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Two rectangular blocks are shown with the right one labeled T one and the left one labeled T two. The blocks are placed on a surface at a distance d from each other, so that their largest face faces the opposite block. The block T one is cold and the block T two is hot. The blocks are connected to each other with a conducting rectangular block of thermal conductivity k and cross-sectional area A. A wavy line labeled Q is inside the conducting block and points from the hot block to the cold block.
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T 2 size 12{T rSub { size 8{2} } } {} on the left and T 1 size 12{T rSub { size 8{1} } } {} on the right, where T 2 size 12{T rSub { size 8{2} } } {} is greater than T 1 size 12{T rSub { size 8{1} } } {} . The rate of heat transfer by conduction is directly proportional to the surface area A size 12{A} {} , the temperature difference T 2 T 1 size 12{T rSub { size 8{2} } - T rSub { size 8{1} } } {} , and the substance’s conductivity k size 12{k} {} . The rate of heat transfer is inversely proportional to the thickness d size 12{d} {} .

Lastly, the heat transfer rate depends on the material properties described by the coefficient of thermal conductivity. All four factors are included in a simple equation that was deduced from and is confirmed by experiments. The rate of conductive heat transfer    through a slab of material, such as the one in [link] , is given by

Q t = kA ( T 2 T 1 ) d , size 12{ { {Q} over {t} } = { { ital "kA" \( T rSub { size 8{2} } - T rSub { size 8{1} } \) } over {d} } } {}

where Q / t size 12{Q/t} {} is the rate of heat transfer in watts or kilocalories per second, k size 12{k} {} is the thermal conductivity    of the material, A size 12{A} {} and d size 12{d} {} are its surface area and thickness, as shown in [link] , and ( T 2 T 1 ) size 12{ \( T rSub { size 8{2} } - T rSub { size 8{1} } \) } {} is the temperature difference across the slab. [link] gives representative values of thermal conductivity.

Calculating heat transfer through conduction: conduction rate through an ice box

A Styrofoam ice box has a total area of 0 .950  m 2 and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned beverages at 0ºC . The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the trunk of a car at 35 . 0ºC size 12{"35" "." "0°C"} {} ?

Strategy

This question involves both heat for a phase change (melting of ice) and the transfer of heat by conduction. To find the amount of ice melted, we must find the net heat transferred. This value can be obtained by calculating the rate of heat transfer by conduction and multiplying by time.

Solution

  1. Identify the knowns.
    A = 0 . 950  m 2 d = 2 . 50  cm = 0 .0250 m; T 1 = C; T 2 = 35 . C, t = 1 day = 24 hours = 86,400 s.
  2. Identify the unknowns. We need to solve for the mass of the ice, m size 12{m} {} . We will also need to solve for the net heat transferred to melt the ice, Q size 12{Q} {} .
  3. Determine which equations to use. The rate of heat transfer by conduction is given by
    Q t = kA ( T 2 T 1 ) d . size 12{ { {Q} over {t} } = { { ital "kA" \( T rSub { size 8{2} } - T rSub { size 8{1} } \) } over {d} } } {}
  4. The heat is used to melt the ice: Q = mL f . size 12{Q= ital "mL" rSub { size 8{f} } } {}
  5. Insert the known values:
    Q t = 0.010 J/s m ⋅º C 0.950  m 2 35. C C 0.0250 m = 13.3 J/s.
  6. Multiply the rate of heat transfer by the time ( 1  day = 86,400  s size 12{1`"day=86,400"`s} {} ):
    Q = Q / t t = 13 . 3  J/s 86 , 400  s = 1 . 15 × 10 6  J. size 12{Q= left ( {Q} slash {t} right )t= left ("13" "." 3`"J/s" right ) left ("86","400"`s right )=1 "." "15" times "10" rSup { size 8{6} } `J} {}
  7. Set this equal to the heat transferred to melt the ice: Q = mL f size 12{Q= ital "mL" rSub { size 8{f} } } {} . Solve for the mass m size 12{m} {} :
    m = Q L f = 1 . 15 × 10 6  J 334  × 10 3  J/kg = 3 . 44 kg. size 12{m= { {Q} over {L rSub { size 8{f} } } } = { {1 "." "15" times "10" rSup { size 8{6} } `J} over {"334" times "10" rSup { size 8{3} } `"J/kg"} } =3 "." "44"`"kg"} {}

Discussion

The result of 3.44 kg, or about 7.6 lbs, seems about right, based on experience. You might expect to use about a 4 kg (7–10 lb) bag of ice per day. A little extra ice is required if you add any warm food or beverages.

Inspecting the conductivities in [link] shows that Styrofoam is a very poor conductor and thus a good insulator. Other good insulators include fiberglass, wool, and goose-down feathers. Like Styrofoam, these all incorporate many small pockets of air, taking advantage of air’s poor thermal conductivity.

Thermal conductivities of common substances At temperatures near 0ºC.
Substance Thermal conductivity k (J/s⋅m⋅ºC)
Silver 420
Copper 390
Gold 318
Aluminum 220
Steel iron 80
Steel (stainless) 14
Ice 2.2
Glass (average) 0.84
Concrete brick 0.84
Water 0.6
Fatty tissue (without blood) 0.2
Asbestos 0.16
Plasterboard 0.16
Wood 0.08–0.16
Snow (dry) 0.10
Cork 0.042
Glass wool 0.042
Wool 0.04
Down feathers 0.025
Air 0.023
Styrofoam 0.010

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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