Video Transcript
A fluid is in a container that is
steadily heated from the base. The region of the fluid that is
most directly heated thermally expands, reducing its density, as shown in the
diagram. Which of the following diagrams
most correctly shows both how lower and higher density fluid regions would be
distributed through the fluid and how these regions would heat each other?
Alright, to start out, let’s ignore
diagrams A, B, C, and D. And instead just focus on this one
here. What we see here is a heat source
being applied to a fluid that’s in a container. And from this diagram we can see
that the bottom portion of the fluid is thermally expanding, whereas the top portion
of the fluid is labeled as higher density. Along with this, we can assume that
the heating of this fluid is evenly spread out over the bottom of the fluids
container and that it goes on continuously.
Now, based on this diagram, our
question asks which of the following diagrams, A, B, C, or D, most correctly shows
two things. First, how the lower and higher
density regions in the fluid would be distributed? And, second, how these regions
would heat one another? In other words, how heat would
transfer throughout the fluid. To start answering this question,
let’s go back to our original diagram. And in particular, we can notice
that the bottom portion of our fluid is labeled as thermally expanding. Now, this tells us two things about
this region of our fluid. First, since the region is
expanding, we know that expansion will lead to lower density. And second, we’re told that this is
thermal expansion. That is, expansion due to heating,
meaning that this region will also be the hotter portion of our fluid.
Now that part is important, and
here’s why. Say that we have two objects. We have a cold object right here,
and then we have a hot object right here in contact with a cold one. In this situation, heat will travel
in a particular direction. It will travel from the hot object
to the colder one. And in fact, that’s always true of
the transfer of heat energy. It always moves from hot toward
cold. Knowing this and reviewing our four
answer options, we realized that whichever option is correct must show heat moving
from hot to cold. That is, it must be moving from a
higher temperature region to a lower temperature region and not the opposite
way. We saw that the two things we can
say about the lower portion of our fluid is that, one, it’s less dense than the
upper portion and, two, it’s hotter than the upper portion.
Now, in each one of our answer
candidate diagrams, we see heating that’s going on between these two regions,
between lower and higher density in our fluid. What we can do is go through these
options and eliminate any of them that do not show heat moving from hot to cold. And we see that, in our context,
that means from the lower density region towards the higher density region because,
as we’ve seen, the lower density portion of our fluid is also hotter.
So then, taking a look at answer
option A. We see on the left hand side that
heat is moving from the lower density region to the higher density region. That makes sense because that’s
from hot to cold. But over here on the other side,
heat is moving the opposite way from higher to lower density. That’s like saying that heat is
moving from cold to hot opposite what we saw here in our example. But that can’t be. Heat always moves from higher
temperature regions to lower temperature. Therefore, we cross off option A as
our answer choice.
Looking at option B, we see that
something similar is going on here. Heat is purportedly moving from the
higher density, that is, cooler part of our fluid, to the lower density, that is,
warmer part. But this has it backwards. Heat will move the opposite way
from lower density and hotter to higher density and cooler. And then the same thing happens
with option C. Once more, heat is purportedly
moving from the cooler region to the hotter region. But that doesn’t happen, so we
cross off option C as well.
This leaves us just with option D,
which correctly shows heat moving from the hotter to the cooler parts of our
fluid. Since this option also shows that
the lower density hotter regions would primarily expand of the sides of our
container, while the cooler higher density fluid would settle towards the
middle. Option D is our choice for our
final answer.
