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Egg Slide Rule

The one kitchen utensil you did not yet own...

The physicist Charles Williams of Exeter University has a published formula[1] that solves an old problem: how long should you boil an egg.
The formula looks like this:

  t=\frac{M^\frac{2}{3} c \rho^\frac{1}{3}}{\kappa \pi^2 (\frac{4}{3}\pi)^\frac{2}{3}} \ln \Big(0.76 \frac{T_{egg}-T_{water}}{T_{yolk}-T_{water}}\Big)
where t = boiling time,
M = mass of the egg,
c = specific heat of the egg,
ρ = density of the egg,
κ = thermal conductivity coefficient,
Tegg = initial temperature,
Twater = 100 °C = temperature of boiling water,
Tyolk  =  desired yolk temperature: 62 °C for soft, 65 °C for intermediate and 69 °C for hard boiled.[2]

The formula assumes that the water is already boiling before the egg is put into the water, and that the process takes place at an air pressure of 1 atmosphere.

The following constants apply[3]:
  C κ ρ
Yolk   2.7 J g-1 K-1   3.4 × 10-3 W cm-1 K-1   1.032 g cm-3
Protein    3.7 J g-1 K-1   5.4 × 10-3 W cm-1 K-1   1.038 g cm-3

It is not easy to use this formula in the kitchen. A slide rule would be a great help. However, I have never seen an egg boiling slide rule, not even in the patent literature.

Therefore I offer here my design of an egg slide rule:[4] Move the arrow of the Tegg-slide to the weight, choose the Tegg-scale corresponding to your taste, locate the initial temperature of the egg and read the cooking time above this temperature value. For convenience, standard refrigerator temperature * and room temperature [] are highlighted on the Tegg-scale. The EU standard weight classes[5] are indicated below the weight scale.


In the derivation of the formula several approximations are used, like the egg being spherical, and not cooking at an high altitude.
So use the results with a grain of salt.

Notes

  1. Charles D.H. Williams, "The Science of Boiling an Egg".
  2. H. de Lang, "Molecular gastronomy", Nederlands Tijdschrift voor Natuurkunde [Dutch Journal of Physics], 7412 (2008) page 431–433.
  3. S. L. Polley, P. O. Snyder, P. Kotnour, Food Technol., 3411 (1980) page 76–94.
  4. In the attachments you can find a higher resolution PDF version of this slide rule.
  5. Regulation (EC) No 589/2008 of the Commission of 23 June 2008 laying down detailed rules for implementing Council Regulation (EC) No 1234/2007 regarding marketing standards for eggs.
A Dutch version of this paper appeared in MIR 50, april 2009.
Ċ
egg.pdf
(48k)
Andries de Man,
Nov 25, 2010, 12:47 AM
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