1. Radioactive decay of granite and other rocks in the Earth\'s interior provide
ID: 1539183 • Letter: 1
Question
1. Radioactive decay of granite and other rocks in the Earth's interior provides enough energy to keep the interior molten, heat lava, and provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. How many years are required for a chunk of thermally insulated granite to increase 600° C in temperature (assume the specific heat of granite is 800 J/kg ° C)?
million years
2. In a 25°C room, hot coffee in a vacuum flask cools from 72°C to 48°C in eight hours. What will its temperature be after another eight hours?
°C
Explanation / Answer
1) Q = mCp*DT
m = 1 kg, Cp = 800 J/kg, DT = 600 oC
Q = 1*800*600 = 480000 J
0.03 J per kg energy released in 1 year
480000 J per kg energy released in N years
N = 480000*1/0.03 = 16 million years
2) Tf = To *e^(-k*t)
(48+273) = (72+273)*e^(-k*8)
k = 0.009
Tf = (72+273)*e^(-0.009*16)
Tf = 289.73 K= 289.73 -273
Tf = 16.73 OC
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