Baked Alaska!

     Alaska Jones can't believe how warm it is on the Florida beach. It's no place like Nome! The sand is piled high, the sun is shining, and Alaska is baking. 

     Are you ready for a challenge? Alaska is under 12 kg of sand with a surface area of 
1 m2 and a specific heat of 0.84 kJ / (kg-C°). The sun delivers 1.4 kW / m2 but the sand reradiates heat at the rate of 1.3 kW / m2. If the sand's (and Alaska's) initial temperature was 37° Celsius; what will the temperature of the sand be after two hours of baking? 

      Dessert is waiting, if you get this right! 

The temperature increase equals the total energy delivered by the sun, less that reradiated, divided by the specific heat capacity and the mass of sand. The energy retained is (1.4-1.3) kJ/s x 7200 s = 720 kJ. 

720 kJ / (12 kg x .84 kJ/(kg-C°) = 71.4 C°.

The final temperature of the sand will be (37° C + 71.4 C°) = 108° C. That's hot!

Dessert is served! 

 
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Last updated 4/19/98