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SOLUTIONS TO EXERCISE 8

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energy: TOC for Knowledge Concepts, Exercises, and Solutions


(a) From Exercise 6 above, the atomic bomb detonated over Hiroshima
released 1.8 * 10^13 Joules.  Thus, the energy released by the Tunguska
explosion is estimated to be

     10000 * 1.8 * 10^13 = 1.8 * 10^17 Joule.

(b) If 65% of the energy manifested as heat, that would be

     0.65 * (1.8 * 10^17 Joule) / (4.2 Joule/cal) = 2.8 * 10^16 cal.

(c) Remember that the heat capacity of water is 1 cal/g/degC.  So to
raise the temperature of one gram of water by 40 degrees C, you would
need 40 calories.  Thus, this Tunguska detonation could have heated
2.8 * 10^16 / 40 = 7.0 * 10^14 grams of water.  Since 1 gram of water
is one cubic centimter, the detonation could have heated up
7.0 * 10^14 cm^3 of water.

(d) A lake with an area of 100 km^2 has an area of 100 * (100,000 cm)^2
or 10^12 cm^2.  Since we know from Question 4(c) that this amount of
energy can heat 7.0 * 10^14 cm^3 of water by 40 degrees C, such a lake
would be thus heated down to a depth of

   7.0 * 10^14 cm^3
   ---------------- = 700 cm, or 7 m, or about 22 feet.
      10^12 cm^2 

Since a 40 degree rise in water temperature is generally fatal for 
water-borne animal life, this means that if a Tunguska meteorite
explosion occurred over a Manhattan-sized lake, everything down 
to a depth of 22 feet would die.  Of course, this assumes a perfectly
efficient transfer of energy from the explosion into the water, which
would never happen; still, it gives some sense of the scope of 
destruction that such a meteorite could produce.