| |||||||
SOLUTIONS TO EXERCISE 8
(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. |