00:02
There is a lot in this problem about temperature scales and celsius kelvin and fahrenheit.
00:09
So let's just jump right on in.
00:11
The first part of our question asks us to talk about what is the absolute temperature scale.
00:16
So this is the scale of kelvin.
00:20
That is the temperature scale that we use in the metric system, even though we are probably more familiar with degrees celsius.
00:27
Kelvin relates to a molecule's actual movement.
00:30
And when we have zero kelvin, we have no molecular movement in the material at all.
00:39
So temperature is a measure of how fast on average molecules are moving.
00:43
And so when something is zero kelvin, there's no movement whatsoever.
00:47
We can convert between kelvin and celsius by saying that our kelvin temperature is equal to our celsius temperature plus 273, technically 0 .15.
00:57
But sometimes people will just round it off to 273.
01:01
This basically accounts for the fact that at zero degrees celsius, there's still molecular movement, but zero kelvin, there's no molecular movement.
01:08
So we just add some numbers to reset that zero, and otherwise it's a one -to -one, unlike celsius and fahrenheit, which we'll see later.
01:16
The second part of our problem asks us to find where tc, temperature celsius, is equal to temperature fahrenheit.
01:25
So does there exist a temperature? this is a fun little trivia, fact, the temperature is actually negative 40.
01:31
But let's figure out why that is mathematically.
01:34
I basically want to take one of my conversion equations and solve for the temperature, right? so we're going to say, in this case, let's say tf is equal to 9 5th t .c plus 32.
01:55
I just picked that one because i like it.
01:58
And we know in this case, tf is equal to, we want to know when is tf equal to tc equal to some variable x? like, what is that number? so, x is equal to nine -fifths x plus 32.
02:14
We rearrange this to have, ultimately, x is equal to negative 32 divided by nine -fifths minus one.
02:27
If you're not entirely sure where that algebra came from, i encourage you to walk through moving this equation and solving that equation for x.
02:38
Ultimately, you'll see x is negative 40, as we knew from our trivia.
02:46
Part three is asking us to figure out how to correlate or convert between the two temperature scales, temperature in fahrenheit and temperature in celsius.
02:55
So you'll notice we've already used tf here.
03:00
Tc is just the opposite.
03:04
So again, tf is nine -fits, the temperature in celsius plus 32.
03:09
We can rearrange that to solve for the temperature in celsius is five -ninths, open parentheses, temperature in fahrenheit minus 32.
03:21
The thing i see students do most commonly here is forget these parentheses, and that can mess up your conversion.
03:30
The fourth part of this question is asking us to look at absolute zero on a graph, so an ideal gas graph.
03:43
And for an ideal gas, you know, you can look at temperature, and this could be pressure or volume.
03:51
Let's not do a fraction there.
03:53
We're not talking about p over v.
03:55
This is pressure or volume.
03:57
And it's going to be some kind of linear relationship.
03:59
But the point we want to identify here is that for a variety of gases, absolute zero is going to be the point where they cross the x axis.
04:13
Let me make that a little more clear.
04:14
There we go.
04:15
So absolute zero is what's sitting back here.
04:18
It's that theoretical, no pressure, no volume, theoretically, no molecular movement.
04:26
So no apparent pressure, no apparent volume.
04:30
I did realize that i just on part two mixed some of the, i missed some of the question.
04:38
So we're going to go back to part two again.
04:43
You're given three cups of water.
04:45
Each have a different temperature.
04:47
So a, b, and c.
04:50
Cup a, 320 kelvin, cup b, 20 degrees celsius.
04:57
And cup c, 90 degrees fahrenheit.
05:00
To solve that problem, i encourage you to make a table.
05:04
You have cup a, b, c.
05:07
And using the equations that were given, you have kelvin degrees celsius and degrees fahrenheit.
05:15
So you would know 90, you would know 20 and 320.
05:21
And if you use the equations that are on this slide here, let me highlight them for you.
05:26
Here's your kelvin conversion.
05:29
Here's your fahrenheit from celsius, and here is your celsius from fahrenheit.
05:35
If you do that, you're going to get the following values so that you can check your work.
05:39
This is 46.
05:41
This is 116.
05:43
This is 16.
05:44
This is 68, 293, 305, and 32.
05:53
Okay.
05:53
That was a lot of numbers if you weren't looking at the screen.
05:55
So just look, try to recreate that table.
05:58
And you'll notice that the hottest one in this case is cup a.
06:03
And that makes sense.
06:04
Hottest across the board, right? so that is the rest of part two.
06:09
I apologize for missing that.
06:12
Part five, we start looking at some chemistry or the movement of gases.
06:18
We're looking to determine the root mean square speed of nitrogen and of oxygen.
06:24
So our root mean square velocity, which is related to temperature, we want to know at 300 kelvin.
06:34
So that is our temperature.
06:37
And we're trying to find the velocity.
06:44
My equation for root mean square speed is equal to three times some constant k times the temperature t, divided by m, which is the mass of the gas in question.
07:01
So in this case, k is what we call boltzmann's constant, and it has just a constant value.
07:12
You can look it up in your textbook of 1 .38 times 10 to the negative 23.
07:19
And there are some units attached to that, but just in the interest of clarity for the slide, and there's a lot of numbers in this problem.
07:24
So i'm going to leave out the units...