Skeptics of the proposed hyperscale data center in Box Elder County are sweating about a lot more than its energy demands and potential toll on water supplies.
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.
Let’s also assume the heat capacity of the hot dog is about 3000 J/kg*K
So the specific heat of water at those temperatures is 4184 J/kg K, and those food court hot dogs are probably about the same as Kirkland dinner franks, which have about 73g of water, 31 g of fat (specific heat of about 2300 J/ kg K), 16g of protein (1500 J/kg K), and 3g of sugars/carbs (1200 J/kg K), and let’s say negligible ash, so we’re left with a weighted average of about 3280 J/kg K.
That’s within 10% of your assumed value, so I think I just wasted my time trying to check your assumption, which was pretty close to my number that took a lot more work.
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.
Finally someone speaking english.
Well, there you go, free lunch for every schoolkid. Silver lining.
So the specific heat of water at those temperatures is 4184 J/kg K, and those food court hot dogs are probably about the same as Kirkland dinner franks, which have about 73g of water, 31 g of fat (specific heat of about 2300 J/ kg K), 16g of protein (1500 J/kg K), and 3g of sugars/carbs (1200 J/kg K), and let’s say negligible ash, so we’re left with a weighted average of about 3280 J/kg K.
That’s within 10% of your assumed value, so I think I just wasted my time trying to check your assumption, which was pretty close to my number that took a lot more work.
The math you just did terrifies me and I have no way of verifying it, so I’ll just say good job and leave it at that.
I think it’s also important to have a hotdogs per day figure, and the math from here is super simple, so I can do it.
384,1236060*24 = 33,188,227,200 hot dogs per day.