INSTRUCTOR: In this short screen cast,
I'm going to remind you what a correlation is.
So a correlation is a mathematical relationship
based on experimental data that relates
one or more inputs to an output.
That's the important thing here is experimental.
So a lot of these correlations are,
most of these correlations are experimentally derived.
So let's go through a couple examples.
Maybe somebody, a scientist goes out there
and looks at the density of something,
maybe a gas at different pressures.
So they come up with this, the data here shown in blue.
And then what they do is they set up a regression model.
They create a regression model,
maybe a polynomial or an exponential regression model
that's shown in red that attempts to fit most of those data.
And you know, maybe the, the scientist comes up with density
in grams per centimeter cubed
is equal to 1.13 times
the exponent of 1.2 times 10 milliliter.
times the pressure.
The important thing here is that the pressure
is in pascals and the output,
the density is in grams per centimeter cubed.
So the user creates this using the units that they choose.
So they change pressure and pascals
and they measure density in grams per centimeter cubed.
In a followup screen cast,
we're going to show you how you can change this.
So maybe you want to use pressure in atmospheres
and you wanted to compute the,
you wanna be able to predict using
this equation or modified equation,
the density in pounds per cubic foot or pounds.
You know, something else,
some other unit of measure for density.
Another example,
maybe the thermal expansion coefficient of water.
So the scientist goes out there
and collects data shown in red.
They fit maybe a quick a second order polynomial model
and they get the following.
The important thing here,
thermal expansion is in per Kelvin
and they put temperature in degrees Celsius.
So, in this model equation,
you have to make sure temperatures in Celsius
and the output's going to be per
Kelvin for the thermal expansion.
Maybe another one.
this is the density of water as a function of temperature.
Same thing.
maybe the experimenter goes out there,
collects data, the data aren't shown,
but you know, you might have a co,
you might have a bunch of data points and not perfect,
but you'd come up with a model that best fits those
experimental data and the user gets this third order
polynomial in temperature in Celsius to predict the density
of water in kilograms per cubic meter.
Finally, you might have the heat capacity of something
like acetone in the gas phase.
They experiment or adjust or calculates the heat capacity
at a bunch of different temperatures and degrees Celsius.
And they measure the heat capacity
and kilojoules per mole per degree Celsius.
And again, any followup screen casts,
I will show you how we can change this.
Maybe the user wants to be able to use temperature
in Fahrenheit to predict he capacity in BTU per pound,
mole per degree Fahrenheit as an example.
So again, this is a third order polynomial here.
So the experimenter comes with up with a model.
There are different ways to create models,
but they come up with a model and that is a correlation.
And we use a lot of correlations in science and engineering.
I wanted to quickly mention one more thing about,
something that's important about these correlations.
These coefficients. So a b c and d.
again, those are experimentally determined,
but those actually have units.
So remember Cp in this example is in kilojoules
per mole per degree Celsius temperatures in degrees Celsius.
So as an example, a here has to be in units of,
it's not multiplied by anything,
it's not multiplied by temperature.
So a is going to have units
of kilojoules per mole degrees Celsius,
just like Cp.
Now when b times t, when b is multiplied by t ,
that has to have the units of Cp.
So we can calculate the units that b has
to be inb times t has to be kilojoules
per mole per degreeS Celsius, right?
That's what b times t is.
So I'll just say like that's in units
of b times degrees Celsius.
So if I divided both sides by degrees Celsius,
b then would be in units of kilojoules per mole degrees,
Celsius squared.
All right?
So that's what the units of br,
so when b is multiplied by c,
we get one of those to cancel.
And that product is in units
of kilojoules per mole degrees Celsius.
And we could do a similar analysis for c and d,
but remember that those experimentally determined
coefficients actually have units,
but we typically do not express those units when
we write it out as our correlation.
Thanks for watching.