Using Units

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En provenance du cours de The University of Chicago

Global Warming I: The Science and Modeling of Climate Change

157 notes

The University of Chicago

Global Warming I: The Science and Modeling of Climate Change

157 notes

This class describes the science of global warming and the forecast for humans’ impact on Earth’s climate. Intended for an audience without much scientific background but a healthy sense of curiosity, the class brings together insights and perspectives from physics, chemistry, biology, earth and atmospheric sciences, and even some economics—all based on a foundation of simple mathematics (algebra).

À partir de la leçon

Heat, Light, and Energy

A primer on how to use units to describe numbers when describing temperature, energy, and light. Even if you don't plan on doing calculations yourself, understanding how units work will help to follow the rest of the lectures in the class. If you are interested in practicing your analysis skills, using units to guide calculations, there are some exercises in the Part II of this class.

Using Units3:43

Units of Energy5:12

Rencontrer les enseignants

David Archer
Professor
Geophysical Sciences

[MUSIC]

So one of the most useful skills that you can pick up in

scientific quantitative analysis, is the ability to look at and

manipulate the units that are attached to the numbers.

This is called the factor label method, and once you get it it seems

very intuitive, but it seems to me that nobody is born knowing how to do this.

So you might have to work at it a little bit to get it.

Say we have a number which is a velocity in units of kilometers per hour.

And then we want to convert that into different units of meters per second.

Instead of trying to remember a formula to do that,

we can actually use the kilometers and the hours, and meters, and seconds,

to construct the formula that we need to do the conversion,

such that make the units work.

So we'll start with a velocity in kilometers per hour.

Say we're driving along and it's 100 kilometers per hour, and

you want to know how many meters per second that is.

So we need to find factors that can convert these

units into the ones that we want.

And so let's start with the time units.

We wanna convert from hours to seconds, and so we'll start by writing a factor,

which can cancel out the units of hours here, and give us something shorter.

And I don't remember in my head how many seconds there are in an hour.

So, I'll write it out.

Do this in two stages that there are 60 minutes in an hour.

And so, now we can cancel the units of hours here, and

that's the first step in our factor label method.

Now, because an hour equals 60 minutes,

if you take a quantity, which is the same on the top and

the bottom of a fraction, then that quotient is equal to one.

So by multiplying our original information, which is 100 kilometers per

hour, by this conversion factor, we're just multiplying by one.

And so we're not actually changing the value at all.

We're changing the units, and so that changes the numbers but

the actual quantity stays the same.

So the next factor will be from minutes to seconds.

There 60 seconds equals one minute.

And so now the minute units are gone away, and we have kilometers per second so

that's getting closer, but now we have to deal with the kilometers to meters and

so the conversion factor here is a kilometer is equal to 100 meters.

And I have to put the kilometer on the bottom, I can see because I have to cancel

kilometer here, and end up with meters on the top.

So after we have constructed this whole thing to cancel out the units, so

we're left with what we want, meters per second.

All we have to do is multiply the numbers.

100 times 1,000 divided by 60 divided by 60, gives us this answer.

And so the units have told us how to do the math.

[MUSIC]

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