What's more fun than cooking a turkey? The answer: thinking of new ways to cook a turkey. I've already thought about cooking a turkey by dropping it, but what about something else?
Of course, the goal here is to use batteries. Who knows, maybe you are stranded in the snow with a truck load of batteries and a turkey. It wouldn't be too hard to wrap the turkey with copper wire and hook the wire up to a whole bunch of batteries. The wires would get hot, and in theory they would cook the turkey. Simple, right? But how many batteries? There are several things to consider.
Specific Heat of Turkey
The goal of cooking a turkey is to increase the temperature to some value - maybe 170°F or 77°C. When we are talking about batteries, clearly we will be looking at energy. But what is the connection between temperature and energy? It's the specific heat.
The specific heat tells you how much energy it takes per mass to change the temperature of an object. Maybe this equation will help.
Of course the more massive the object you have, the more energy it takes to increase the temperature. The type of material matters too, this is the c (specific heat). As an example, let's consider water and aluminum. If I add one joule of thermal energy to 1 gram of material, the two objects will have different temperature changes. Aluminum has a specific heat of 0.9 J/(gm°C) and water is 4.186 J/(gm°C). For this 1 Joule, the aluminum will have a temperature increase of 1.11°C but the water will just increase 0.24°C. Yes. The specific heat of water is quite large. This is why you can really get cold swimming in room temperature water. It takes a lot of energy from your body to warm up the little bit of water near your skin.
Enough about specific heat, let's measure turkey. Oh, I am going to use a chicken breast instead. Why? Because I found a chicken breast in the fridge but I didn't have any turkey? You're not happy about that? Too bad.
Here is the plan. Take a chicken breast and put it in some hot water (in an insulated cup). If I know the mass and initial temperatures of the turkey (I am going to call the chicken turkey now), all I need to do is find the final temperature of the stuff. Assuming there is no loss of energy, then I could write this equation (Tw the initial temperature of the water, Tt the starting temperature of the turkey-chicken and Tf the final temperature of the stuff).
With just a few measurements, I could get a value for the specific heat of turkey-chicken. However, I am going to make it more complicated (and better). Using a couple of Vernier temperature probes, I can plot the temperature of both the water and the turkey as a function of time. I get something like this.
You can see that the chicken warms up and the water cools off. From this (and mass measurements), I get the following data:
- Mass of chicken = 172.98 grams.
- Mass of water = 200 grams.
- Initial water temperature = 85.9°C.
- Initial turkey temperature = 23.06⪚C
- Final temperature of stuff = 40°C
Putting these values into the above expression (along with the specific heat of water), I get:
That is way too high. Crazy high. I think the problem is that I am assuming all this energy from the water went into the chicken. However, my little foam cup container wasn't perfectly insulating the chicken-water from the surroundings. How about another little experiment. Here is just 400 grams of water (about the same as the chicken plus the water) in the same cup.
You can see that over a 60 minute time interval, the water dropped by about 30°C. If I assume that the the chicken-water mix had the same drop in temperature (I know, that's a bit of a stretch) then I could say that the starting temperature of the water was just 55°C. Using this value, I get a specific heat of chicken with a value of 4.29 J/(g*°C). Seems more realistic.
What about another method? It seems that Wolfram Alpha will give a specific heat of chicken. I never knew it could do that. This reports a value of 3.21 J/(g°C). Also, this says that one of my assumptions was crazy. The specific heat of turkey is a little bit lower with a value of 2.81 J/(g°C).
Note: the goal was to get the specific heat of the turkey. Yes, I could have easily just looked this up instead of making a mess with raw chicken. However, I always like to build crazy calculations on some type of real data. It didn't work in this case, but it was still fun. Also, my original plan was to look at the numerical derivatives of these temperature curves to calculate the specific heat. Maybe I will try this again with some other material.
Battery Heater
After wasting too much time on the specific heat (well, maybe it wasn't wasted) I need to now look at my electric cooker. It's just a wire connected to a battery, can you get any simpler than that? I doubt it.
Above is a test wire. I can find the total energy needed to heat up my turkey, but how much energy from the battery would actually go into an increase in temperature? To get an idea of the efficiency, I used the above test wire. After hooking it up to a battery, I can measure the current and voltage to get the power. Also, I can record the change in temperature of the water. In this case, I will use 400 grams of water in the same container I used before. Here is a plot of the temperature of the water as a function of time.
That turned out a little bit nicer than I expected. The slope of this line is 0.02698 °C/min. Using the mass and specific heat of water I can use this to calculate the power output of the battery at 0.753 watts.
What about the power from the battery? The voltage across the battery during this time was fairly constant at 1.024 volts with a current of 1.17 amps. This gives a power of:
Looking at the ratio of power for the heated water to power output of the battery, I get an efficiency of 0.628.
What about the total energy in a battery? In the above experiment, I used a Duracell D cell battery. These have a listed capacity of 14000 mAh. If it ran for 1 hour with a 1.5 volt potential, it would produce 1.4 amps. That would be a total energy of 7560 Joules.
Turkey Batteries
We have everything we need. We have the specific heat of turkey (which I failed at) and the efficiency of a battery.
How big is our turkey? A 10 pound (4.54 kg) turkey seems nice. We should have plenty left over for turkey sandwiches. If it starts at room temperature (21° C), I need to increase its temperature to 77°C. I will assume a battery efficiency of e = 0.628. Now I can calculate the number of needed D-cell batteries:
Let's call it 151 D-cell batteries. That's at least doable. But wait! What if I want to get this turkey cooked and I want it now. Let's say I will wait just 1 hour for this turkey to be finished. This might require more batteries. Not because of the energy, but because of the power.
If I calculate the power to cook a 10 pound turkey in an hour , it would require 198 watts. Since each battery (in the configuration I used) delivered a power of 0.753 watts to the water. This means I would need 263 D-cell batteries.
That's it. Go get your batteries and your turkey and start cooking.
