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.
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.
Finally someone speaking english.
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.
Well, there you go, free lunch for every schoolkid. Silver lining.