# Time&Temperature vs energy needed for molecules structure's changes

Recently I've read an interesting post about time vs temperature (Time vs. Temperature - What changes what?)

I've been thinking about this problem for a long time. and I'd like to share an idea.. "A single piece of meal, need certain amount of energy to modify its molecules structure."

Sous vide technique for cooking pork cheeks says (made by a well known Chef):

48h at 65ºC or 24h at 80ºC

This long time is needed to denature the myosin and other internal transformations...and so For those transformations, we need to give energy to the meat.

So, if we asume, that both temperature/time alternatives, give us the perfect result.

Is it possible to know how much energy is used in each situation? could it be a similar amount of energy?

If this hypothesis is valid, then, we could use that value, to answer two questions: 1.-how many hours will be needed if we cook it at 70ºC? 2.-if we'll cook it for 36h, what should be the temperature than we need to keep?

anyone could help us with the formulas? thanks a lot!

The hypothesis is somewhat valid. The version which is true is: there is a correlation between the total amount of energy which went into the meat and the degree of doneness. And because the total energy is the rate of energy input multiplied by the time you are adding energy to the system, time and heat are interchangeable to some extent.

However, there is no constant "total amount of energy" which needs to go into the meat. Protein denaturing is a complicated stochastic process. If we were to assume that we have a uniform thin layer of meat and a perfectly uniform heat source parallel to it, we still wouldn't have a constant total amount of energy. It is a bit less noticeable with meat, where preparation methods are limited (*), but in eggs it is easy to observe that the speed at which yolks are heated will have a noticeable difference on the final texture of a custard.

Even if you could get away with a usable range for the "total amount of energy", you could still not predict the time needed by a given piece of meat at a given temperature. We are talking about a complex nonlinear system here. That part is a duplicate of another question, so I will simply post a link to my older answer.

So in the end, there is a very good reason why you should check for doneness instead of try to predict doneness. Or, in the special case of sous vide, use the empirically determined charts somebody else went to all the trouble compiling. Calculating it for yourself is completely impractical.

• I think even the version you've given as true is a little misleading in the context of long, slow cooking, where "done" doesn't just mean it's cooked through, it means it's had enough time to break down as desired. In that case, there's not really an energy correlation anymore, unless you mean the energy you're wasting as you hold it at that temperature :) – Cascabel Jul 19 '16 at 17:58

There are two big things going on when you cook meat:

• bringing it up to the desired temperature
• holding it there long enough for desired changes to occur

For some meat, the temperature is basically all that matters. The most common example of this is a steak: once it's the temperature you want, it's done. You might finish it off by searing it to cook the outside a bit extra, but the doneness of the bulk of the meat depends purely on the temperature.

For other kind of meat, the temperature is just the first step, and the cooking you really want happens as you hold it there. Anything with a really long cooking time is likely in this category, like the 24-48 hour pork cheek you mentioned, or perhaps more commonly, slow-cooked pork shoulder or ribs. That long cooking lets the connective tissue break down (notably collagen turning to gelatin), taking it from chewy and tough to pull-apart tender. It'll break down at temperatures as low as 50C/120F, but as you increase the temperature it'll break down faster and faster, up to 80C/180F.

Some of those reactions might be endothermic, but protein hydrolysis is actually slightly exothermic. The energy is also way, way smaller than the energy you use to heat the meat - for cooking purposes, you can ignore it. In any case, trying to model heat transfer and heat input is kind of pointless: it's the reaction rate that matters, not the energy you're using/wasting to keep it at that temperature. The reaction rate does increase with temperature, as mentioned above, but again that's about temperature, not energy input.

So how does that all connect to your energy hypothesis?

Bringing meat up to the desired temperature is basically all about energy: you have to transfer a fixed amount of heat energy to bring a given amount of meat to a given temperature. So in that sense, you're spot-on.

But when you're holding meat at a temperature to cook it, you're not transferring significant heat into it anymore. It's really just about time. The amount of time it takes does often depend on the temperature, since the reaction rates are temperature-dependent, and that's why you've see the variation in time and temperature in recipes. But it's no longer a simple matter of energy input as you guessed. Yes, you'll have an initial period of bringing the meat up to temperature, which is simple heat transfer, but the real cooking happens after that.

• thanks! I got it.. and you are right. One thing is to reach certain temperature inside the meat, and when it´s reached.. is done. But for long cooking recipes, after reaching the final temperature, we are just maintaining that value waiting for some molecular reactions... According to your answer , it seems to be something complex to predict, but somehow it should be something related to the movements that the atoms of that meat and other structures have at a certain temperature.., is there any way to measure that energy based on mass at certain temperature during x hours? – Hugo Jul 19 '16 at 19:21
• @Hugo I tried to make it clear that it's more about time than energy. Breaking down collagen into gelatin will proceed at a certain rate at a given temperature, meaning breaking it down "enough" will take a certain amount of time at that temperature. Modeling the specific reactions is doesn't seem worth it; all you actually need to know is how long they take. (It's possible that you could get a nice function for reaction rates vs temperature, but... those things are experimentally measured anyway, so you might as well just use the experimental results, aka tested recipes, directly.) – Cascabel Jul 19 '16 at 19:29
• @Hugo Those reactions require energy that is consumed. If you do not continue to supply energy those reactions stop. In a lab you would measure the energy to an empty oven over the same period and the difference is what is required for cooking. – paparazzo Jul 19 '16 at 22:56
• @Paparazzi As described in my answer, the main reaction is actually exothermic, and in any case, peptide bond energy is small enough that any reaction energy is going to be drastically smaller than the energy it took to heat the food/water in the first place. You can't treat those reactions as an energy input problem. The factor that matters here really is time, not energy. – Cascabel Jul 20 '16 at 0:09
• If just bring the meat rapidly to temp and then it is a time thing then the middle would not less done then the outer. If the reaction is exothermic then ovens would be catching on fire and houses burning down. – paparazzo Jul 25 '16 at 8:30

Heat transfer is going to be the temperature difference X area X coefficient X time.

Since the temp of meat changes it would really be an integral equation but let's not make it hard.

There is also obviously a minimum temp as meat does not cook in a refrigerator. The guideline from USDA is cook pork to 145 F / 63 C so that would be the minimum cooking temperature and it would take a while. That 65 is very close to the finish temp.

What meat temp would have those two heat transfer the same

48(65-t) X a X c = 24(80 - t) X a X c
2(65 - t) = 80 - t
130 = 80 + t 50 C = t = 122 F
But that is taking a constant temp so finish temp would be higher

If you extrapolate this to 36 hours you are going to be pretty much at final meat temperature.

The meat has an initial and final state. It takes fixed amount of heat to break it down. Temperature is not what cooks the meat. Heat cooks the meat and temperature is what drives the heat transfer. It is done when it gets to a final temperature but heat transfer is what got is there. The cooking temperature needs to be at least final meat temperature or heat transfer stops.

You would need to take case by case. You are only going to get estimates with heat transfer equations.

• Don't know about the voter, but the big issue I see here is that cooking isn't just a heat transfer problem. Some things are that simple: if you get your steak to the temperature you want, it's done. But other things along the lines of what the OP mentioned are reactions with a temperature-dependent rate, so just modeling heat transfer won't really tell you much. – Cascabel Jul 19 '16 at 15:44
• @Jefromi Did not mean to argue the vote. Want to know what the problem is. The stated question IS a heat transfer question. "Is it possible to know how much energy is used in each situation? could it be a similar amount of energy?" I exactly answered the stated question. Getting your steak to temperature is heat transfer problem. – paparazzo Jul 19 '16 at 16:28
• I'm not arguing either, just pointing out a problem. The stated question is not just getting meat to a temperature, it's asking about processes that take time. The OP is speculating that it might be a total energy thing, in which case it might pretty much be heat transfer, but that doesn't mean that's actually the whole story. As I said, there's plenty of cooking that isn't that simple. The OP's example certainly isn't: pork cheeks for 24-48 hours are going to be up to temperature after a few hours, and all the rest of the time is doing something interesting besides heat transfer. – Cascabel Jul 19 '16 at 16:50
• @Jefromi The ? mark is on heat transfer. Besides heat transfer? I get you are moderator here so let's just stop at that. – paparazzo Jul 19 '16 at 16:56
• Being a moderator grants me no special powers for pointing out issues I see with answers. I believe you've oversimplified and missed the point a bit, but you're still free to ignore my thoughts just like you can ignore anyone else's. That might not always be a great way to end up with good answers for future readers, but do as you like! – Cascabel Jul 19 '16 at 17:06