Problem 61P
Geologists measure conductive heat flow out of the earth by drilling holes (a few hundred meters deep) and measuring the temperature as a function of depth. Suppose that in a certain location the temperature increases by 20°C per kilometer of depth and the thermal conductivity of the rock is 2.5 W/m∙K. What is the rate of heat conduction per square meter in this location? Assuming that this value is typical of other locations over all of earth’s surface, at approximately what rate is the earth losing heat via conduction? (The radius of the earth is 6400 km.)

Step-by-Step Solution:
Solution 61P

To solve this question, we shall have to consider the Fourier heat conduction law. The mathematical equation for Fourier heat conduction law is written as …..(1)

Here, amount of heat

time taken for the heat to flow

thermal conductivity

area of cross-section

change in temperature

change in length

We need to calculate .

Step 1</p>

Given,

Thermal conductivity

Considering the magnitude only, from equation (1)

The rate of heat conduction per square meter in this location is .

Since the solution to 61P from 1 chapter was answered, more than 284 students have viewed the full step-by-step answer. This full solution covers the following key subjects: EARTH, heat, rate, Conduction, location. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The full step-by-step solution to problem: 61P from chapter: 1 was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. The answer to “Geologists measure conductive heat flow out of the earth by drilling holes (a few hundred meters deep) and measuring the temperature as a function of depth. Suppose that in a certain location the temperature increases by 20°C per kilometer of depth and the thermal conductivity of the rock is 2.5 W/m?K. What is the rate of heat conduction per square meter in this location? Assuming that this value is typical of other locations over all of earth’s surface, at approximately what rate is the earth losing heat via conduction? (The radius of the earth is 6400 km.)” is broken down into a number of easy to follow steps, and 97 words.