Welcome back guys! In this new video, we're going to take a look at calorimetry under
a constant volume. Now first we're going to say that every object
has its own heat capacity. And just remember heat capacity uses a capital C, and this is
just the amount of heat that's required to change an object's temperature by 1 Kelvin
(K). Here we're just going to say heat capacity is simply heat/the change in temperature,
so Final - Initial. And we're going to say the units are usually in Joules (J)/Kelvin
or kiloJoules/Kelvin. q J
C = ∆T [ in units of K ]
Sometimes your professor may even do it over Degrees Celsius, so just look to see what
units were they want the answer to be in. That's what you always have to make sure so
that you get the correct answer. Now similar to heat capacity, there's another
property. This property is known as Specific Heat Capacity, and notice that this one is
lower case c, and this is the amount of heat that's required to change 1g of substance
by 1K. So here we're just going to introduce the
concept of mass, and mass here would be in grams. So it's similar to heat capacity but
more in depth, where talks about mass. Now what we're going to say here is if we know
the specific heat capacity of a substance, we can rearrange this formula here so that
we can solve for the amount of heat absorbed or released. So if we want to rearrange this
equation up here, so C = q/m * change in temperature. q
C = m * ∆T
Just multiply both sides by mass * change in temperature.
q m * ∆T (C) = m * ∆T m * ∆T
And then you say that q = mcAT. q = mc∆T
So just remember q = mcAT, just read the delta sign, the triangle as an A. So that's the
easy way for you to remember the equation, q = mcAT. This is the equation that we use
anytime they give us specific heat capacity, and we know that change in temperature, and
they give us the mass of an object. Now based on the concept we've just looked
at let's take a look at this Question here. It says:
At constant volume, the heat of combustion of a particular compound is -4621.0 kJ/mol.
We say when 2.319 grams of this compound (molar mass = 192.75 g/mol), remember it has a molar
mass that I give to you, was burned in a bomb calorimeter, the temperature of the calorimeter
(including its contents) rose by 3.138 oC. What is the heat capacity of the calorimeter
in J/K? First of all, this image that we have here
is called a bomb calorimeter. It's a way of us actually figuring out how much energy does
an object contain in it. The way it works is, we have our sample put inside to the small
little bowl here, and that is placed inside of those water. This whole unit is referred
to as a bomb. And what's going to happen is, we're going to actually use these rods here,
and we're going to send an electrical current, and it's actually going to cause this sample
to explode inside of the bomb calorimeter. So that's why it's called the bomb calorimeter
because we actually cause the contents to explode. And when they explode, they're going
to give off some heat. Now there's a temperature in the water, this temperature is actually
going to record how much the water temperature increases by. In that way, we can figure out
how much heat that that sample release and from that we can figure out how many calories
it has, how much heat it started with, we could find out a lot of information. This
is the way to do certain food sciences, to figure out the calories we have in a food.
They use similar technique such as this. Now we talked about Joules as being the standard
type of energy for heat, but remember you could also have instead of Joules for q you
could have kiloJoules, but you could also have calories, large calories, these are the
calories that you see in food, and kilowatt-hours. So these are other units, energy conversion
factors that we can use in place of Joules for q. Now we're not going to work on converting
from Joules to calories or kilowatt-hours, I just want to give you guys these tables
so that you can see all the different types of energy conversions that you should know
for lecture. Now let's take a look at this question, we
want to calculate heat capacity. Remember this is capital C, and so heat capacity = q/change
in temperature. And what we need to realize here is, we need to isolate Joules, we need
to find Joules for q, and we need the temperature to be in Kelvin. We already have half of it
right off the bat, the easy part. The easy part here is I told you that the temperature
rose by this much.