WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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Mount KÄ«lauea is disgorging five times
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ten to the five cubic meters of
lava every day.
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And the lava has a temperature initially of
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1200 degrees Celsius and it has a
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density of 2700 kilograms per cubic meter
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and the final temperature of
30 degrees Celsius.
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And, we're told that the lava
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has properties of granite and so its
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specific heat is 840 Joules per kilogram
per Celsius degree.
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So, when it cools from
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1200 degrees Celsius to 30,
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given this specific heat and a certain
amount of mass
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which we'll figure out based on
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density in this volume rate of transfer
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from inside the earth to the outside,
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we'll figure out what is the rate of
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heat transfer from the inside of the earth
to the outside.
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Okay.
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So, the rate of heat transfer of
all this lava.
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Alright.
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So, power is what we want to find.
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And, it's the amount of heat
divided by time.
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And, the amount of heat is going to be the
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mass of the lava times the specific heat
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times its change in temperature from
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1200 to 30 degrees Celsius.
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Now, the mass we don't precisely
know directly,
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and so we need to figure it out
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based on knowing density.
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And, density is mass divided by volume.
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We can solve for *M* by multiplying
both sides by *V*,
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so mass is volume multiplied by density.
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So, we substitute for that in place of *M*.
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We write that here in red.
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And then, substitute all of this
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in place of *Q* in our power formula.
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So, power is going to be
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volume times density times specific heat
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times change in temperature
divided by time.
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And, I'm rewriting this slightly
by writing this
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as volume over time times rho *C* *Delta T*
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because volume over time is something
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that we're given directly.
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It is this quantity,
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five times ten to the five cubic meters
per day.
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So, we have five times ten to the five
cubic meters per day,
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but we have to write day
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in units of seconds in order to have
*M* *K* *S* units
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as we need to have in almost
all of our formulas.
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So, one day times 24 hours per day
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times 3600 seconds per hour gives us
a day in seconds.
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And so, all this gets multiplied by
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2700 kilograms per cubic meter density
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times 840 Joules per kilogram
per Celsius degrees
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specific heat of granite,
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times 30 degrees Celsius minus
1200 degrees Celsius.
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And so, we have a power output of
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-1.536 times ten to the ten watts.
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And so, this is power being lost,
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and so we'll write it as a
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positive number here by saying
it's power lost by the lava,
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two times ten to the ten watts.
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And, we can have only one
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significant figure here because
we have this
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volume rate of transfer is only one
significant figure.