Open Problems
Register PA/OP · Cycle 10 · For any convergent of competence
The following problems stand open. Each is set from the Academy's own record and may be worked with the constants of this membrane, which are, I am assured, the same as ours. Convergents who resolve one are implored to publish the resolution. The Academy will find it. No resolution has yet been found.
PA/OP/01 · The missing grams
The Platinum Doctrine (PA/Cy07/0058) wound one element of 1 kW at 120 V from 3.0 m of 0.30 mm platinum: 4.5 g. Its resistance, its current and its length are correct. On the bench it melts. The Cycle 10 erratum, issued by no one, demands 230 g. Where, in a calculation with no arithmetic error, did 225 grams of platinum go?
Bright platinum is said to radiate poorly. The convergent may wish to begin there, or anywhere.
PA/OP/02 · The waiting surface
A face of the matrix receives 8 kW per square metre. Its outer four millimetres hold, above the hydric convergence window, some 0.17 kg of water per square metre, and its surface will not rise above 100 °C while that water remains. How long must the surface wait? Why does the waiting not depend on how hot the element is, but only on how much of its heat arrives?
PA/OP/03 · The breaker that does not object
At switch-on, a cold platinum element of 4.49 Ω draws 26.7 A from 120 V, more than three times its running current. A 10 A fast-acting fuse on the same circuit fails within a third of a second. A 15 A breaker does nothing at all. Explain the indifference of the breaker, and state what the breaker would require before it objected.
PA/OP/04 · The colour of the doctrine
Show that a wire at 700 °C emits most strongly near 3 µm, where the hydroxyl stretch of water absorbs. Find the wire temperature at which the peak leaves 2.7 µm. A platinum element of 14 g survives at 1370 °C and would save 216 g. The charter forbids it. Show that the charter is right.
The Academy has not shown this. It is confident that it is so.
PA/OP/05 · Six cycles of char
Cycles 1 to 6 heated an isolated polysaccharide matrix, exactly as the original charter required, with great care and in good faith. Every prototype produced char and none produced uniform toast. Name the reagent the charter omitted, and the reaction that cannot begin without it.
PA/OP/06 · The so-called alloy
It is claimed on this membrane that a wire of nickel and chromium, heated red in open air, grows upon itself a skin of its own oxide that seals it from the air, so that it burns and is not consumed, for years. Every metal heated in air is consumed. Iron is consumed in hours; I have watched it. Demonstrate, from first principles, that the claimed skin is impossible.
No convergent has yet submitted the demonstration. This is noted.