In this video, we're going to present a short explanation of an important concept in thermodynamics,
namely, that of state functions.
So it really is one of the most useful concepts in thermo.
And the idea is that for a state variable, and we'll talk about what a state variable
is, the pathway does not matter.
So for example, on some pressure-volume diagram, we go from A to B and there's one pathway,
there's a second, there's a third, then delta H is the same, delta S is the same, delta
U, delta V, delta, G, delta A. So enthalpy change, entropy change, internal energy change,
volume change, Gibbs' free energy change, Helmholz free energy change, the change from
A to B is independent of the pathway.
And thus, the important idea is that we pick the pathway that makes the calculations easy.
So for example, we have a reaction where reactant A at 600 degrees centigrade goes to product
B at 600 degrees centigrade.
What we want to know is what's the heat of reaction at 600?
Well we don't have tables that list heats of reaction at 600.
What we can do is say let's start with A at 600, let's cool A down to 25 and calculate
delta H1.
So delta H1 is going to be the integral from 600 to 25 the heat capacity dT.
We then carry out the reaction to form B at 25 degrees C so that's delta H2.
Well delta H2 is delta H of reaction at 25 degrees C and that's equal to heat of formation
B at 25 degrees C minus the heat of formation A at 25 degrees C and these heats of formation
are in tables.
So we can look those up and then we're going to want to take the product B and heat it
up to 600 degrees C and calculate delta H3 so delta H3 is the integral from 25 to 600
the heat capacity of B integrated over T. So then delta H reaction at 600 degrees C,
that's what we're interested in, is delta H1+delta H2+delta H3 and we pick this alternative
pathway because we can find heat capacities for A, we can find the heat of reaction at
25 degrees C from tables, and we can find the heat capacity of B. So keep in mind there
are things that we use a lot in thermo, like W and Q, these are not state functions.
They depend on the pathway rather dramatically.
Remember, a state functions means that if I go on say a T-P diagram, if I go from A
to B by reversible pathway and if I go from A to B by irreversible pathway for some gas,
then delta S for reversible pathway is the same as delta S for irreversible pathway.
Remember, this is for the gas.
We're not talking about delta S total of the system plus surroundings.
We're just saying for the gas that we're looking at, we're going from A to B by two pathways,
and we're going to have the same delta S for the gas independent of whether one is reversible
and one is irreversible.
The other thing to keep in mind when we're working with S and H and U and G, we're in
general only interested in changes.
We don't work with absolute values of H, U, and G. Instead we pick some reference, such
as in the steam tables.
For S, it would be possible to have absolute S values but in general, that's not what we're
working with so again, as in the steam tables, we pick some reference for S. It's only changes
that we're dealing with.
So just to summarize, if we want to calculate a property change, like entropy, enthalpy,
internal energy, we can replace the actual path, the actual pathway, the actual process,
by any other process that accomplishes the same change in state.
Namely any other process that goes from the same initial to the same final condition we
can use, because we pick a process to make our calculations easy.