In this module we're going to look at how we find the entropy of the universe
to determine whether or not a process is spontaneous.
Our objective is to understand how temperature affects the entropy of the
surroundings,
and in turn, how that affects the entropy of the universe.
When we look at entropy of the universe we know that we must have a positive value
in order to have a spontaneous process.
We also know that the change in entropy of the universe is equal to the change in
entropy of the system
plus the change in entropy of the surroundings. these are not necessarily
negatives of one another. What we have to look at
are the individual components to determine whether or not a process is
spontaneous.
when we look at the values at the delta S of the system and delta S of the
surroundings
we see that we can have both values as positive numbers, both fighters negative numbers,
or have one value that's positive and one value that's negative.
It's the balance and the signs of these numbers that determine whether or not a
process is spontaneous. Let's take an example where
this process is not always spontaneous. Looking at the freezing of water we know
that at lower temperatures this happen spontaneously. At higher temperatures
it is a non spontaneous process, so what we have to look at is
where's the energy going? We're dispersing energy
so we have to look at the temperature of the surroundings to see
which one is going to favor
the spontaneous process. For both of these we see that the Delta S of the system
is the same, but we see that the Delta S of the surroundings
is different and therefore the Delta S of the universe ends up being
different. It's the Delta S of the surroundings that depends on the temperature
because that's going to determine how that energy is dispersed.
So remembered that energy tells us about the dispersal of energy,
and the qualitative value tells us that entropy is a measure of energy dispersed
per unit of temperature.
As the temperature increases the amount of entropy for a given amount of
energy dispersed decreases, therefore, something at a higher temperature
has a lower impact and will not change the Delta S of the system as much.
As the temperature decreases or drops the amount of entropy for a given amount of
energy dispersed increases.
This means that at a lower temperature
we have a higher impact, so looking at the relative values of the Delta S
of the system
versus the delta S of the surroundings the temperature will determine
how much the Delta S of the surroundings will impact
the value of the delta S of the system and therefore how it will impact the
delta S of the universe.
So, how do we find the delta S of the surroundings? We know it's dependent on
temperature but we have to find the actual value of it.
For endothermic reactions, so that will be a reaction
where Delta H is less than zero,
so a negative value, we see that the delta S of surroundings is greater than zero
because an exothermic reaction is releasing energy. We're dispersing that energy
and so the Delta S of the surroundings is increasing.
An endothermic reaction when Delta H
is greater than zero, or a positive value,
shows we're absorbing energy from surroundings. We're
decreasing the dispersal of energy, and therefore delta S of the surroundings
will be
less then zero. But this doesn't give us the exact value of delta S of the
surroundings
to do that we have to combine both the enthalpy and the temperature
to understand how they are related.
So if I want to look at the relationship between
enthalpy and delta S of the surroundings I have to take the negative
of the delta H value, the negative enthalpy of the reaction of the system,
and divide it by the temperature. Remembered that the temperature must be
in units of Kelvin.
So now
we can find delta S of the universe if we know delta S of
the system and delta S of the surroundings. We have our way to find
delta S of the surroundings.
We looked earlier at how to find delta S of the system
by looking at products minus reactants, and from that information we could then
find delta S
of the universe, and then we can finally determined is a reaction
spontaneous or not
based on the Delta S of the universe.
so as we said before a small T, or a low temperature,
we have a large delta S of surroundings. For a large T
we have a small Delta S of surroundings.
Let's look at an example. Under which of the following conditions will Delta S
of the universe
always be positive?
