Before we get into the amount of energy produced from these hot dogs, I will go over some basics of cellular respiration. In very simple terms, cellular respiration is a metabolic process by which the mitochondria of a cell tries to break down mainly organic molecules, like glucose, into a more easily accessed form of energy for cells, ATP. This aerobic process is defined by three main steps: glycolysis, the Krebs Cycle (also known as the Citric Acid Cycle) and oxidative phosphorylation in the electron transport chain (ETC). Glycolysis operated in the cytoplasm is when glucose is split into two pyruvate molecules releasing energy in the form of ATP (a small amount) and electrons which are captured by NAD+ producing NADH. These pyruvate molecules then enter the mitochondria and the Krebs cycle where their molecular structure is manipulated and altered to produce NADH, FADH2, the biproduct CO2, and a small amount of ATP. Lastly with oxidative phosphorylation, the ETC of the mitochondria utilizes all of the electrons in the NADH and FADH2 molecules to move hydrogen molecules out of the cell thus creating a concentration gradient. When the hydrogen molecules cross the ETC through ATP synthase in an attempt to achieve equilibrium, they provide the energy needed to add a phosphate to ADP thus making ATP! The gradient is sustained by O2 molecules that adopt extra hydrogen ions to produce water (H2O). If oxygen is not present, glycolysis is followed by anaerobic fermentation (either alcoholic or lactic acid) to provide a steady supply of NAD+ to sustain glycolysis.
Now back to hot dogs! Hot dogs do not have glucose, but they are known to have fat. Fat is commonly used by the body to store energy. This is why if you eat a lot of food without "burning" this energy through exercise, odds are your body will have a substantial amount of fat. According to the USDA, one hot dog has approximately 13 grams of fat. Using Avogadro's number (6.0223 x 10^23), we can determine one hot dog has approximately 78,289,900,000,000,000,000 molecules of fat. That is cool, but we are well aware Joey Chestnut does not eat only 1 hot dog. Maybe "inhales" is a better word to describe how he scarfs down hot dogs.
Last year, Joey Chestnut won the competition by eating 61 hot dogs (Thanks Wikipedia)! Based on information from this source, a molecule of fat produces 112 ATP molecules. Therefore it can be determined that when Joey Chestnut won the hot dog contest last year, he ultimately gained 53,487,659,680,000,000,000,000,000,000 ATP molecules. I usually hate people who make comments like the one I'm about to say, but it has to be acknowledged that millions of people are starving in the world without a reliable source of food, and meanwhile in America, we are gorging ourselves with hot dogs for fun!
The cells receiving all of this energy in the form of fat will most likely not break all of it down into ATP at one time. That's just dumb. The human body would not need all of this energy at once, and if you do, then you should see a doctor. For example, would you use an entire gallon of paint if you only had to paint a small piece of paper? No. This paint could be saved and used for when it's needed. This is the basic idea behind feedback mechanisms. Feedback mechanisms, or feedback inhibition, is where a product of a metabolic reaction inhibits an enzyme that is important in making an early step of the catabolic process possible. So if there is a large amount of ATP in the body, ATP will inhibit an enzyme involved in a step like glycolysis to inhibit the production of ATP. Then when the body needs more ATP, the enzyme will no longer be inhibited. You could also argue that instead of relying on feedback inhibition, you could just refrain from eating 61 hot dogs. That is very true, but you see, an alpha male does what an alpha male wants.