And that temperature experimentally, to be measured to turn out to be 28.3

degrees centigrade. So the final temperature in this process

is 28.3 degrees centigrade. What we'd like to do is figure out from

this, what is the heat capacity of the iron?` How could we do that?

Well, one thing we could do is to measure the heat which goes into the water as a

consequence of being in contact with the hot iron.

Clearly, we know that it has gained energy because we went from 25 degrees

centigrade to 28.3 degree centigrade. So according to our formula before, we

take the mass of the water and we multiply by the specific heat of the

water which is known and we multiply by the temperature change of the water which

is now being measured. Lets see we have a thousand grams of

water, the specific heat capacity is 4.184 joule per gram degree centigrade.

And the temperature change can be measured as 3.3 degree centigrade because

it is 28.3 minus 25 multiplying those numbers together, we get 13,800 joules.

So I'm going to write that as 13.8 kilojoules of heat absorbed by this

kilogram of water as a consequence of being in contact with the hot iron.

How much energy does the iron lose? Certainly it loses energy, because it

went from 90 degrees centigrade to 28.3 degrees centigrade.

So, it's temperature has dropped by 61.7 degrees.

The amount of energy that it lost must be exactly equal to the amount of energy

which was gained by the water. And that must be minus 13.8 kilojoules.

But that must also then be equal to the mass of the iron times the specific heat

of the iron, times the temperature change of the iron.

The, let's see, minus 13.8 kilojoules, must therefore be equal to 500 grams of

iron. We don't know the specific heat of iron.

That's what we're trying to find out. And the temperature change of the iron is

minus 61.7 degrees centigrade. That's an equation with is relatively

straightforward. So we can just find then by dividing up

that the specific heat of the iron turns out to be 0.447 joules per gram degree

centigrade. This method could actually be fairly

easily used for a variety of substances to determine what the specific heat

capacity is for any substance. Consequently, we can actually tabulate a

set of specific heat capacities. Here is a table showing the rather great

variations that occur as we move from one substance to the next.

There's the iron calculation that we've just done.

There's methane. We've got water is in here as well.

Notice that the heat capacity of the water does depend upon the temperature of

the water and varies somewhat over those ranges.

In each of these circumstances, remember that the heat capacity is the

proportionality constant between the heat and the temperature change.

That is sometimes a confusing fact because what it actually tells us is that

there is an inverse relationship between the heat capacity and the temperature

change for a fixed amount of heat. So, any time I provide a fixed amount of

heat so a substance, the smaller its heat capacity, the larger its temperature

change. Or, conversely, the smaller the

temperature change the smaller is heat capacity.

Substances with high heat capacities have a tendency to resist temperature changes

and will undergo small temperature changes.

So when your'e dealing with a substance that doesn't seem to heat up very much,

what you're observing is something which has a high heat capacity.

All right, we spent quite a bit of time here talking now about heat capacities.

What about, getting back to chemical reactions?

The process of measuring the energy of a chemical reaction by using the heat

capacity of the known substance and measuring the temperature change, is a

process called calorimetry. It is a means by which we can measure the

chemical reaction's energy by measuring temperature changes for a substance that

has a known heat capacity. Let's see, how would we do this?

Let's imagine that instead of putting that piece of hot iron in there, we burn

a gram of methane, right? So we're going to take methane, react it

with oxygen, and form carbon dioxide and water.

And we are interested in the energy of this particular chemical reaction.

So we'll burn a fixed quantity of methane.

1 gram, that's 1 16th of a mole of methane.

We're going to use the heat that comes out of that and capture that again in a

bucket of water which has 1 kg of water in it.

And which therefore has a known heat capacity.

If we know the energy, the, the energy absorbed by the water, or the temperature

change of the water, we can measure the energy change absorbed by the water, from

the mass of the water. Times the specific heat capacity of the

water Times the temperature change of the water.

The mass, again, is a thousand grams, the specific heat capacity is 4.184 joules

per gram-degree centigrade, and the temperature change is given to be, 13.3

degrees Centigrade. Consequently, we can measure the energy

just by multiplying these numbers together.

We get, I'm going to put this in terms of kilojoules, 55.6 kilojoules of energy

absorbed by the water. The energy released by the reaction must

be the negative of the energy absorbed by the water.

Because all the energy that came into the water came out of the reaction.

So the energy of the reaction, it's exothermic because the energy is less

than 0, so it's releasing energy to us in an amount 55.6 kilojoules.

That is for 1 gram of methane burned. From this, we can actually then measure

the chemical reaction, the energy associated within a chemical reaction,

that is sufficiently fast that I can capture the energy released or absorbed

by the amount of water by measuring the temperature change there.

That's the essence of calorimetry. There are some limitations associated

with this, including the fact that we have to carry out a chemical reaction

every time we would like to measure the energy.

We're going to actually develop an expansion beyond this to make it possible

for us to measure energies more simply in the next lecture.