INSTRUCTOR: Here we're gonna look at
how to calculate entropy changes if we have a liquid
or solid, temperature changes,
or if we go through a phase change
from say a liquid to a gas.
And the way we're gonna do this
is to start with our definition, entropy change,
which is the integral dQ reversible over T,
where T is absolute temperature.
The idea is if we're at state one,
and we go to state two,
if we pick a reversible pathway
and then the heat transfer at any point
divided by the temperature of that point integrated
gives us the entropy change.
And so to get the heat transfer,
we're gonna use the first law,
so let me write down the differential form,
first law for a closed system.
So Q reversible and work reversible.
So work reversible would mean
pressure times the differential.
It turns out changing pressure has very little effect
on a liquid or a solid, we don't change the anthopy,
we don't change the entropy,
we don't change the volume, et cetera.
So to our first approximation for a liquid solid,
we can write this as minus the differential PV.
Now, what I'm going to do is take this term,
bring it to the other side of the equation,
and we'll see that we have on the left dU plus d[PV]
and u plus PV is H, so this is dH is dQ reversible.
dH for a liquid or solid is heat capacity, Cp times dT.
So that means if we now want to calculate
the entropy change, and again let's rewrite our definition,
and dQ reversible is CpdT over T.
Heat capacity for liquid or solid
does not change much with temperature,
some reasonable temperature range,
so if that's a constant,
then the entropy change starting temperature,
our final temperature.
Here's entropy change as we change temperature
for a liquid or a gas.
Well, the other case we want to look at now
is entropy change for a phase change.
So we want to look at entropy change for a phase change,
an important aspect of a phase change is
it takes place at constant temperature
and at constant pressure.
So our equation for first law is identical
for a constant pressure reversible process,
and so we have dH is dQ reversible.
The difference is dH is the anthopy change
for a phase change.
So this is a number, right, we're at one temperature.
And so at a given temperature, this is gonna be a constant,
so when I go back to my definition of dQ reversible over T
for a phase change dH over T integrated,
T is a constant so with delta H over T
and so for a phase change, entropy change,
and again this is per mole,
and could we change per mole
divided by absolute temperature.
Again let's emphasize this is per mole.