Radioactive decay of granite -> How many years does it take?

[Voltman123]

Radioactive decay of granite ---> How many years does it take?

Homework Statement

Radioactive decay of granite and other rocks in the Earth's interior provides sufficient energy to keep the interior molten, to heat lava and to provide warmth to hot springs. This is due to the average release of about 0.03J per kilogram of granite each year. How many years are required for a "chunk" of thermally insulated granite to increase in temperature by 400°C. The specific heat capacity of granite is 800J/Kg°C.

Homework Equations

It looks like we've been given the change in temperature and the specific heat capacity for granite so it is likely that we will need to be using the equation:
Q=mcΔT

The Attempt at a Solution

Q=m(800)(400)
Not sure where to get the mass or value for Q though. So far, we have two unknowns.

Any help would be appreciated!

 

[SteamKing]

Assume the chunk of granite has a mass of 1 kg.

Q is given in the problem statement (re-read it very carefully).

 

[Voltman123]

Assume the chunk of granite has a mass of 1 kg.

Q is given in the problem statement (re-read it very carefully).

Q=mcΔT
0.03 =m(800)(400)

Are we trying to work out the mass here?
If so, after finding out the mass, how does this help us in enabling us to find the number years required for a chunk of thermally insulated granite to increase in temperature by 400°C?

Any help would be appreciated!

 

[SteamKing]

Hello! Assume the mass = 1 kg.

 

[Voltman123]

Hello! Assume the mass = 1 kg.

But then we have all numbers?
I still don't get how I'm supposed to find the number of years using all this information. :(

 

[Voltman123]

Hello! Assume the mass = 1 kg.

Also, when I do assume mass=1kg,
Q=mcΔT = 1(800)(400)= 320 000 joules


(320 000 joules)/(0.03 J/kg per year)
=10 666 666.67kg per year.

Am I on the right track.

How do I get rid of the Kg sign?

By dividing it by something in kg? But how?

 

[SteamKing]

If m = 1 kg, then the Q necessary to raise the temperature 400 C is 800 J /kg-C * 400 C = 320 kJ.

Alternatively, one could say that the amount of heat necessary to raise the temperature of an insulated piece of granite is 320 kJ/kg. Now, if the heat generated by radioactivity is 0.03 J/kg/year, how many years will it take to generate 320 kJ?

 

[Voltman123]

If m = 1 kg, then the Q necessary to raise the temperature 400 C is 800 J /kg-C * 400 C = 320 kJ.

Alternatively, one could say that the amount of heat necessary to raise the temperature of an insulated piece of granite is 320 kJ/kg. Now, if the heat generated by radioactivity is 0.03 J/kg/year, how many years will it take to generate 320 kJ?

10 666 666.67 years?

 

[Voltman123]

As (320 kJ/kg)/(0.00004 kJ/kg/year)
=10 666 666.67 years?

 

[Voltman123]

Please help me someone. I don't understand. Is this right or wrong?

 

[gneill]

Your method looks fine, and the result has the right value. Watch the significant figures though; use scientific notation.