Wikipedia:Reference desk/Archives/Science/2020 March 31

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March 31

intriguing experiment in Thermodynamics

A blech is destined for preserving the heat of cooked food during Shabbat, in accordance with jewish religious law. In an experiment performed is Jerusalem. a small towel has been put on on one blech, and an identical one on another blech, which was covered by an Aluminium foil before. The resulting temperatures were different significantly - so much so, that the 2nd towel has been scortched, and even a light wind coming from an open window caused the burst of a flame. Surely, there must a reason to this temperature difference, even though it's 'only' a thin metallic coat over a metallic plate that makes the difference. I'll glad to hear your opinion or hypothesis regarding this phenomenon. בנצי (talk) 22:36, 31 March 2020 (UTC)

Just to clarify, it was the blech that was covered by foil in the second case, not the towel itself? And it was just a thin layer of foil that did not extend beyond the blech itself (to change the overall surface area or air circulation)? DMacks (talk) 03:28, 1 April 2020 (UTC)

• The "obvious" thing (well, obvious for someone with a PhD in the domain, I guess) would be a difference in thermal radiation. I highly recommend reading the lede of our article emissivity, which is IMO really well-written.

Qualitatively, aluminium foil emits a low amount of radiation (our article says emissivity is 3%; unsourced but seems plausible to me), and hence cools down more slowly. More precisely, if you assume the whole burner-blech-foil system reaches a steady state, the outbound heat flux must compensate the heat of combustion of the burner; to have the same outbound radiative heat flux, a lower-emissivity surface will need to be hotter.

Quantitatively, if we assume that the loss of heat by convection is negligible (dubious, but will do as a first-approximation), and that the emissivity does not depend much on temperature in the relevant range (source: trust me, or look for emission spectra and do nasty integrals weighted by Planck's law at temperatures between ambient and 500°C; the materials we are dealing with are grey bodies in the relevant ranges), we have a similar outbound heat flux in both situations when $\epsilon _{foil}T_{foil}^{4}=\epsilon _{unfoiled}T_{unfoiled}^{4}$ (see Stefan-Boltzmann law, where absolute temperatures (i.e. in Kelvin) are used; the constant σ cancels out in both sides). Assuming $\epsilon _{foil}=0.03$ (from Emissivity#Emissivities_of_common_surfaces), $\epsilon _{unfoiled}=0.9$ (a fairly typical value for most ceramics, non-metal construction materials etc. - impossible to be precise without knowing the exact material of the blech), and $T_{unfoiled}=70^{\circ }C\approx 350K$ (might be off by 20°C or more but it would not change much), one finds $T_{foiled}\approx 820K\approx 540^{\circ }C$ which is extremely hot. That is due to a very high ratio $\epsilon _{unfoiled}/\epsilon _{foil}$ of about 30 ; if we take 10 instead (for instance $\epsilon _{unfoiled}=0.8$, $\epsilon _{foil}=0.08$, in the realm of the plausible) we get 350°C, still very hot.

Tigraan^{Click here to contact me} 09:07, 1 April 2020 (UTC)

I opine that the more plausible "obvious" explanation is that there is some kind of misreporting about how perfectly scientifically this so-called control-experiment demonstrates the desired result. Whether this is a case of honestly-naïve observer bias or outright religiously-motivated fraudulent pseudoscience - perhaps I might be so bold as to lob an accusation that no such experiment was even performed! - the probable explanation is that there is no such effect: the natural laws that govern thermal behaviors are statistically unlikely to take a day of rest to respectfully honor any particular human notion of piety. Regarding the so-called experiment ... may I rhetorically entreat "citation needed"? I'm not so interested in actually reading about it - more so, I'm just encouraging our readers to consider whether they should ever put stock on anecdotal reports about miraculous occurrences, religious or otherwise. Science is built on a foundation of healthy philosophical skepticism; most of the time, the simple explanation doesn't need much detailed analysis beyond a broad recognizance of the generally-faulty ability of humans to report the things that they think they know to be truth. Nimur (talk) 12:32, 1 April 2020 (UTC)

@Nimur: I do not see the OP making any religious interpretation of their claimed observations (they do say in Jerusalem and presumably it was on a day of Shabbat, but I doubt they think the result would be different on another day or in another place). They claim the "experiment" was well-controlled or novel either; I would presume that "experiment" was intended as a colloquial term. Finally, I see no indication that the OP is a refdesk troll that should not be fed.

Regardless of whether the OP did indeed make the observations they claim, the numbers I plugged suggest that an aluminium-foiled blech can indeed go very hot (be it used on Shabbat or any other day). I would even go so far as to say that if the question had been "should I cover a blech with aluminium foil for (whatever reason)", I would have made the same calculations and warned against the danger of so doing because of thermal considerations. If you think the calculation result is erroneous by a large margin, please point out the error either in the reasoning or in the initial assumptions.

By the way, I think the whole Shabbat interdicts are inane nonsense, between "the Torah says no fire, so no electricity either because electricity is fire" and "actually fire/electricity is OK but only if you do not touch the controls". That mention should have no impact either way on the credibility of my calculations, but it might cut short some drama. Tigraan^{Click here to contact me} 13:38, 2 April 2020 (UTC)

For an overview of the positions and arguments, see Electricity on Shabbat.  --Lambiam 08:22, 4 April 2020 (UTC)