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 takes about 12.5 million years. (Assume that the specific heat capacity c of granite is 800 J/ kg*C (celcius) Use the equation Q =cm \Delta T.)

Question

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 takes about 12.5 million years. (Assume that the specific heat capacity c of granite is 800 J/ kg*C (celcius) Use the equation Q =cm \Delta T.)

Answer 1

To find the increase in temperature for a thermally insulated chunk of granite over a period of 12.5 million years, we can use the equation Q = cmΔT, where Q is the heat energy, c is the specific heat capacity of granite, m is the mass of the granite, and ΔT is the change in temperature.

Given:
Specific heat capacity of granite (c) = 800 J/kg*C
Time (t) = 12.5 million years = 12.5 × 10^6 years = 12.5 × 10^6 years × 365 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute (to convert years to seconds)

We are looking for ΔT, the change in temperature. Rearranging the equation Q = cmΔT, we can solve for ΔT by dividing both sides of the equation by cm: ΔT = Q / (cm).

We are given the value of Q as the average release of 0.03 J per kilogram each year. Since we want to find the temperature increase over 12.5 million years, we need to multiply Q by the total time in seconds.

Let's calculate the change in temperature:

First, convert the time to seconds:
12.5 million years = 12.5 × 10^6 years × 365 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 12.5 × 10^6 × 365 × 24 × 60 × 60 seconds

Now, multiply Q by the time:
Q = 0.03 J/kg/year × (12.5 × 10^6 × 365 × 24 × 60 × 60 seconds)

Next, we need to find the mass of the granite. Since it is not provided, let's assume a typical value of 1 kilogram for simplicity.

Now, substitute the values into the equation ΔT = Q / (cm):
ΔT = (0.03 J/kg/year × (12.5 × 10^6 × 365 × 24 × 60 × 60 seconds)) / (800 J/kg*C × 1 kilogram)

Simplifying the equation, we get:
ΔT = (0.03 × 12.5 × 10^6 × 365 × 24 × 60 × 60) / 800

Calculating this expression will give us the change in temperature.