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Cake day: June 12th, 2023

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  • Let’s assume Costco size hot dogs (1/4 lb, or 0.11 kg), with an internal temp increase from fridge temperatures (37 F, or 276 K) to 165 F (347 K). Let’s also assume the heat capacity of the hot dog is about 3000 J/kg*K. To heat up a single hot dog takes this much energy:

    q=mc*deltaT => q=(0.11 kg)*(3000 J/kg*K)*(347K-276K)=23,430 J of energy.

    The heat capacity here is 9GW. That is 9 gigajoules of energy per second, or 9 billion joules every second. Divide this by the number of joules to cook each hot dog gets us the number of hot dogs that could be cooked every second:

    9,000,000,000/23,430=384,123 hot dogs/second

    With this hot dogs per second figure, we can find how long this energy source would take to feed the entire US population a Costco hot dog.

    342,000,000 people/384,123 hot dogs per sec=890 seconds

    Converting this to minutes:

    890/60=14.8 minutes

    So, this source of energy could feed the entire population of the US a Costco hot dog in less than 15 minutes if properly harnessed.