Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q. 1.61 (page 40)

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 by20∘Cper kilometer of depth and the thermal conductivity of the rock is 2.5W/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 the earth's surface, at approximately what rate is the earth losing heat via conduction? (The radius of the earth is 6400km.)

Short Answer

Expert verified

Rate of heat conduction and the rate at which the earth loses heat via conduction

QΔt=0.05W

QtotalΔt=2.573×1013

Step by step solution

01

Calculation of ratio

Because the rock that makes up the Earth's crust has a thermal conductivity and there is a temperature differential between a point underground and the Earth's surface, the Earth loses energy through heat conduction. We've calculated the following using Schroeder's values:ΔT=20∘Kper Δx=1000mand kt=2.5W∘K−1, the rate of heat conduction in an area of 1m2is, therefore:

localid="1651746825640" QΔt=ktAΔTΔx=2.5×1×201000=0.05W/m2

localid="1651746839506" QΔt=0.05W/m2

02

Calculation of heat

Even if the rate of heat loss for a square metre is fairly low, if we assume that this figure applies to the entire Earth, the total heat loss is:

QtotalΔt=Loss per meter square×Total area of earth

QtotalΔt=0.05×4πr2=0.05×4π6400×1032

QtotalΔt=2.573×1013W

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in the given figure.

Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are "frozen out." Also assume that the only type of work done on the gas is quasistatic compression-expansion work.

(a) For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of P1,P2,V1,andV2. (Hint: Compute ΔUbefore Q, using the ideal gas law and the equipartition theorem.)

(b) Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.

(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.

In analogy with the thermal conductivity, derive an approximate formula for the viscosity of an ideal gas in terms of its density, mean free path, and average thermal speed. Show explicitly that the viscosity is independent of pressure and proportional to the square root of the temperature. Evaluate your formula numerically for air at room temperature and compare to the experimental value quoted in the text.

A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule(i,e., its "atomic mass"), you know the approximate mass(in grams) of a mole of these molecules. Referring to the periodic table at the back of this book ,find the mass of a mole of each of the following : Water, nitrogen (N2), lead, quartz (Si O2)

Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecule are moving faster, on average? By what factor?

Derive the equation 1.40 from the equation 1.39
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Space Physics

Read Explanation

Thermodynamics

Read Explanation

Oscillations

Read Explanation

Torque and Rotational Motion

Read Explanation

Quantum Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free