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.

Find an increase in temperature for a thermally insulated chunk of granite that takes about 12.5 million years to change temperature. (Assume that the specific heat capacity c of granite is 800 J/kg⋅C∘. Use the equation Q=cmΔT.)

Respuesta :

Answer: [tex]468.75^0C[/tex]

Explanation:

The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.

[tex]Q=m\times c\times \Delta T[/tex]

Q = Heat absorbed

Given : heat released in 1 year = 0.03 J/kg

heat released in 12.5 million years=[tex]\frac{0.03 J}{1}\times 12.5\times 10^6=375000J/kg[/tex]

m= mass of substance = 1 kg

c = specific heat capacity = [tex]800J/kg^0C[/tex]

Initial temperature of the water = [tex]T_i[/tex]

Final temperature of the water = [tex]T_f[/tex]

Change in temperature ,[tex]\Delta T=T_f-T_i=?[/tex]

Putting in the values, we get:

[tex]375000J/kg=1kg\times 800J/kg^0C\times \Delta T[/tex]

[tex]\Delta T=468.75^0C[/tex]

The increase in temperature for a thermally insulated chunk of granite is [tex]468.75^0C[/tex]

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