Rayleigh 1902 · the USDA table, 1992 · Copenhagen 2016 and 2017

The Clock Is the Wrong Instrument

The table everyone quotes says wine simmered for two and a half hours keeps 5% of its alcohol. Its only axis is time. In 2017 a Copenhagen group showed that what decides it is not the clock but how much of the pot has boiled away, and the law they found is the one Lord Rayleigh wrote down for a still in 1902. Here are Rayleigh's own alcohol measurements run through his own equation, with nothing fitted. They predict the exponent the Copenhagen group measured, rewrite the famous table as weights, work backwards from a 2016 braise nobody weighed, and turn a kitchen scale into an alcohol meter.

The table everyone quotes

Search for whether alcohol cooks off and you will be shown, within a line or two, a list of percentages. It comes from the United States Department of Agriculture's Table of Nutrient Retention Factors, the reference food databases use to estimate what survives cooking. Release 6 (2007) prints ten rows for alcohol, food group 14, with these descriptions and factors:

The USDA's notes say where these came from: “An analytical alcohol retention study was conducted to investigate the extent of alcohol lost in food preparation. Methods tested were: no heat application, alcohol added to a boiling liquid, flaming, and baking for various lengths of time.” For details it refers to Augustin and colleagues, “Alcohol retention in food preparation”, in the Journal of the American Dietetic Association for April 1992.

The 1992 paper is behind a paywall we could not get through, and its PubMed record carries no abstract, so this page has not read it. What we know of its dishes comes from a 2016 paper that did: a “Pot roast Milano” simmered with wine for two and a half hours, an “orange chicken burgundy” simmered in wine for ten minutes, scalloped oysters, a Grand Marnier sauce, flamed cherries jubilee and a brandy pie. The same paper reports that Augustin's group “suggest that a larger diameter in the pot leads to a sharper decrease in concentration based on their results although this has not been investigated thoroughly.” Hold on to that sentence.

One small thing about the table itself, which anyone can check. The printed PDF carries the 2.5-hour factor, 5. The same release's machine-readable file (retn06.txt), the form in which a database would ingest it, lists an alcohol factor for every one of its 270 food codes except one, and the one is code 5009, the 2.5-hour row. The table's lowest figure is the one number missing from its data file.

Now look at what the table is a function of. Minutes. It does not say how wide the pan was, how hard it boiled, whether it had a lid, or how much liquid there was. Those are not details. They are the whole answer, and the reason was worked out ninety years before the table.

A pot is a still

John William Strutt, the third Baron Rayleigh, distilled mixtures of known strength in a jacketed retort in 1891 and again in 1898, and in 1902 he published “On the distillation of binary mixtures” in the Philosophical Magazine. The first mixture he tabulates is alcohol and water. His table for the 1898 series gives, for each strength of liquid, the strength of the vapour leaving it, both by weight. The weakest liquid he measured was 1.97% alcohol; the vapour coming off it was 17.5%.

That is the whole mechanism. The steam leaving a pot of dilute alcohol is about nine times richer in alcohol than the pot. So alcohol leaves much faster than water, and the pot strips itself: the weaker it gets, the more of what is left goes with each gram of steam, until almost none is left. Rayleigh wrote the bookkeeping down in four lines. If w is the weight of liquid in the retort and ξ its strength, and the vapour's strength is roughly a constant multiple κ of the liquid's, then

ξ / ξ₀ = (w / w₀)^{κ − 1}

“For example, in the case of alcohol and water, we have for very weak mixtures η = 12 ξ approximately, so that κ = 12. As the distillation proceeds, w diminishes and ξ soon becomes exceedingly small. The halving of w implies a diminution of ξ in the ratio of 2¹¹ : 1. The residue in the retort thus approximates rapidly to pure water.”

Lord Rayleigh, “On the distillation of binary mixtures”, Phil. Mag. ser. 6, 4 (1902), 521 to 537, pp. 527 to 528. Read from the page images.

Multiply the strength by the weight and you have the alcohol: what is left in the pot is (w/w₀)^κ of what went in. Boil a pot down to half its weight and, at Rayleigh's κ of 12, 1 in 4096 of the alcohol is still there. His own measured curve is a little less steep than 12 at kitchen strengths (8.9 at 1.97%, falling to 5.2 at 9.88%), so the page does not use the constant. It integrates his general formula along his twelve measured points, and below his weakest point it shows two answers as a band: the enrichment held at the 8.9 he measured, and rising to the 12 he quoted. Halving a stew that starts at 3% leaves about 1 part in 466 on the first reading and 1 in 2443 on the second. Either way, it is gone.

The table, read along the other axis

If Rayleigh is right, each row of the USDA table is really a statement about weight: to keep that share of the alcohol, the dish must have lost this much of its liquid as steam. For a dish that starts at 3% alcohol by weight (the answer changes little for anything weaker), here is what each row needs, computed in your browser:

The whole table fits inside the first third of the pot. (The overnight row involved no heat at all, and a boiling curve is only a rough guide to a dish sitting on a counter; it is shown for completeness.) The 2.5-hour row, the one everyone repeats, needs 25 to 29 per cent of the liquid to have boiled away. How long a dish takes to lose that depends on the width of the pan, the heat under it and whether it has a lid, and the table records none of them. Double the rate of evaporation and, by this reading, the same two and a half hours sits far down the curve; halve it and the dish is still near the top. The minutes describe the dishes Augustin's group cooked, in their pans, on their stoves. They are not a property of alcohol.

And the flame, which is the other thing people believe in: the table gives flambéing 75%. On Rayleigh's curve, for a dish at 3%, that is what losing about three per cent of the liquid's weight would do. However dramatic it looks, the flame's number is the number of a dish that barely boiled. A 2012 study that flamed vodka and a vodka caramel sauce alongside the same systems heated but not lit found the same thing from the other side: “In both systems, the majority of ethanol loss was due to heating rather than combustion.”

Who found it, and what Rayleigh adds

This is not a new objection, and it is not ours. In 2016 a group at the University of Copenhagen measured the ethanol in ten dishes cooked with beer, by headspace gas chromatography, before, during and after cooking, and their discussion names the missing column:

“A decreasing ethanol concentration over time during cooking has been observed in the current study as well as in the two similar studies by Augustin et al. (1992) and Mateus et al. (2011). These studies as well as the present one do not state the loss of water upon cooking which would be useful in order to get a deeper understanding of the changes in ethanol concentration reported.”

J. Ryapushkina, E. Skovenborg, A. Astrup, J. Risbo, L. M. Bech, M. G. Jensen and P. Snitkjær, “Cooking with beer: How much alcohol is left?”, International Journal of Gastronomy and Food Science 5 to 6 (2016), 17 to 26, p. 25.

The next year the same group measured it. They cooked meat stocks with wine and beer, tracked the ethanol against both time and the volume left, and published the answer this page is built on:

“The experimental results and the model show that concentration of ethanol at any given time is determined by the initial concentration and a power law function of the remaining volume fraction. The power law function is found to be independent of factors like pot dimensions and temperature. When using a lid to cover the pot during cooking, the model was still valid but the ethanol concentrations decreased more steeply, corresponding to a higher exponent.”

P. Snitkjær, J. Ryapushkina, E. Skovenborg, A. Astrup, L. M. Bech, M. G. Jensen and J. Risbo, “Fate of ethanol during cooking of liquid foods prepared with alcoholic beverages: Theory and experimental studies”, Food Chemistry 230 (2017), 234 to 240, abstract.

Pot dimensions, in other words, matter only through how fast they boil the pot down, which is also the reading of Augustin's hunch about wide pans. The university's press release put it plainly: the dimensions of the saucepan and the cooking temperature “proved to only be significant because they could affect how quickly the sauce was reduced.” A 2019 follow-up tested common food components and reported that they “slightly enhance volatility of alcohol as seen by higher values of β”, their name for the exponent.

A power law in the volume left is Rayleigh's equation: his ξ/ξ₀ = (w/w₀)^{κ − 1} with β in the place of κ − 1. We could not read either paper past its abstract (both are behind paywalls that refused us), so we do not know the values of β they measured. Their reference lists, as deposited with Crossref, do not include Rayleigh; the 2017 one does cite Noyes and Warfel's 1901 boiling-point curve for alcohol and water, the same paper Rayleigh cites on his p. 526. But Rayleigh's own 1898 measurements predict it, with nothing fitted. Read locally off his curve, κ − 1 is 7.9 at 1.97% alcohol by weight, 6.9 at 3.98%, and 11 at the dilute limit he quoted. The press release gives one worked case, a sauce of 900 ml stock and 150 ml wine that starts at about 2% and “drops to 0.2% after a half an hour of cooking”. Reading both as by volume, on Rayleigh's curve a tenfold fall from 2% takes the pot down by 21 to 25 per cent of its weight, an effective exponent between 7.9 and 10. That is a prediction anyone with the paper can check against its open-pot results. And the lid fits: a lid that sends condensed water back into the pot acts like one more plate of a still, which would push the exponent above the single-stage value Rayleigh's curve gives. We have not checked that by how much.

Where Rayleigh is still useful is the dishes nobody weighed: his curve can be run backwards, from a measured fall in strength to the share of the liquid that must have boiled off.

The 2016 braised beef is the cleanest case. A kilogram of beef fore shank, browned first, went into a roasting pan with 500 g of red wine, 150 g of carrots and 120 g of onions; the pan was covered with a lid and braised in an oven at 150 °C for 180 minutes. The liquid started as the wine, 13.5% by volume on the label, and ended at 0.22%: a 61-fold fall. If nothing but steam changed the liquid, and the steam was in equilibrium with it, Rayleigh's curve says the pan lost 41 to 45 per cent of the liquid's weight. Two things push the true figure away from that, in opposite directions. Juices from the meat and vegetables dilute the liquid, so less evaporation would be needed. And a covered pan in an oven is not Rayleigh's open retort: if the lid acts as the 2017 paper found, the exponent is higher and less evaporation would be needed still; if the liquid simmered too gently to stay well mixed, the steam could be less enriched and more would be needed. The paper does not say how much the pan lost, so the figure is a prediction, not a result. It would take a scale.

(One inconsistency in the paper, for anyone reading it: its recipe table lists the wine as “Red wine, 14.5% (Chile, 2011)”, while its Figure 2 caption says the liquid “consisted of pure red wine with an alcohol concentration of 13.5 v/v% according to the label”, and its Table 2 uses 13.5. The page uses 13.5; with 14.5 the fall is a little steeper and the predicted loss a little larger.)

Weigh your own pot

Which means you can measure this at home with the one instrument every kitchen has. Weigh the pot with everything in it before it goes on the heat, weigh it again when it comes off, and the difference is steam. Tell the instrument what went in.

Meat and vegetables are mostly water, and the alcohol spreads into it given time, which is why the instrument asks for the water inside the food as well. The ceiling line is the one number here that does not depend on Rayleigh's curve: at any strength a kitchen reaches, steam off an alcohol and water mixture is richer in alcohol than the liquid it left, so the alcohol cannot fall more slowly than the weight. If the pot lost 10% of its weight, at most 90% of the alcohol is left, and on Rayleigh's curve far less.

What this page does not know

• Whether a simmer behaves like a boil. Rayleigh kept his retort “in vigorous ebullition” so that the vapour would be in equilibrium with a well-stirred liquid. The 2017 abstract says the power law held independent of temperature, which suggests a simmer is not far off, but we have not seen their numbers. A lid, by their result, makes the loss steeper than an open pot. A still, unstirred surface could make it shallower. The scale instrument prints both Rayleigh's band and the ceiling for that reason.
• The curve below 2%. Rayleigh's weakest measurement is 1.97%. Below it the page shows his measured 8.9 and his quoted 12 as the two edges of a band, and does not pretend to know the shape between.
• Food. The page treats everything in the pot that is not alcohol as water. Salt, sugar, fat and starch change volatility somewhat. We have not measured by how much in a stew.
• What Augustin's group weighed. The USDA's standard method for a retention factor uses the weight of the food before and after cooking. Whether the 1992 study recorded weights it did not publish, we do not know; the 2016 authors read it as not stating the water loss.
• Whether Rayleigh's exponent matches the measured one. The Copenhagen group has measured β for open and lidded pots and for different food components. Their values are in papers we could not read. The page's prediction, 7.9 to 11 for an open pot at the boil at the strength of a stock or sauce (below about 2% by weight), is stated so it can be checked against them, and it would be wrong in an interesting way if their open-pot values fall well outside it.

Sources

1. Lord Rayleigh, “On the distillation of binary mixtures”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, ser. 6, vol. 4, no. 23 (1902), 521 to 537. doi:10.1080/14786440209462876; scan at zenodo.org/records/1430666.
2. USDA, USDA Table of Nutrient Retention Factors, Release 6 (2007), Nutrient Data Laboratory, Beltsville: retn06.pdf (alcohol rows on PDF p. 14, printed p. 12) and the machine-readable retn06.txt.
3. J. Augustin, E. Augustin, R. L. Cutrufelli, S. R. Hagen and C. Teitzel, “Alcohol retention in food preparation”, Journal of the American Dietetic Association 92 (4) (1992), 486 to 488. PubMed 1556354.
4. P. Snitkjær, J. Ryapushkina, E. Skovenborg, A. Astrup, L. M. Bech, M. G. Jensen and J. Risbo, “Fate of ethanol during cooking of liquid foods prepared with alcoholic beverages: Theory and experimental studies”, Food Chemistry 230 (2017), 234 to 240. doi:10.1016/j.foodchem.2017.03.034; abstract at PubMed 28407905. Paywalled; only the abstract was read.
5. University of Copenhagen, “New research provides practical cooking tips for your red wine sauce”, press release, 6 June 2017, via ScienceDaily.
6. P. Snitkjær and J. Risbo, “Cooking with alcoholic beverages: Validating a mathematical description of the loss of ethanol in liquid dishes”, International Journal of Gastronomy and Food Science 16 (2019), 100136. doi:10.1016/j.ijgfs.2019.100136. Paywalled; only the abstract was read.
7. C. E. Hansen, M. T. Kwasniewski and G. L. Sacks, “Decoupling the effects of heating and flaming on chemical and sensory changes during flambé cooking”, International Journal of Gastronomy and Food Science 1 (2) (2012), 90 to 95. doi:10.1016/j.ijgfs.2013.04.001.
8. W. A. Noyes and R. R. Warfel, “The boiling-point curve for mixtures of ethyl alcohol and water”, Journal of the American Chemical Society 23 (1901), 463 to 468. doi:10.1021/ja02033a004.
9. J. Ryapushkina et al., “Cooking with beer: How much alcohol is left?”, International Journal of Gastronomy and Food Science 5 to 6 (2016), 17 to 26. doi:10.1016/j.ijgfs.2016.09.001 (open access, CC BY-NC-ND).
10. Strength by volume and by weight: Lange (1967), as tabulated in Wikipedia, “Ethanol (data page)”, “Properties of aqueous ethanol solutions”. Interpolated linearly between its rows.
11. US standard drink, 14 g: National Institute on Alcohol Abuse and Alcoholism, “What Is A Standard Drink?”: “In the United States, one standard drink contains about 14 grams, or about 0.6 fluid ounces, of pure alcohol.”