### Video Transcript

In this video, we’re talking about
specific latent heat. As we’ll see, this term refers to
an amount of energy that is exchanged, either absorbed or released, when an object
changes state without changing its temperature. We see an example of this on
screen, where we have solid water, ice, at zero degrees Celsius, melting into liquid
water, which is also at zero degrees Celsius. In this case, heat is being
absorbed by the ice to cause it to melt without raising its temperature. To see how this works, let’s
consider a block of ice that we put inside a dish, and we put that dish on top of a
hot plate, a device whose surface we can heat up to some temperature we set.

Then, say that we turn on the hot
plate and we set its temperature to be 200 degrees Celsius. The hot plate begins to heat up to
that temperature, and it transmits this heat to the dish and to the block of
ice. Now, as time goes on, say that we
keep track of two quantities; first, we track the temperature of the water, which is
currently the block of ice. And we also keep track of how much
energy is absorbed by the water over time. If we set up a graph like this so
that data points would appear on it in real time, we might see a graph looking like
this. As points began to appear, we would
see that more and more energy is going into the water and its temperature is going
up.

After some time, though, we would
notice two things changing. First, we would see that our curve
starts to level out, indicating that energy is being added to the water but its
temperature is not going up. And we would also notice that our
block of ice is starting to melt. And this would continue on until
eventually the entire block was completely melted. The water is now all liquid. Once that took place, as we
continue to watch our curve, we would see that once again it starts to slope
upward. This means we’re continuing to add
energy to the water, and now its temperature is going up in response. If we continued on and kept heating
the water closer and closer to its boiling point, eventually, when the water got hot
enough, it would start to evaporate. And as it did, we would once more
see this curve start to level of.

Now, if we were to stop our
experiment right here and look at the graph so far, we would see that there are
portions of the graph where we’re adding energy to the water and its temperature is
increasing. But there are also portions where
we are adding energy, but its temperature is not changing at all. On those portions, where the
temperature of the water is going up, we can understand where the added energy is
going. It’s going into increasing the
temperature of the water. But what about these regions? These are places where the energy
being added isn’t going into increasing the temperature. It must be doing something
else. And in fact, we’ve seen what it was
doing. It was going into changing the
state of matter of the water, first from ice to water and then from water to
steam.

And if we think about the total
energy that went into changing the water from a solid to a liquid and then from a
liquid to a gas, we can give names to these amounts of energy. We could say that the total energy
input to melt the water without raising its temperature is 𝐸 sub melt, and that the
total energy that went into boiling the water, again without raising its
temperature, we can call 𝐸 sub boil. If we wanted to show these
quantities on our graph, then they would correspond to the flat portions of our
curve. The energy difference from here,
where the water started to melt, to here, where it was completely melted, is 𝐸 sub
melt.

And then, if we consider 𝐸 sub
boil, we see that we have truncated our experiment here. But if we had kept going, this line
would’ve stayed flat for some distance farther. Let’s say we had run the experiment
up till here, at which point all of the water was evaporated out of the dish. It’d been boiled away. In this case, we can figure out how
much energy 𝐸 sub boil is by dropping vertical lines from this flat portion of our
curve. Just like before, the distance
between these two lines on the horizontal axis indicates how much energy went into
the water simply to cause it to boil. That is, to change the state of all
the water in the dish from liquid to gas without raising its temperature.

Now, there are a couple of things
worth noticing about these two energy amounts, 𝐸 sub melt and 𝐸 sub boil. First, we can notice that they’re
not equal to one another. They don’t represent the same
amount of energy. In fact, we can see that for water,
𝐸 sub boil is greater than 𝐸 sub melt. And we know that because this
distance here, representing 𝐸 sub boil, is greater than this distance here. Physically, this tells us that it
takes more energy to boil, say, a gram of water than it does to melt a gram of
water. Or put it more precisely, it takes
more energy to take one gram of liquid water at 100 degrees Celsius and convert it
to a gas than it does to take one gram of frozen water at zero degrees Celsius and
convert it to a liquid. It’s important to note, though,
that this is true for water, but not necessarily for all materials.

The second thing we’d like to say
about these results is that each one of these amounts of energy, 𝐸 sub melt and 𝐸
sub boil, corresponds to what is called a latent heat. The energy it took to melt our ice
into water without raising its temperature is called the latent heat of fusion. The reason for this name, latent
heat, is because this word latent indicates that the heat is in some sense
hidden. And indeed, since it doesn’t raise
the temperature of the water, it is. In general, the energy that it
takes to convert a material from its solid phase to its liquid phase is called its
latent heat of fusion. The particular value of the latent
heat of fusion depends on the material. Water has one value, for
example.

Now, at this point, let’s recall
that we were adding energy into our system to lead to this state change from a solid
to a liquid. In this case then, energy was being
absorbed by the water as it was changing state. We can imagine, though, that it’s
possible to move in the opposite direction. That is, it’s possible to start out
with liquid water and then cool that sample down until it freezes. In that case, the same amount of
energy is involved in changing the state of the water. But, when we go from a liquid to a
solid, this energy is being released rather than absorbed.

So, just to be clear, for any given
material, whenever it transitions from a liquid to a solid or a solid to a liquid,
the amount of energy involved in the exchange is called the latent heat of
fusion. That amount of energy doesn’t
change, but whether the energy is being absorbed or released does change. In the case of cooling a liquid
down until it freezes, in that case, energy is being released by the liquid. But going the opposite direction
and heating a solid up until it melts, energy is being absorbed by the material. So, this amount of energy for a
given material can be either released or absorbed but the total magnitude of that
energy will be the same either way. And it’s called the latent heat of
fusion.

Knowing all this about 𝐸 sub melt
gives us good background to consider similar ideas about 𝐸 sub boil. In general, the amount of energy it
takes to transition a material from its liquid phase to its gas phase is called the
latent heat of vaporization of that material. And just like with the latent heat
of fusion, it can go either way. The material can either be
transitioning from a liquid to a gas or from a gas to a liquid. That will affect whether this
amount of energy is being absorbed or released by the material. But it won’t change the total
magnitude of the energy involved. It won’t change the latent heat of
vaporization for that material.

Now, in our experiment so far,
we’ve been talking about some amount of water, but we haven’t been specific about
how much water is involved. We just know that however much
water we were melting and then boiling, some amount of energy we called 𝐸 sub melt
was required to melt it, and then some greater amount of energy we called 𝐸 sub
boil was required to make it steam. But let’s say that instead of
dealing with an unknown mass of water, we were working with a known mass of exactly
one kilogram. In that case, the energy required
to melt our one-kilogram block of ice is no longer just called the latent heat of
fusion of water, but it’s now called the specific latent heat of fusion. The word specific tells us that
this is an amount of energy corresponding to the phase transition of one kilogram of
this material, in our case, water.

And the same thing, by the way,
happens with the energy required to boil this one kilogram of water. We’re no longer talking about the
latent heat of vaporization, but rather the specific latent heat of
vaporization. We’re now ready to give a
definition for this term, specific latent heat. Specific latent heat is the energy
that’s released or absorbed by one kilogram of a material during a phase
transition. In the case of a transition from
solid to liquid or liquid to solid, we call this the specific latent heat of
fusion. And in the case of going from a
liquid to a gas or a gas to a liquid, we call it the specific latent heat of
vaporization.

And as we saw, the reason for these
two different names is that these amounts of energy for a given material are
typically not the same. For example, when it comes to
water, we saw that the specific latent heat of vaporization, what we called 𝐸 sub
boil, is greater than the specific latent heat of fusion, what we called 𝐸 sub
melt. Knowing this definition of specific
latent heat, let’s clear a bit of space on screen and see how to work with this
value as a variable.

Typically, we represent specific
latent heat using the symbol capital 𝐿. And we can recall from the
definition of 𝐿 that this is an amount of energy that’s either released or absorbed
by a one-kilogram mass. That is, 𝐿 represents an amount of
energy per mass. So, if we wrote out the units of
the specific latent heat, they would be units of energy, we’ve used joules here,
over units of mass, here we’ve used kilograms.

Now, if we look up specific latent
heats for various materials in a table, we’ll often see them quoted in units of
kilojoules per kilogram. Know that this is still an amount
of energy per an amount of mass. Knowing that specific latent heat
is represented by these units, we can see that if we multiplied the specific latent
heat of some material by some amount of mass of that material, then from a units’
perspective, when we multiply kilojoules per kilogram by some amount of kilograms,
we see that that unit of kilograms cancels out. We’re left with a unit of energy
often in kilojoules.

This shows us that if we multiply
the specific latent heat of some material, either the heat of fusion or the heat of
vaporization, by some amount of mass of that material, then what we’ll calculate is
the energy required to change the state of that mass of material. This could be energy that’s
released or energy that’s absorbed by the material. But in general, we can think of it
as the energy transferred over this phase transition. Knowing all this about specific
latent heat, let’s get a bit of practice with these ideas through an example.

The table lists the specific latent
heat of fusion for various metals. A student has 200 grams of an
unknown metal. The student heats the metal to its
melting point and then measures how much energy is absorbed by the metal for all of
it to melt, and gets a value of 79.6 kilojoules. Which of the four metals listed in
the table does the student have?

Okay, taking a look at this table,
we see that it has two rows. The first row lists four different
kinds of metal, aluminum, cobalt, iron, and nickel. In the second row, the specific
latent heat of fusion of those metals is given in units of kilojoules per
kilogram. When we talk about the specific
latent heat of fusion, that refers to the amount of energy that a substance needs to
go from a liquid to a solid or a solid to a liquid. In other words, it’s an amount of
energy needed to solidify or liquify one kilogram of some material.

Now, in our scenario, we’re told
that a student has a 200-gram mass of some unknown metal. The metal begins as a solid but
then is heated up to its melting point. And the student then measures how
much energy is absorbed by the metal in order for all of it to melt. So, our 200-gram sample has now
gone from completely solid to completely liquid. The student measures the energy
required for that phase transition from solid to liquid to be 79.6 kilojoules. Based on this information, we want
to figure out whether the student is working with aluminum, cobalt, iron, or
nickel. To figure that out, let’s recall a
mathematical relationship between specific latent heat, mass, and energy.

In general, the energy, 𝐸,
required to affect a phase transition is equal to the mass of the substance going
through that transition multiplied by the specific latent heat of that
substance. Looking again at our table, we’re
given the specific latent heat, in particular of fusion, for these four different
metals. In other words, for these metals,
we know capital 𝐿. But we don’t yet know the specific
latent heat of fusion of the unknown metal that our student is working with. It’s that that we want to identify
to know which of the four metals we’re using. Now, here’s what we do know about
our unknown metal and the energy involved. First, we know the mass of our
sample. That’s given as 200 grams. And we also know how much energy it
took to completely melt this sample of metal. We can call that energy 𝐸, and
we’re told that it’s equal to 79.6 kilojoules, 79.6 thousand joules.

Now, taking a look back over at our
expression for the energy 𝐸 in terms of the mass and the specific latent heat. We can see that if we divide both
sides by the mass involved, then that term cancels from the right and we arrive at a
mathematically equivalent statement. That the energy involved in this
transition divided by the mass of the substance is equal to the specific latent heat
of that substance. And it’s that value, capital 𝐿,
that we want to solve for for our as-yet-unknown metal.

So, to do it, we’ll divide the
energy we needed to melt the metal by the mass of the sample. In other words, we’ll divide 79.6
kilojoules by 200 grams. But before we do that, notice the
units in which our specific latent heats of fusion are given. They’re kilojoules per
kilogram. And we have kilojoules per
gram. So, before we do this division,
we’ll want to convert our mass into units of kilograms. We can recall that one kilogram of
mass is equal to 1000 grams, which means that to convert 200 grams into kilograms,
we’ll shift the decimal place three spots to the left, at which point we can see
that 200 grams is equal to 0.200 kilograms.

Looking at the units in our
fraction now, we see that they’re kilojoules per kilogram. They’re a match for the units in
terms of which the specific latent heats of fusion of these metals are given. So, we’re ready to divide. When we do, we find a result of 398
kilojoules per kilogram. And looking through our table, we
see that this is a match for the specific latent heat of fusion of aluminum. These tells us that the metal the
student is working with is aluminum.

Having seen this, let’s summarize
what we’ve learned in this lesson about specific latent heat. Starting off, we saw that when a
substance changes phase, that is, goes from a gas to a liquid or a liquid to gas or
a solid to liquid or a liquid to solid, then that substance absorbs or releases
energy. But it doesn’t change in
temperature. This energy is known as latent
heat. It’s the energy that a substance
either absorbs or releases specifically to change state. When the latent heat of a substance
is indicated per unit mass, its name changes to become specific latent heat. Specific latent heat is symbolized
using a capital 𝐿. And its units are units of energy
per unit of mass.

For this reason, if we multiply the
specific latent heat of some substance by a given mass of that substance, then that
tells us the amount of energy that’s either absorbed or released during a phase
transition of that amount of that substance. And lastly, we saw that the
specific latent heat of a material depends on the particular phase transition the
material goes through. For a material that’s either
freezing or liquefying, that is, going from a solid to a liquid or a liquid to a
solid, we refer to the specific latent heat of fusion. But when a material is going from a
liquid to a gas or a gas to a liquid, we refer to the specific latent heat of
vaporization. For a given material, in general,
these two values are not the same.