Saturday, May 28, 2011

On benefit of buying smaller eggs

It has been brought to my attention that eggs have been one of the items that has been affected by the recent price rises. This increase has been reflected unequally among the different stores, some charging considerably more for the same size eggs than others. Furthermore, there seems a disproportionate premium on "jumbo" size eggs. As a result my wife has started buying the eggs one size down - the extra-large ones.

Due to an occasion of needing to "look after myself" I have had the opportunity to purchase eggs in the store we frequent most (Save on Foods). I noticed availability of not only the usual 12-egg cartons but also 18-egg cartons, the latter only in the "large" category. A quick calculation led me to conclude that this should be a good deal compared with the same size eggs in a box of 12 (although these inexplicably were not priced). I decided to do an experiment. I purchased the 18-egg carton and proceeded to compare them with the 12-egg carton of  "extra-large" at home.

The hypothesis was that :

1) Buying slightly smaller eggs will lead to disproportinate savings without sacrificing significant nutritional content.
2) Smaller eggs are less likely to burst on boiling thus leading to further savings due to reduced losses.

Method:

The eggs in each carton were weighed on a kitchen scale reading to 1 gram accuracy. Some were weighed twice to assess repeatability of the measurment.

The mean weight and standard deviation for each sample were calculated.

The samples were compared using the unpaired Student's T-test.

The eggs were cooked using the standard soft-boiling method by immersing them in cold water and bringing this rapidly to boil where they were kept for 4 minutes and then cooled rapidly by running water.

Due to the curved nature of the shell the shell  thickness could not be measured reliably with the existing instruments (outside micrometer, calipers).

Results:

1) The mean weight of the extra-large egg is 65.08 grams. SD = 1.73 n=12
2) The mean weight of the large egg is 60.17 grams, SD = 1.95, n=18
3) The difference between the means is 4.91 grams or the larger eggs are 8.16% heavier.
4) The difference between the samples is highly significant with p<0.0001
5) The cost of the 18 large eggs was $3.99. This translates to a cost per dozen of $2.66.
6) The cost of extra-large eggs and a 12-carton of large eggs at Save-on Foods could not be reliably ascertained due to continuing lack of labelling and a verbal information thought to be unreliable at best. The cost of 12 large eggs at Quality Foods was $2.99, extra-large $3.29. Quality Foods do not sell jumbo eggs.
7) None of the extra-large eggs boiled in the fashion described burst during cooking and so far none of the large eggs have done so either.

Discussion:

The egg weights correspond to the modern Canadian standards for each size class. The extra-large eggs are significantly heavier by 8.16% than the large eggs. Survey of literature (such as could be accessed on the Internet) reveals that about 10% of the total weight of the egg is the shell, the yolk is about 30%, the white 60% of which 90% is water. None of the literature sources indicated whether these proportions are maintained across the weight scale. It would seem likely that with increasing size the proportion of the egg contents (yolk+white) would increase as the shell represents the surface of the egg and increases proportinately to radius squared whereas the content represents volume which increases with radius cubed. Whether the shell thickness also increases could not be determined due to lack of suitable measuring equipment (a point micrometer would be most suitable). Most cookbooks recommend adjusting the number of eggs for baking according to their size, however, the evidence basis for this is presumably empirical, based on the quality of cakes etc. In any case, assuming that the proportions are maintained the increase in the nutritionally active ingredients would only be of the order of  2.9 grams.

Although I was not able to price the eggs accurately at the source where they were obtained a representative pricing from elsewhere shows that the price increase from large to extra-large is 10%,  i.e. disproportionate to the 8.16% size increase. Anecdotal evidence suggests that this disproportion is even larger in the case of jumbo eggs. On the other hand buying large eggs in a packet of 18 is even more advantageous economically.

At the table this size difference was not obviously noticeable.

None of the sub-jumbo size eggs burst while cooking. This may be due to unusually resilient shell in our two batches or may in fact represent an increased relative strength of the shell in the smaller eggs. Some postulate air pocket in the eggs as the cause for the shell burst. However, air is already present as gas and as such follows the law of Gay Lussac stating that the pressure of gas in presence of a constant volume is proportinal to the absolute temperature. Thus increasing the temperature of the egg from 8 degrees C (281.15K) to boiling (373.15K) will increase the pressure of air within the egg by only 32%. However, air is compressible so it is not at all clear that this pressure increase is enough to cause the shell burst by itself. There is however, a significant water content in the egg, 54% of the total weight which, in a 60g egg is 32.4g. If this amount of water were converted entirely into steam it would render a whopping 54 litres of steam at 760 mmHg. It is unlikely that such complete conversion in fact occurs (otherwise all eggs would surely burst while boiling), however, I suspect that it is the steam formed during boiling the egg that is reponsible for the eggs bursting rather than the air pocket. Only 2% of the available water converted to steam will generate over a litre of steam.

The reduced amount of water in the smaller eggs is unlikely to play a role in the increased resistance to bursting as the available volume of steam is still appreciable. I feel the answer lies in the increased ability of the shell to withstand transmural pressure due to the reduced diameter. The egg, in fact, follows the Laplace law, P=2T/r, where P is the transmural pressure, T is the wall tension (here represented by the strength of the shell) and r is a radius of a sphere which the egg approximates. It is clear that a smaller wall tension will contain higher transmural pressure if the radius is reduced. This phenomenon is well described in medicine where e.g. larger aneurysms are more likely to burst than smaller ones.

The only indirect observation suggesting that the explanation is correct is that the larger eggs invariably burst only once the water reaches the boiling point, i.e. steam production inside the egg is ramped up.

An alternative explanation is that the smaller eggs have stronger shells. Thre is at present no way to ascertain this but there is also no reason to believe that this is so.

Conclusion:

1) Buying smaller eggs is economically advantageous as the price premium on size is disproportionate, particularly in the case of jumbo eggs.
2) The benefits of buying eggs in large quantities are also evident and consistent with most other grocery purchases.
3) The smaller eggs appear to have a better resistance to boiling-induced shell bursts. This needs to be confirmed by boiling other batches of both extra-large and large eggs to confirm this and determine the threshold level of this phenomenon. The scientific reasons for such resistance are discussed. Decreased losses from boiling-induced bursts, if confirmed, contribute further to the economic benefit of buying smaller eggs.

Comment:

At this time the eggs in BC are priced as above. The information available on the Internet suggests that the price of similar eggs in the USA is of the order of $1.75 per dozen. This difference is entirely due to built-in subsidies that the Canadian producers continue to enjoy as well as their protection from US competition by cross-border levies.

References:

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Acknowledgment:

The author wishes to express his thanks to his esteemed colleague Dr. Sheldon Cooper without whom such foolishness would not have been attempted let alone brought to fruititon.

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