<< Chapter < Page Chapter >> Page >

Conduction is caused by the random motion of atoms and molecules. As such, it is an ineffective mechanism for heat transport over macroscopic distances and short time distances. Take, for example, the temperature on the Earth, which would be unbearably cold during the night and extremely hot during the day if heat transport in the atmosphere was to be only through conduction. In another example, car engines would overheat unless there was a more efficient way to remove excess heat from the pistons.

How does the rate of heat transfer by conduction change when all spatial dimensions are doubled?

Because area is the product of two spatial dimensions, it increases by a factor of four when each dimension is doubled A final = ( 2 d ) 2 = 4 d 2 = 4 A initial size 12{A rSub { size 8{"final"} } = \( 2d \) rSup { size 8{2} } =4d rSup { size 8{2} } =4A rSub { size 8{i"nitial"} } } {} . The distance, however, simply doubles. Because the temperature difference and the coefficient of thermal conductivity are independent of the spatial dimensions, the rate of heat transfer by conduction increases by a factor of four divided by two, or two:

Q t final = kA final T 2 T 1 d final = k 4A initial T 2 T 1 2d initial = 2 kA initial T 2 T 1 d initial = 2 Q t initial . size 12{ left ( { {Q} over {t} } right ) rSub { size 8{"final"} } = { { ital "kA" rSub { size 8{"final"} } left (T rSub { size 8{2} } - T rSub { size 8{1} } right )} over {d rSub { size 8{"final"} } } } = { {k left (4A rSub { size 8{"initial"} } right ) left (T rSub { size 8{2} } - T rSub { size 8{1} } right )} over {2d rSub { size 8{"initial"} } } } =2 { { ital "kA" rSub { size 8{"initial"} } left (T rSub { size 8{2} } - T rSub { size 8{1} } right )} over {d rSub { size 8{"initial"} } } } =2 left ( { {Q} over {t} } right ) rSub { size 8{"initial"} } } {}
Got questions? Get instant answers now!

Summary

  • Heat conduction is the transfer of heat between two objects in direct contact with each other.
  • The rate of heat transfer Q / t size 12{Q/t} {} (energy per unit time) is proportional to the temperature difference T 2 T 1 size 12{T rSub { size 8{2} } - T rSub { size 8{1} } } {} and the contact area A size 12{A} {} and inversely proportional to the distance d size 12{d} {} between the objects:
    Q t = kA T 2 T 1 d . size 12{ { {Q} over {t} } = { { ital "kA"` left (T rSub { size 8{2} } - T rSub { size 8{1} } right )} over {d} } } {}

Conceptual questions

Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot placed over a heating element will be heated, while it is safe to touch the surface only a few centimeters away. Why is ceramic, with a conductivity less than that of a metal but greater than that of a good insulator, an ideal choice for the stove top?

Got questions? Get instant answers now!

Loose-fitting white clothing covering most of the body is ideal for desert dwellers, both in the hot Sun and during cold evenings. Explain how such clothing is advantageous during both day and night.

The figure shows a group of musicians wearing long, loose-fitting lightly colored robes that go down to their feet.
A jellabiya is worn by many men in Egypt. (credit: Zerida)
Got questions? Get instant answers now!

Problems&Exercises

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is 120 m 2 and their inside surface is at 18. C , while their outside surface is at 5 .00º C . (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

(a) 1.01 × 10 3 W

(b) One

Got questions? Get instant answers now!

The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly the windows transfer heat by conduction, calculate the rate of conduction in watts through a 3 . 00-m 2 window that is 0 .635 cm size 12{0 "." "635"`"cm"} {} thick (1/4 in) if the temperatures of the inner and outer surfaces are 5 .00ºC and 10 . C , respectively. This rapid rate will not be maintained—the inner surface will cool, and even result in frost formation.

Got questions? Get instant answers now!

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is 37 . C , the skin temperature is 34 . C , the thickness of the tissues between averages 1 .00 cm , and the surface area is 1 . 40 m 2 .

84.0 W

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask