Radioactive decay of granite and other rocks in Earth’s interior provides sufficient energy to keep the interior molten, to heat lava, and to provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. Show that a 500°C increase in temperature for a thermally insulated chunk of granite takes about 13.3 million years. (Assume that the specific heat capacity ?c? of granite is 800 J/kg·C°. Use the equation Q ? ? =? m??? ?)
Specific heat formula is given Q = mcT Given data: Specific heat capacity of granite c = 800 J/kg c 0 Change in temperature T = 500 C Rate of energy production Q = 0.03 J/kg year Assume mass of granite as m = 1 kg Q = mcT Q = 1(800)(500) Q = 400000 J 400000 J/0.03 J/kg year 4/3 × 10 kg/year 7 1.33 × 10 kg/year 6 13.3 × 10 kg/year 13.3 million year Hence A 500°C increase in temperature for a thermally insulated chunk of granite takes about. 13.3 million years.