>> Welcome to Measurement Part 5.
In this video, we're going to look
at energy and specific heat.
Let's get started.
All right, now we've already talked briefly about energy,
that it's the capacity to do work,
and we're all feeling that, right?
Because this class is a lot of work,
and then heat is one type of energy, right?
There's mechanical, electrical,
that type of thing chemical energy, so for now we're going
to focus on heat, and then we need to look at temperature.
All right, so we're already looked at the units
of temperature, and we know it's a measure of hotness or coldness
of an object, but heat and temperature,
they can be used interchangeably,
and we don't want to do that.
We want to discern those differences.
So let's think about some boiling water.
All right, so if we have boiling water, we could have one drop
of boiling water, or we could have a gallon
of boiling water, right?
So in this sense, they're both boiling,
so they're the same temperature.
Right? About 100 degrees C. Okay, but now let's think
about what happens if we have our hand sitting here.
Yeah, art's not by strength.
So if one drop of boiling water falls on our hand, you know,
it hurts for a moment, but it's not so bad, right,
but let's say we had our hand here, and someone was going
to try to pour a gallon of boiling water on our hand.
No way, right?
That would be ouch.
Oh, this pen doesn't work.
Okay, so let's go for an ouch, right?
Because this has more heat, okay.
So that's our discernment, right?
Same temperature, different amounts of heat.
We can accomplish a lot more with a gallon of boiling water
than we can with a drop.
Okay, now looking at the units of heat, which is also energy,
right, when we have the uppercase C for calorie,
we recognize that as a nutrition unit,
and then if we have the lowercase C, right,
that's our science unit, and so we see
that the nutrition calories are a thousand times greater
than the science calories, and in science,
we also use a unit known as a joule.
It's a upper case J for joule.
Okay, so that's another energy unit, and we're focusing
on heat here, and just to make sure, right,
I think we all know the word calorie.
Yeah, there we go.
Okay, so now we're going to look at this relationship
between temperature and heat a little more closely.
So specific heat we're going to symbolize with a SH,
and it's the heat needed to raise 1 gram of any substance
by 1 degree C. All right, so if we look at what that means,
here we have it in words.
Now let's look at it as an algebraic
or mathematical expression, right?
So we want to heat.
So what's our symbol for heat?
So our symbol for heat is Q. All right,
so I should put that back up here.
Right? So for heat, the accepted symbol is an upper case Q. All
right, so now I'm going to go into algebra.
So the specific heat is the heat there that we need in Q,
right, to raise a gram.
So gram, right?
That's a mass unit.
All right, and then we have our temperature, right?
And so we're going to raise the temperature, so we're going
to change the temperature.
So we're going to use a delta T, right?
So there's our Greek delta,
and in this instance it means change, right?
So our change in temperature would be our final temperature
minus our initial temperature.
Okay? Final minus initial.
All righty.
Okay, so now let's look a little closer at specific heat,
and as you would imagine, right, every substance is going
to have a unique, specific heat value.
All right?
So specific heats aren't something we memorize.
They're things we look up in a table.
Water, right, has a very high specific heat.
That is why we use it as a coolant, right?
Because it can absorb a lot of heat
without changing temperature.
Right? If we compare that example to, like,
iron or, like, aluminum.
Right? We like to cook with iron or aluminum.
Not aluminum, copper.
Don't cook with aluminum.
It's linked with Alzheimer's, right?
But iron, copper, we see they have allow,
all the metals have low specific heats.
So they heat up quickly.
So if we're wanting to cook our food,
we want a low specific heat so it heats up quick
and we can get busy eating.
All right, so let's look at the different types of questions
that you can answer using your understanding of specific heat.
All right, so the first thing let's do, well, let's write it
out in words one more time, make sure we're all clear, right.
So the heat, that's needed, right?
Is going to be the mass of the object that we're trying
to raise the heat of, and then, of course,
we'll have the specific heat, which we're always going to look
up in a table or we could try to calculate it,
and then we have our temperature change.
All right, so too many letters.
Let's go to symbols, right?
Q is heat, mass specific heat, and temperature change.
So in these type of questions,
we have four different parameters that are all related.
So we're going to need to given three of the parameters
and solved for the fourth, but before we jump that that,
let's look at the units for a minute.
So here we go, right?
So if we look here, right?
Q, that's heat, so that's calories
and then mass is in grams, right?
And temperature is in degrees C, temperature change.
So now let's look at those units of specific heat
from the previous page.
Right, it's calories per gram degrees C, right?
So we see why those crazy units are good, right?
Because the grams will cancel.
The degrees C will cancel,
and notice we have calories and calories.
So any time you're trying to solve these type of questions,
the units are a great resource to let you know
if you're on the right track.
Okay, now let's get started on solving problems.
All right, so calculate the number of calories
of heat energy required to heat 25 grams of copper
from 23 degrees to 34.7 degrees C. Okay,
so the units some in handy.
We look here, and the grams, right,
they tell us this is the mass, and then here we have degrees C.
So this is our temperature, right?
So delta T. So the final temperature,
we're raising the temperature.
So the final temperature is higher,
and then we subtract the lower temperature,
and there's our delta T, 11.7 degrees C. All right, okay,
now this is asking for calories.
So we don't need to do any algebra here.
We just want to use our formula directly.
So the amount of heat we need in the form of calories, right?
So here's our mass.
So there's our mass, 25.0 grams.
Okay, and then comes our specific heat.
I think I'll keep doing that in red for consistency, right?
So we're doing copper.
So we go back up to our table.
So here we see the specific heat for copper.
All right, so that's - oh, we can just squeeze it.
Awesome. Okay, 0.92 calories per gram degrees C,
and then we've already calculated delta T,
11.7 degrees C. So now let's do an inventory of our units here.
All right, so we can slide this up now.
So the grams are canceling.
The degrees C are canceling, there's our calories,
which is the units we would expect for heat.
All right, so we punch this in our calculator,
and the calculator spits out 26.91,
and then old sig figs are alive and well.
So we look back at our data.
Three. How many sig figs here?
What about those leading zeros?
Right? Leading zeros never count.
So here's only two sig figs.
So this is going to limit our result.
I'll color code there the specific heat,
and so our final result is 27 calories.
Okay, so now there's a couple more practice problems,
so this would be a good spot to stop the video for a minute
to test yourself, and see how you're doing,
and then come back and compare answers.
Okay, so welcome back.
I hope you were able to solve these with confidence.
If not, let's work through them together, make sure.
So calculating the final temperature,
so this one's a little trickier, right?
So we want to figure out of final temperature.
So we're going to add 175 calories of heat
to the 7.73 grams of water,
and the initial temperature of the water is 43.2.
All right?
So there's our T initial.
So I think to start, let's just focus on delta T,
and then we'll go back and figure out the final.
Okay, so using the units as our guide, there's our calories.
So we know that that is the Q, and then there's the grams.
So that lets out know it's the mass.
So here, right, so we have the heat is the mass times the
specific heat, times the temperature change.
All right, so we want to solve for the temperature change.
So we'll just go ahead and do some basic algebra
and isolate our temperature.
Okay, so what are we left with?
All righty, so these are going to cancel.
That was the whole point.
All right, so the change in temperature is going
to be Q divided by the mass and the specific heat.
Okay, so looking through the information in our question,
we know that the heat is 175 cals,
and the mass was 7.73 grams, and then the specific heat, right?
Where do we get that?
Remember, we get in a from the table.
So if we go back to the previous page,
we see that the specific heat
of water is 1 calorie per gram degrees C. Now,
if what I did just bugged you,
let's have a time out for a minute.
All right?
So remember, if we have 1 over 1 over X,
that is the same as X. All right?
So if we have 1 over calories per gram degrees C,
that's the same thing as grams degrees C over cal.
All right, so this is some old fraction review.
If this is bugging you, please talk with me during office hours
or during lab or something, so we can get this sorted out.
Okay, so where do we stand here?
All right, calorie.
Calorie cancel.
Ah-ha! Grams cancel, perfect, we're left with temperature,
and that's perfect because this is a temperature question.
Okay, so when we solve this value, we find that the change
in temperature is 22.6 degrees C, all right?
So that's our delta T,
and so then that's T final minus T initial, right?
And we know T initial, it was given to us
in the question, 43.2.
All right, so we just have some basic algebra,
and we just determined that the final temperature is 65.8
degrees C. Okay?
So a little more complicated.
A couple more steps but still pretty straightforward,
and units are a great resource
for helping to solve the problem.
Okay, let's work one more practice problem here,
so try to work all the different angles and then I'll leave you
to practice on your own.
Okay, what is the mass in grams of a piece of aluminum
if its temperature changes for 30 degrees to 350 degrees
when it absorbs 1770 calories?
All right, so using our units, calories, we know that's the Q,
and then here is going to be our temperature change.
All right, 315 minus 30.
Okay, so that puts us at 285.
All righty, so we have the Q. We have the delta T. Let's
reconnect with our formula.
All right, so the heat is going to depend on the mass
of the sample, its specific heat, which we look
up in a table, and the temperature change.
Okay, so this time, all right, we're trying
to figure out the mass.
That's what we're trying to figure out.
So we'll do a little algebra to isolate the mass.
All right, there we go.
Okay, so then that, we rearrange that, and it tells us.
All right, that's all gone.
So we're going to have Q, the heat divided
by the specific heat, and temperature change.
All righty, plug and chug.
Okay, so heat, 1770 calories, and the specific heat.
Oh, I wish I would've switched those.
I'm going to do temperature first, 285 degrees C. Okay,
now we're going to do the specific heat.
So, if we go to our table and we look up the specific heat
of aluminum, we'll see that it's 0.22 calories per gram degrees
C. All right, now let's use our units to double check
and make sure that we've set this up properly.
All righty, so you have calories on the top
and calories on the bottom.
They cancel.
The degrees C on the bottom,
degrees C on the top, they cancel.
Okay, so we're left with grams, which is a mass unit.
Perfect. All right, so we plug all these values
into our calculator, and the calculator spits out a big,
long number, but then we write down some digits,
but then we look back at our data.
All right, the calories, how many, three sig figs, right?
No decimal.
Three sig figs for our temperature.
Only 2 sig figs for our specific heat.
So for our final answer,
28 grams of aluminum would have been in this sample.
All righty, so that concludes our video on measurement,
heat, and specific heat.
So take some time now to review the concepts,
work a few practice problems, and I'll look forward
to seeing you in class.