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This is College Physics Answers
with Shaun Dychko.
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One foot is standing on a ceramic tile
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and the other foot is standing on
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Sobel carpet and the top of the ceramic
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or wool is meant to be at a temperature of
33 degree Celsius
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or we are gonna call that *T2*
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because in our formula for thermal rate of
thermal conduction, we have *T2*
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representing the body from which the heat
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leaves and it goes towards body one
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and so we have heat going from the top
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so thatâ€™s at the higher temperature
so that's *T2*
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going towards the bottom of this thickness
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of ceramic or thickness of wool
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and the bottom is *T1* and that's
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temperature 10 degree Celsius and so
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the question is at what rate must heat be
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be transferred from the foot
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to the top of the ceramic or wool,
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in order to maintain this 33 degree
Celsius temperature
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and that'll be the same as the rate
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with which the top is losing energy
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to the bottom and so that's why
we are calculating this.
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This is the rate at which energy is
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transferred from the top of the ceramic to
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the bottom of the ceramic.
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And so since the top is losing
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energy at that rate,
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it needs to gain that same rate of energy
from the foot.
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Now the foot area is 80 square centimeters
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which we multiplied by one meter for every
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100 centimeters squared to get
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0.008 squared meters and the thickness is
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two centimeters which is two times ten
to the minus two meters.
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Taking care always of unit conversions.
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In this step we rewrite down the information
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that we know so we don't have to think
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about this later.
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All right.
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So we have the rate of thermal energy
conduction is the
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thermal conductivity of the material
which in the case of ceramic
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we take to be that of
concrete or brick
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0.84 Jules per second per meter per
Celsius degree
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and the thermal connectivity of wall
is 0.04.
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OK.
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So if thermal conductivity multiplied by area
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times the temperature difference divided by
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the thickness of a material and so
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we can substitute for all of these things
except for *K*
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and to get a formula into which
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we just plug *K* for ceramic
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and then *K* for wool to get our answers.
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So if K times 0.008 squared meters
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times 33 degree Celsius minus
10 degree Celsius
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divided by two centimeters giving us *K*
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multiplied by this 9.2 meters
Celsius degrees
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which are kind of nonsensical units
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but they are what works out from multiplying
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and dividing all these things and then
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when you multiply by *K*, it will end
up being watts.
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So for ceramic the rate of heat transfer is
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going to be 0.84 Joules per second
per meter per Celsius degree
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times 9.2 meter Celsius degrees
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and the meter and Celsius degrees cancel
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and sure enough the units are
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joules per second which is watts,
7.7 watts,
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of energy needs to be given to the top
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of the ceramic from the foot in order to
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maintain this rate of heat transfer
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across the thickness of the ceramic
towards the bottom
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and then for the wool
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we plug in 0.04 instead of 0.84
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and we end up with 0.4 watts
and so you can see
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the wool is a much better insulator
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due to its lower thermal conductivity
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and we are seeing that in this
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rate of heat transfer is much lower
than that for ceramic.