14.5 Conduction  (Page 4/8)

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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 specific heat capacity of watee
what is mass
Siyanbola
@siyanbola Resistance to acceleration
Dillon
The specific heat capacity of water is 1 calorie/1C°/ for 1 gram of water . it means that number of calories required to raise the temperature of 1g of water from 15 to 16C° is 1.
Khalil
understood?
Khalil
I think it's 1 in joules/kgC
Dillon
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Khalil
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Khalil
Micheal
lawrence
what is acceleration
lawrence
rate of change of velocity is acceleration
Khalil
its amount of heat to raise the temlrature through one kelvin of substance .
ghulam
The amount of heat energy required to raise the température of water by 1K
Cffrrcvccgg
infact a it must be a unit mass of water
Cffrrcvccgg
approximately equal to 4184J/Kg/K
Cffrrcvccgg
Just got through thermodynamics last semester. Also a change in 1 degree in celcius is equivalent to a change in 1 degree kelvin
Dillon
Also it's 1J/kgK or 4.184 cal/gK or /gC
Dillon
I think, at least
Dillon
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Khalil
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Dillon
Numericals 🙄
Khalil
4200kJ/kgk...
Trevor
J
Trevor
SHM and uniform circular motion
Ishaq
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fitzgerald
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lawrence
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lasisi
In Inelastic collision cunculate the vilocity
elucidate
Usman
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Shii
explain how a body becomes electrically charged based on the presence of charged particles
induction
babar
induction
DEMGUE
definitely by induction
Raymond
induction
Raymond
induction
Shah
induction
Korodhso
please why does a needle sinks in water
DEMGUE
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Korodhso
induction
Auwal
what are the calculations of Newton's third law of motiow
what is dark matter
(in some cosmological theories) non-luminous material which is postulated to exist in space and which could take either of two forms: weakly interacting particles ( cold dark matter ) or high-energy randomly moving particles created soon after the Big Bang ( hot dark matter ).
Usman
if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
what is a galaxy
a galaxy is a type of phone e.g samsung galaxy there are diff types of samsung galaxy there is s5 s6 s7 s8 s9
lasisi
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flow rate is the volume of fluid which passes per unit time;
Rev
flow rate or discharge represnts the flow passing in unit volume per unit time
bhat
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
incomplete question
lasisi
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
nehemiah
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i don't know
y
nehemiah
what are the relationship between distance and displacement
They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
Thanks a lot
Usman
I'm beginner in physics so I can't reason why v=u+at change to v2=u2+2as and vice versa
Usman
what is kinematics
praveen
kinematics is study of motion without considering the causes of the motion
Theo
The study of motion without considering the cause 0f it
Usman
why electrons close to the nucleus have less energy and why do electrons far from the nucleus have more energy
Theo
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praveen
plz what is the third law of thermodynamics
third law of thermodynamics states that at 0k the particles will collalse its also known as death of universe it was framed at that time when it waa nt posible to reach 0k but it was proved wrong
bhat
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Hey Rev. it will
Jeff
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Chidera
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lasisi