# 8.5 Conduction  (Page 4/8)

 Page 4 / 8

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 $\left({A}_{\text{final}}=\left(2d{\right)}^{2}=4{d}^{2}=4{A}_{\mathrm{initial}}\right)$ . 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:

${\left(\frac{Q}{t}\right)}_{\text{final}}=\frac{{\text{kA}}_{\text{final}}\left({T}_{2}-{T}_{1}\right)}{{d}_{\text{final}}}=\frac{k\left({\text{4A}}_{\text{initial}}\right)\left({T}_{2}-{T}_{1}\right)}{{2d}_{\text{initial}}}=2\frac{{\text{kA}}_{\text{initial}}\left({T}_{2}-{T}_{1}\right)}{{d}_{\text{initial}}}=2{\left(\frac{Q}{t}\right)}_{\text{initial}}\text{.}$

## Summary

• Heat conduction is the transfer of heat between two objects in direct contact with each other.
• The rate of heat transfer $Q/t$ (energy per unit time) is proportional to the temperature difference ${T}_{2}-{T}_{1}$ and the contact area $A$ and inversely proportional to the distance $d$ between the objects:
$\frac{Q}{t}=\frac{\text{kA}\left({T}_{2}-{T}_{1}\right)}{d}\text{.}$

## 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?

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.

## 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 $\text{120}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ and their inside surface is at $\text{18.}0º\text{C}$ , while their outside surface is at $5\text{.00º}\text{C}$ . (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

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 $3\text{.}{\text{00-m}}^{2}$ window that is thick (1/4 in) if the temperatures of the inner and outer surfaces are $5\text{.00ºC}$ and $-\text{10}\text{.}0º\text{C}$ , respectively. This rapid rate will not be maintained—the inner surface will cool, and even result in frost formation.

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is $\text{37}\text{.}0º\text{C}$ , the skin temperature is $\text{34}\text{.}0º\text{C}$ , the thickness of the tissues between averages , and the surface area is $1\text{.}\text{40}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ .

84.0 W

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!