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March 24

Smallpox vaccine vs survivors

What is difference of quantity of smallpox needs to be injected in smallpox vaccinated person to make him ill and one not vaccinated but already had smallpox once and survived?

The experiment would be unethical. Even if some present-day Dr. Mengele performed the experiment, no decent journal would publish the results. --Lambiam 17:09, 24 March 2022 (UTC)[reply]

The term is Minimal infective dose, which has been worked out indirectly for a number of bacteria. Abductive (reasoning) 02:37, 26 March 2022 (UTC)[reply]

2nd law of thermodynamics & black holes

okay so i probably have a lot of incorrect assumptions but here i go. If we cant get all heat into work because it will escape, and that's because there is no perfect insulator. What if we somehow used a black hole (which to my knowledge is pretty cool at keeping heat) to trap heat into the engine? Pigeonbloodblues (talk) 23:38, 24 March 2022 (UTC)[reply]

That kind of reasoning reminds me of Will Rogers' "solution" to the U-boats problem: "Boil the ocean!" --←Baseball Bugs ^{What's up, Doc?} carrots→ 01:42, 25 March 2022 (UTC)[reply]

The Second law of thermodynamics isn't because we haven't got perfect insulators. We don't have them, but we can get arbitrarily close and even if we had perfect insulators, the second law would still stand. The second law says that any system, coming from one state and returning to the same state, can only convert heat into work if it also dumps some waste heat. How much waste heat it has to dump depends on the temperature of the input heat and the temperature of the waste heat. Black holes are fairly close to absolute zero (not exactly at absolute zero, thanks to Hawking radiation), so if your heat engine dumps its waste heat into a black hole, it can be very efficient. There are some practical problems though.

You can put a black hole in a heat engine. Now the heat engine doesn't have to dump waste heat to its surroundings, as it can be dumped into the black hole, but this also means that the heat engine doesn't return to its starting state, as the black hole has become more massive. PiusImpavidus (talk) 09:17, 25 March 2022 (UTC)[reply]

The Carnot cycle shows (as a theoretical construct) how even in an ideal situation, with perfect insulation, only part of the heat can be converted to work. It establishes a limit on the efficiency of heat engines. If we accept the mathematically formulated laws of thermodynamics as axioms, this limit follows as a mathematical theorem. --Lambiam 10:38, 25 March 2022 (UTC)[reply]

Also, it's important to note that the second law of thermodynamics is a thermodynamic concept, which means it is a state function, and does not depend on kinetics. It is path independent... Which is also to say that there are no time restrictions on it being true. A process can, locally and over a short time period, cause a decrease in entropy; universally however entropy always increases in the long term. It is true for black holes because, due to Hawking radiation, black holes do give off heat. It's extremely slow; which is to say that even the smallest known black holes today would not have had time to evaporate even a little bit had they existed since the beginning of the universe, but that's okay. They are still going to evaporate over the long scale, so the second law still applies, even if it is on stupidly long time scales (googolplexes of years, perhaps). --Jayron 32 10:59, 25 March 2022 (UTC)[reply]
Gas guzzlers waste heat all the time. It's almost never a problem, at least not to the point that we would ever need to use, much less make, black holes. Of course, whatever creations are possible can't be strawmanned if they are real and not imaginary which is why hindsight is 20/20.--Modocc (talk) 13:27, 25 March 2022 (UTC)[reply]

How much energy would be required to create such a black hole? --←Baseball Bugs ^{What's up, Doc?} carrots→ 21:47, 25 March 2022 (UTC)[reply]

See http://en.wiki.x.io/wiki/Black_hole#High-energy_collisions. "...some braneworld scenarios for example put the boundary as low as 1 TeV/c2... ...if micro black holes could be formed, it is expected that they would evaporate in about 10−25 seconds, posing no threat to the Earth." --Modocc (talk) 22:20, 25 March 2022 (UTC)[reply]

And hence being useless for the OP's scenario? --←Baseball Bugs ^{What's up, Doc?} carrots→ 22:25, 25 March 2022 (UTC)[reply]

Yes, the black holes are useless. --Modocc (talk) 22:37, 25 March 2022 (UTC)[reply]

hm, okay. thanks everyone for answering this. Pigeonbloodblues (talk) 00:36, 26 March 2022 (UTC)[reply]

To clarify, "entropy always increases in the long term" in both directions. See Wikipedia:Reference desk/Archives/Miscellaneous/2017 February 10#Understanding the solution to Loschmidt's paradox. 92.31.142.60 (talk) 15:42, 26 March 2022 (UTC)[reply]