Or, if you like, let me write it out more, more generally.
So, if I want to know the entropy at temperature 2, relative to the entropy at
temperature 1, ST2 minus ST1. It's the integral from T1 to T2 of the
heat capacity, which may depend on the temperature.
So we'll keep it inside the integral, dT over T.
And indeed if we start from 0 Kelvin as T1, that actually gives us a way to
express the absolute entropy at a given temperature.
It's equal to whatever the temperature, sorry, excuse me, whatever the entropy is
at absolute zero, plus the integral from zero to that target temperature, T2.
Again, CPT dT over T. So what this says is that we can
calculate the entropy of a substance at any temperature, T2, if we know the
entropy at zero kelvin and the constant pressure heat capacity.
And you may recall, when we talked about enthalpy, we talked about the measurement
of the heat capacity. That's just how much heat does it take to
raise the temperature 1 degree. And so that's a readily accessible
quantity. So with heat capacities in hand, we can
go and measure entropies. So that's actually something we're going
to take a look at in, in more detail and the first step of doing that will be to,
in fact, explore and express the third law of thermodynamics.
Now, before we do that I think it is time maybe to slot in another demonstration.
And in particular, a demonstration that illustrates the importance of entropy as
one goes to higher temperatures. So I'll let you watch that, and then,
we'll return to look at the third law of thermodynamics.
[SOUND] Have you ever tried to polish silver in order to remove tarnish?
It can be a lot of work with a physical polish, rubbing every square centimeter
of surface. Some of you might know, that you can also
immerse silver, in a hot solution sodium bicarbonate, that is, baking soda, that
also includes immersed aluminum foil. That's an example of an electrochemical
process that can be described in fascinating detail using thermodynamics.
But that is beyond the scope of this course, unfortunately.
However, there is another approach that one might employ.
And one that we already have the thermodynamic tools necessary to
understand. The tarnish on silver is silver oxide.
That is, there is a small layer on the surface of the silver where oxygen atoms
have bonded to the surface to form silver oxide, which instead of being a lustrous
metallic color, is dark and opaque. Tarnish on silver can also be silver
sulfide but we'll ignore that complication here.