WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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A person is inhaling
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one and a half liters of air
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which has a temperature of
37 degrees Celsius
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and a relative humidity of 40 percent.
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And, you have to go back to section 13.6
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if you want to review what
relative humidity means
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and it is the vapor density of
the water, in this case,
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divided by its saturation vapor density.
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And so, this is the maximum vapor density
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that can occur for water at
37 degrees Celsius.
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And so, we want to know
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what is the available density,
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how much water can still evaporate
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given that we're 40 percent to capacity,
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what capacity is remaining to contain
some more water vapor
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that is going to be evaporated from
inside the lungs.
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And, so that'll be, you know, 60 percent
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times the saturation vapor density.
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But I have written it out maybe
in a more rigorous way.
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So, we have the available density
is going to be
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the maximum possible
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saturation vapor density minus
the amount of density
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already taken up, which is 40 percent
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divided by 100 percent or 0.4 times this
44 grams per cubic meter.
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I had to look up this number,
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44 grams per cubic meter,
in section 13.6.
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That's the saturation vapor density
for water at 37 degrees Celsius.
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And so, we have 26.4 grams
per cubic meter of space,
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so to speak, available for evaporation.
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And so, let's figure out how much
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mass of water can fill that.
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And so, density of water is
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mass divided by volume
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and we can solve for mass by multiplying
both sides by *V*.
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And, we have *M* is density times volume.
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And so, the density that is available is
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26.4 grams per cubic meter,
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and then we're multiplying by
one and a half liters of air.
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And, that needs to be converted into
cubic meters
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by multiplying by one cubic meter
for every 1000 liters.
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And, we're left with this many grams
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which is 39.6 milligrams.
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So, this is the mass of water
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that can still evaporate into this
air that's been inhaled,
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one and a half liters of air.
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And, the amount of heat that would
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be transferred away from the body
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by having some mass evaporate
will be this much mass,
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0.0396 grams converted into kilograms
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times by the latent heat of vaporization
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for water at 37 degrees Celsius.
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So, this number is not the number
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you'll find in your data table for
latent heat of vaporization
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because that data table is created for
water that is boiling.
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But, this water is at 37 degree Celsius
body temperature
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and latent heat of vaporization is higher
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at these lower temperatures.
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So, this works out to
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96.2 Joules of energy.
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Now, assuming that there are
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ten breaths per minute or in other words
60 seconds per ten breaths,
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we can figure out the
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rate of energy transfer due to this
heat loss due to evaporation.
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So, there's 96.2 Joules of energy
lost per breath
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and then we divide that by
60 seconds per breath
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and the breath units cancel,
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leaving us with Joules per second,
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and this works out to 16.0 watts.