Making a solar hot-dog oven is a science fair standby, but JohnW539's CNC-milled Sundogger Instructable really digs into the classroom portion, drawing on the creator's experience as a physics/astronomy/computer science prof at Middle Tennessee State University.
Detailed scientific measurements have show that a typical hot dog has a diameter of about 1 inch of about 2.5 cm. This gives us a hot dog radius of about 1.25 cm. (Precision measurements of hot dogs put this number at 2.726 cm in diameter - but your actual hot dog diameter may vary.) The volume of a hot dog - or anything - is its length times its cross sectional area. The cross sectional area is going to be A = Pi times the radius squared. This means that every linear centimeter of the hot dog has a volume of (1.25 x 1.25 x 3.14) = 5ish cubic cm.
The mass of any object is the density times the volume. According to the manufacturer of the hot dogs I used, each dog has a mass of 57 grams. With the length of the hot dog measured at about 12 cm, this gives us a volume of about 4.8 grams per hot dog cm. This estimate puts the typical hot dog density just below 1 grams per cubic cm.
Combining these energy input per centimeter and the mass per centimeter, we find that we have 117 / 4.8 = 24 calories of energy per gram being added to the hot dog every minute. Thus in every second, we get enough energy to raise the hot dog temperature about 24 degrees Celsius every minute when it's internal temperature is about 20C.
The Sundogger [JohnW539/Instructables]
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