delivering L/2 at each end, but when they were fused together, the 'expansive force' of wire 1 which cased it to expand was cancelled by that of wire 2 at the junction... and the reaction pair of wire 1 caused further L/2 expansion on wire 2 and the reaction pair of wire 2 did same to wire 1. But to use this logic on a disk with hole says "The hole wants to decrease as the bounday particles want to go in because the bulk, ie. the remaining body wants to expand hence the boundary should expand, but if they expand ie. if hole contracts then the shear stress will increase, its a fight between shear stress on the new boundary compared to the 'expansive force' due to heating"
2.4) so logic 2 requires "comparison" between unknown magnitudes of forces and says "if shear forces win, it expands. Or else it contracts", It doesnt "predict" answers, it says "the answer can be calculated, I cannot predict"
2.5) logic L2 correctly predicts the answer when a gas tube is inflated by heating, the hole or the inner diameter decreases as "the molecules need space for moving, not vibrating as its a gas so they move apart if they can, ie. if no force constraints their motion", the rubber or polymer of the tube or toroid doesnt return large shear stresses like the metals, thereby allowing the tube to inflate and radius to decrease.
3) Some people claim "Superimposition principle for heating" they say, mark a black circle on the metal then heat it, every theory agrees that this circle will expand, they say "Since the circle expanded, now you cut it, it will be as if hole expanded"... they say "cutting then heating is same as heating then cutting" please do not 'claim' superimposition principle. If you can explain it then only use it, because it is not very obvious like the vector's law of parallelogram addition.
So I request everyone to join the discussion to help me find an answer to the riddles of heating metals.