Physics of boiling an egg - what am I missing? (heat capacity and coagulation question) Update:
1) I originally posted this because the numbers seemed to make no sense to me (seemed very counterintuitive to only need 60-100ml of water to cook an egg when you usually have to boil it continuously in a saucepan of water...). I expected that perhaps the "latent heat" (activation energy, rather) of denaturing will contribute significantly to why it might not work. Well, I ended up just trying it out and it actually worked - I put a 63g egg with about 100ml of water in a thermos flask for one and a half hours and it turned out perfectly. You can see the process and results in this photo album - http://imgur.com/a/J0Hzc
This is consistent with what tom10 said in the reply, which is that the denaturing would be negligible. I did some of my own calculations too, which agreed with that. I couldn't believe that it would really be negligible, but well here we go...
2) That said, I must admit I still don't -really- understand this whole denaturing process and how it works, but I'm trying to understand it better, so I'd still appreciate more replies! I'm quite sure the way I'm analyzing it isn't completely right, but at least I know now that it's a good-enough approximation for cooking. 

Original question:
I cook as a hobby, and I was thinking of doing a simple theoretical calculation to see whether there was a better way of preparing soft-boiled ramen eggs, and my numbers don't seem to make sense? I'll explain my process here, but my key question is basically - what am I missing from this analysis, and can you explain egg white coagulation processes to someone who has basic physics but doesn't understand the chemical processes?
Okay so from a cooking perspective, usually, boiling an egg uses a constant source of heat. However, I had the idea of using something like a thermal pot, where ingredients are stored with hot water in a very well insulated container, and just left to cook all day long. The idea is that because there is no heat loss, and water has such a high heat capacity, heat losses are minimized and the ingredients can cook with minimal loss of heat energy (I'm assuming that means that the latent heat involved with whatever chemical changes that occur are small compared to the energy associated with the water changing temperature).
I got some numbers for eggs:
- Heat capacity is in the range of 2.7-3.7 kJ/(kg K)
- Masses of eggs are around 0.05-0.07 kg or so
- Egg whites coagulate at 62-65 degrees celcius, yolks at 65-70.
My objective is to put an egg (at room temperature) with some amount of boiling water (assuming 100 degree celcius) in an insulated container, and leaving it to reach an equilibrium temperature of 63 degree celcius. In theory, if I calculate the mass of water needed correctly, that means that it will never reach above that temperature, so I should get a perfectly cooked egg. I got the number of 63 degrees, among others (googled for "What temperature egg white hardens").
However, assuming no heat loss and minimal latent heat of coagulation, this tells me I need around 40mL of water or so. Based on the numbers given, it makes sense, since the changes in temperature of the egg and water are in the same ballpark, and the heat capacities are in the same range too. I would be inclined to believe these heat capacities, since egg whites/yolks are mostly water. 
Am I missing something important? From a cooking perspective, it doesn't seem intuitive to only need so little boiling water to bring an egg from room temperature to that temperature.
As for coagulation, I don't really understand the chemical processes, but from what I understand, it is a process with a rate that changes with temperature. I'm not sure how to interpret the numbers correctly, but this Google books link here suggests that the process is definitely not as simple as I would like it to be.
Based on that link (and others), I suspect that
1) my estimation that latent heat is negligible is very far off. Is this a correct interpretation of why my numbers make so little sense?
2) I need to treat the numbers given for temperature of hardening/coagulation differently. While technically true that egg whites will begin to coagulate significantly at 62-65 and yolks at 65-70, even with sous-vide cooking, it needs to be held at that temperature for very long periods of time (e.g. 30-45mins) for it to coagulate. So, if I simply set up my hot water + egg insulated system to reach 63 degrees, as the eggs coagulate, the temperature will fall off as energy goes into coagulating the eggs. Is this right?
3) In that case, is there any good way to estimate the thermal energy loss that goes into coagulating the egg? For example, if I wanted to, how would I estimate the amount of energy that a sous vide cooker (essentially a temperature-regulated water bath) supplies to an egg over the coagulation process?
Thanks in advance!
 A: A better term than "coagulation" is "denaturation".  To denature a protein is to unfold it, and this can be done by thermal energy.  Initially the egg white proteins are each folded up into little ball-like bundles which limits their interactions, but when they denature the become strands.  The charges on these strands then attract to each other and form a tangled mess.  Of course, this changes the entropy, but not as much as for simple molecules.  That is, we need to look up the "heat of denaturization" for albumin, which is 12.2 J/g (compared to water melting, 334 J/g, so it's fairly small).
That is, denaturing a 60g all albumin egg, should take 60g * 12.2 J/g or 732 J.  Given the heat capacity of water as 4200 J/kg K, or 168 J/K for 40 mL of water, this should cause a temperate change of about 4.3C in 40 mL.
So the specific answers are:


*

*The heat of denaturation is small but not completely negligible.  Since you start with 100C water, and want to end around 65C, for the small amount of water you mention (40 mL), it's around a 10% error.

*Yes, if you're trying to hit it right at 63C, you'll need to account for the heat going into denaturation.

*For a temperature controlled system like a sous vide cooker, the amount of energy going into denaturation is negligible compared to energy lost to steam from the bath, etc.  (Overall though, this question doesn't quite make sense to me and I wonder whether you're confusing "temperature" with "heat".)
Also, keep in mind that denaturing the albumin does not necessarily mean the egg is cooked sufficiently to be safe to eat.
Finally, I wouldn't trust the 63C number, especially since you're taking the low end of a given range.  If you really want to be exact, you'll probably need to go to the source of those numbers.  (And don't forget the heat capacity of your container, and also I suspect heat loss will, in fact, be significant here.)
