The Physics of Ballpark Fare

As Humphrey Bogart once said, “A hot dog at the ballgame beats roast beef at the Ritz.” That was back in the day when you had two choices – a hot dog or hunger. Now, there are more tubular food choices then there are cable TV stations.

In April of 2015, CBS Sports tried to list some of the best stadium hot dogs. Their list included everything from the bacon-wrapped Beast of Milwaukee to the Arizona D-Bat, a one-and-a-half foot long corn dog. If those aren’t enough to send your cardiologist into an infarction, the Churro Dog will do the trick – a churro nestled in a maple bar bun topped with ice cream, whipped cream, and chocolate sauce. Where’s my Lipitor?!?!?

Hot dogs of all types are cooked by having heat flow from their surface inward toward the center. Since a THT article isn’t worth the paper it’s written on (or bytes it’s made of) unless it contains several heat maps, below are two that describe actual heat as opposed to the never-ending array of sabermetric statistics of yet-to-be-determined utility.

A hot dog sitting on a grill will have heat flow upward into – for lack of a better word – the meat. The dog has the highest temperature where it contacts the grill at the bottom (red). The temperature drops toward the top (blue and violet). Of course, rotating the tube steak as it cooks will yield a more uniform heat distribution.

The D-Bat is not cooked on a grill. Instead, it is plunged into a vat of hot oil, causing it to be heated uniformly from the outside inward. Here’s a heat map that might represent the temperature distribution that is higher on the outside and cooler on the inside.

Now that I’ve delivered the obligatory heat maps and we’ve had our main dish, let’s think about washing it down. Just humor me for a moment, and let’s start by assuming we’ll have a carbonated soft drink. Out west here we call it a “soda,” but I’ve heard others call it a “pop.” Whatever…

Have you ever noticed that a soda stays cold much longer than a beer? I guess you don’t need to be a physicist to understand why. It’s the ice. The air that surrounds the soda supplies heat. It is amazing that somehow the heat is first used to melt the ice, leaving the temperature of the soda/ice mixture unchanged until the last of the ice is gone. Then the heat starts raising the temperature.

Below is a graph of the temperature of soda versus time on an 80˚ day. I estimated it takes about twenty minutes for the last of the ice to melt, so the temperature stays at a constant 32˚F during this time. Once the ice is gone, the temperature increases rapidly at first, eventually approaching the 80˚F ambient temperature of the air.

You might not have ever thought about this, but the fact that ice floats in water means it is less dense than the water it is made from. Pretty strange considering almost all solid objects are more dense than the liquid of the same material.

If ice were denser than water it would sink. Therefor in winter, lakes would freeze from the bottom up. Ice fishing would become a simple exercise of walking out on the frozen lake and picking ‘em up. So much for a day of camaraderie in your man cave…but we’ve wandered far afield from the concessions available at the ballpark.

Back to the physics of soda…the carbonation comes from carbon dioxide gas (CO₂) injected into the liquid at the dispenser. Here lies another fascinating property of many liquids. Instead of the CO₂ gas all immediately leaving the fluid, it prefers to hide between the molecules of the liquid.

It is really complicated to explain why the gas prefers to hide than to leave all at once. So, I’ll just say something stupid like, “It is energetically favorable for the CO₂ molecules to remain in the liquid.” Of course, they don’t remain suspended forever.

The carbon dioxide is happy in the liquid as long as the fluid is still and in a smooth container. Look carefully for the origin of the bubbles. You will almost always find they begin on a small speck of something or an imperfection on the surface of the cup. This provides a place for the CO₂ to collect, forming a small bubble. Once a bubble forms, other carbon dioxide molecules want to join the party.

The bubble eventually gets large enough to break away from the wall and float to the surface – carbonation! You can also coax CO₂ out of the fluid with agitation, as the World Series champions always do by shaking the champagne bottles.

Yes, this is the same carbon dioxide that is wreaking havoc with the planet’s climate. However, you need not feel guilty about the carbonation of your drink for two reasons. The CO₂ emitted from your soda was collected from the atmosphere in the first place, so it doesn’t contribute to increasing the net amount in the air. Besides, you took public transit to the game, saving the much larger amount of carbon dioxide from the petroleum burned by your car’s engine – right?

The source of bubbles in beer is also CO₂, but it is not artificially injected. Instead, beer is brewed by taking a bunch of wet grains and introducing a little creature called yeast. Yeast eats the carbohydrates in the grain and, like all creatures great and small, must eliminate wastes. Yeast’s loss is our gain as it pisses out alcohol and farts CO₂.

Unlike soda with ice, beer begins to warm from the minute it is poured until it reaches ambient temperature. Below is a graph comparing the temperature of beer and soda over time. By my estimates, the beer reaches 75˚F in about fifteen minutes while the soda is still ice cold.

So I guess one solution to a beer’s rapid heating is to drink as quickly as possible. To mitigate the financial and social problems that might ensue, teams often have beer koozie give-aways. Koozies provide insulation, slowing the rate of heat flow from the air into the beer.

Beer is sold in several different containers at the ballpark. Which one do you think provides the most insulation; a thin plastic cup, an aluminum bottle, or a plastic bottle? The answer turns out to be a glass bottle, but good luck finding one of those at the stadium.

Second best is the plastic bottle, next the plastic cup, and in last place is the aluminum bottle. Plastic is a reasonable good insulator, but metals are terrible. Heat flows right through them. So why do they sell so many beers in aluminum bottles? Well, if heat flows into them easily, then heat will flow out of them easily also. They are convenient for the concessionaires because they cool off quickly.

I could go on to dessert, but I’m betting you’re already over-stuffed with food for thought.