Wikipedia:Reference desk/Archives/Science/2024 July 10

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July 10

Kuiper Belt ice cube

If aliens took a spherical Kuiper belt object with the composition of Saturn's highest-water-content ring and the perihelion of Pluto, and reshaped it into a cube, how massive would it have to be for humans to detect the shape change before gravity reverted it? NeonMerlin 05:49, 10 July 2024 (UTC)

Sounds like one for Randall Munroe. 41.23.55.195 (talk) 06:04, 10 July 2024 (UTC)

There are two sensible ways how the shape could be detected: a light curve or an occultation. A light curve uses the fact that for a non-spherical shape (or a spherical shape with non-uniform albedo) the brightness varies as the object spins on its axis. Professional telescopes have other things to do than collecting light curves of KBOs, but if this thing is at least around 500 km in size, it gets into range of bigger amateur telescopes. Some of those occasionally take light curves of some KBOs. But you can't really prove a cubical shape this way, as the light curve can also be explained with a funny albedo variation.

An occultation happens when this object passes in front of a background star. Multiple observers on the ground on Earth can detect the exact times when the star disappears behind the KBO and reappears later. With enough observations, one can see the silhouette of the KBO and confirm it's cubical. Around 10 observers in the occultation path, the width of which equals the diameter of the KBO, should be enough. The KBO doesn't have to be bigger than 50 km or so. Those observers are typically amateur astronomers, whose telescopes don't need to be big enough to see the KBO; seeing the background star with sufficiently short integration time (sub-second) is enough. The difficulty is knowing the orbit of the KBO accurately enough to predict the occultation and finding enough telescopes in the occultation path. PiusImpavidus (talk) 08:51, 10 July 2024 (UTC)

Summation of alcoholic percentages

If I drank a 0,5 l bottle of 5,3% beer and another 0,5 l of a 4,9% beer, would it be correct to say that I drank 1 litre of 10,2% beer from physiological and chemical perspective? 212.180.235.46 (talk) 07:48, 10 July 2024 (UTC)

No, not from any perspective, physiological, chemical, or mathematical. You don't add the percentages, you take the mean. (5.3 + 4.9) / 2 = 5.1% by volume. AndyTheGrump (talk) 08:00, 10 July 2024 (UTC)

But, you can't exactly take the mean of the percentage-by-volume, because the mixture of ethanol and water causes a nonlinear volumetric change... For example, our article about alcohol by volume states: "The phenomenon of volume changes due to mixing dissimilar solutions..." is its partial molar property. The volume change is small, but non-zero... and it makes the ABV of the mixed drink non-equal to the arithmetic mean of its constituent ingredients. Our universe is amazingly complicated! Nimur (talk) 16:56, 10 July 2024 (UTC)

However, if the bottles are marked with their alcohol content in Alcohol units, you can add those. {The poster formerly known as 87.81.230.195} 151.227.226.178 (talk) 14:47, 10 July 2024 (UTC)

The formulas given at Standard drink § Calculation of pure alcohol mass in a serving ignore the nonlinearity, though. They are equivalent to taking the average ABV percentage (weighted by volume) and using that for the sum of the volumes.  --Lambiam 20:31, 10 July 2024 (UTC)

But is the inaccuracy significant in the context of people drinking (say) beer in pints and halves and estimating their likely degree of insobriety? Personal physiological factors are likely (in my experience as a trained beer drinker (really!)) to outweigh the physical chemistry aspects. {The poster formerly known as 87.81.230.195} 94.6.82.201 (talk) 06:56, 11 July 2024 (UTC)

I will ignore the mass/volume difference of alcohol and water. So assume that a liter is a kilogram, and alcohol by volume equals alcohol by mass.

0.5 liters of 5.3% alcohol contains 0.0265 liters of alcohol. 0.5 x 0.053 = 0.0265.

0.5 liters of 4.9% alcohol contains 0.0245 liters of alcohol. 0.5 x 0.049 = 0.0245.

So 0.0265 + 0.0245 = 0.051 liters of alcohol. You had three and a half tablespoons of alcohol.

If you drink one liter of 10.2% alcohol, you consume 0.1 liters of alcohol. Tenth of a liter is a deciliter, right? Which is twice the amount of your two pints above.

In practice, effects of alcohol intake will depend on things like how quickly you gulp the beer vs. hard spirits, how often you will need to drain the weasel, and such.

(Which is AndyTheGrump correctly said above; just showing the math.) 85.76.166.151 (talk) 16:34, 11 July 2024 (UTC)