Geometry of Good Cooking

The size and shape of food plays an important role in how a food cooks.

In the previous blog post, we looked out how heat transfers from your frying pan, grill, and oven to your food.

In this post, we will look at how the size and shape of your food impacts the cooking process.

But first, let’s explore a concept called Specific Heat.

Specific Heat

Simply stated, specific heat is the amount of energy it takes to raise a unit of mass one degree of temperature. For water, this is 1 calorie per gram per degree Celsius.

Most foods that we cook are composed largely of water, so the specific heat will be somewhere near this number. But, for the purposes of cooking, we don’t need to know the exact numbers.

What is important to know is that it takes energy to raise the temperature of a food. And the amount of energy required is dependent on the mass of the food and the temperature change required for cooking.

Practical constraints of cooking usually limit the amount of energy we can add to food in a period of time. For example, if instructions call for baking a cake for 1 hour at 300°F, we cannot expect to double the temperature and cook the cake in half the time.

So when we cook something, we are largely concerned with the amount of time it takes to cook. And because of the concept of Specific Heat, we can know that the larger the food and the larger the temperature change, the longer we will need to cook something.

Practical Applications of Specific Heat

Traditional pasta cooking instructions have you bring a big pot of water to boil and then add the pasta and cook for a specific amount of time. This requires a large amount of water to overcome the drop in temperature that occurs when you add the pasta.

Alternatively you can cook the pasta by placing it in the pot and filling with water to an inch above the top of the pasta and then placing it on the stove.

The second method requires less water, therefore less energy to bring it to a boil and will get the pasta cooked quicker. Less water also means less salt necessary for seasoning the pasta, more on that in a future post about diffusion.

Because less total mass is being heated in the second method, less energy and time are needed. It is also nice to not have to worry about remembering to dump in the pasta when you are cooking the rest of your meal while simultaneously fielding requests from your four-year-old.

The main drawback to the second method is that you have to check the pasta for doneness rather than cooking for a specific amount of time. Also, this method is only suitable for dried pasta and not fresh pasta.

So now that we’ve seen one way to account for the mass of food in our cooking time, what about temperature?

If you are a fan of steaks, you know that the best cooked ones are when there is a nice seared brown crust on the outside and an evenly cooked pink center without much gray or brown cooked area between.

To accomplish this, we need to bring the outside temperature into the 300 to 350°F range to engage our old friend the Maillard Reaction while bringing the inside to somewhere in the range of 130 to 145°F for medium rare to medium well doneness.

This is difficult to do, especially with thicker steaks, as the time needed to bring the internal temperature up to the desired level means that the outer part of your steak is likely going to be overcooked.

But, science of cooking fans like yourself that know about specific heat understand that we can reduce the cooking time on the stove or grill if there is less temperature difference to overcome.

To do this, we can place the steak in the oven at a low temperature to raise the overall temperature of the steak (without browning it) prior to placing it in a pan or on a grill to sear and finish cooking.

This method is commonly referred to as ‘Reverse Searing’. For a full rundown on the process, check out this blog post.

This works to cook beautiful steaks because we reduce the temperature change needed while browning, thereby preserving an even doneness of the interior, and all because of specific heat.

Surface Area to Volume Ratio

The size and shape of a food has a lot to do with how it will cook. As we have gone over in the specific heat section above, larger pieces of food take longer to cook because of their higher mass.

This mass can be distributed in different shapes and the shape determines the surface area to volume ratio of the food.

Why is this ratio important? In the last post, we went over how heat transfers from one object to another, either by atoms bumping into each other or by receiving electromagnetic energy.

With any of the heat transfer methods, the larger the surface area, the more heat that can be transferred into the food over a given time because there is more surface for the energy to be transferred over.

While this may seem somewhat abstract, let’s look at a couple of examples that shows the importance of this concept.

Using Surface Area to Volume Ratio in your Cooking

Let’s say you want to make mashed potatoes, but you are in a hurry. Because you are in a rush, you don’t spend much time cutting up the potatoes and you put them in water to boil in big chunks.

Now let’s say that you have read this post and understand surface area to volume ratio and know that the potatoes will cook much faster if you cut them up into small chunks.

In either scenario, you are cooking the same amount of potatoes, so there is no difference in the energy required by the specific heat of the potatoes. So what makes the second method faster?

For simplicity’s sake, let us assume that the potatoes are cut up in the shape of cubes. The volume of a cube is the height times the width times the depth. The surface area is the area of one face times 6 as there are six sides on a cube.

If we have cubes with sides of 1 unit (small potato chunks) and 2 units (large potato chunks), the volume of the small potatoes would be 1 cubic unit and the large chunks would have a volume of 8 cubic units.

Now you may think that this volume difference is the reason the larger chunks take longer to cook, but if these chunks both had the same proportional amount of surface area, the heat would transfer into the potatoes at the same rate, and both would be cooked in the same amount of time.

But, as you might guess, the surface area to volume ratio is not the same. The small cubes have a surface area of 6 square units for a ratio of 6 to 1. The large chunks have a surface area of 24 square units, which makes only a 3 to 1 surface area to volume ratio.

So the larger chunks can only receive half the amount of heat from the boiling water relative to the volume of the potatoes as the small chunks. And naturally this will take longer to cook.

This relationship works for any shape, whether it be sphere, cylinder, or irregular form. For two similarly proportioned shapes, the larger pieces will always have a smaller surface area to volume ratio.

Nature understands the importance of this ratio very well. As humans, we are reliant on maintaining an internal temperature in the upper 90’s for our body’s to function. As tiny humans, aka babies, we have a higher surface area to volume ratio compared to an adult, therefore body heat can be lost much more quickly.

So nature compensates by increasing the amount of subcutaneous fat (an insulator) over the body of the baby to help hold in the heat, So next time you see a baby, say ‘Good job nature on compensating for the surface area to volume ratio!’ or just say ‘Who’s a cute baby?’, your choice.

Now that we know the larger of two similarly shaped pieces of food will take longer to cook, you may wonder how to determine cooking times for foods with different proportions and shapes,

We can do this without having to lookup formulas for surface area and volume with one simple observation.

When evaluating different shaped items, we can get a sense for cooking time by estimating the distance to the center of the food to be cooked.

The longer the distance to the center, the longer the cook time.

As an example, let’s look at three different shapes that we could use to cook ground beef. We could form the ground beef into a thin patty, a thick burger, or a spherical meatball.

Even though we could use the same amount of meat for each shape, the cook times will be drastically different.

The thin patty has a small distance to the center, so it will not take long for the center to cook and we can use a hot pan and short cook time to get the outside to a nice crisp browned surface.

The thicker burger has farther to go to get to the center and if we tried to cook it like the patty, we would end up with an overdone exterior and raw interior. So we need to reduce the heat of the pan or grill some and cook a little longer to get a nicely finished burger with a nice brown exterior.

The meatball has the longest to go to get to the center and will need the longest to cook. If we just used ground beef, the meatball would become dry and tough by the time the enough heat reached the center.

So the meatball will need to be cooked at a lower temperature for longer with some additions to keep the meat from drying out.

(Lucky for you, we cover the secret to moist and tender meatballs in this post.)

So next time you wonder how long something will take to cook, remember to think about the distance to the center of the food.

One more note on surface area to volume ratio. If you’ve ever watched cooking competition shows, you may have noticed that judges get picky about how uniformly food gets diced up. This is because the differences in sizes will cook at different rates and therefore will cause the food to not be uniformly done when cooked together.

This is a small detail more important to chefs than you and I just wanting to get food on the table. But the next time you see this, pat yourself on the back for knowing the scientific reason behind this critique!

Next in the Series …

We will delve into the world of Diffusion, or why flavor moves into or out of foods.

John and Sarah Gilbert farm with their family in North Central Iowa. They care for pigs, cows, and the land to bring you beef and pork you can love. They have a passion for cooking and helping others develop the skills they need to put healthy and delicious home-cooked meals on the table. They can be contacted by email and through Facebook and Instagram.