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We've come to the end of week 5, a full week, a lot of material mostly devoted to
the first law of thermodynamics. So I'd like to finish then, with a review
of what I think the high points were. So, stated in words, the first law of
thermodynamics most simply would be, energy is conserved.
And mathematically, we go beyond that to express dU is equal to delta q plus delta
w. Where u is the internal energy, q is the
heat, and w is work. And there are conventions for the signs
of heat and work. By convention, heat is positive when it's
absorbed by the system. Work is positive when it's done on the
system, and vise versa. Energy is a state function.
That is, it depends only on the variables defining the state, temperature,
pressure, number of particles, for instance.
Heat and work on the other hand are path functions.
The amount of heat or work that changes depends on how you go from one state
point to another state point. Work, when it's done by expanding a gas,
is equal to minus the external pressure times dv, the change in volume.
Where p ext is, indeed, the external pressure against which the gas expands.
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Another state function is enthalpy. Enthalpy is written capital H.
It's defined as the sum of the internal energy plus pressure times volume.
Delta H for a constant pressure process, is equal to the heat transferred at
constant pressure, which is represented by putting a p as a subscript on q.
That also leads to a definition for a constant pressure heat capacity.
And that's defined as the change in enthalpy with respect to the change in
temperature at a constant pressure. Another way of thinking of it, is the
amount of heat that's required to raise the temperature of the substance by one
degree. For an ideal gas, the difference between
the heat capacity at constant pressure Cp, and the heat capacity at constant
volume Cv, when we talk about the molar quantities, they differ by r.
So the Cp is greater than Cv by r. Enthalpy itself can be measured, or most
more accurately enthalpy changes can be measured.
And in particular, if you want to talk about the change in enthalpy as you go
from absolute zero to some non-zero temperature, that's computed by looking
at the heat capacity as a function of temperature, which since it's a
measurement of how much heat is required to raise the temperature by one degree,
you can measure that degree by degree. And when you integrate all of that heat
that has been transferred, of course that's all contributing to the enthalpy.
That integration gives you the enthalpy change, and then when there are phase
transitions between say a solid and a liquid, or a liquid and a gas phase,
additional heat is required. That's defined as the heat of fusion, or
the heat of vaporization, integration of the heat capacities for the various
phases, also contributes as you get up to the next phase change.
And that allows you then to, through experiment define the enthalpy at a given
temperature relative to that at zero. And I showed an example that I've just
re-capitulated here in these slides for the case of benzene.
So, these are the measured heat capacities, these are the integrated heat
capacities which is the enthalpy. Enthalpy being a state function that
implies that it is a additive property, and so that leads to the convenient Hess'
Law. Which says if you'd like to know the
enthalpy change for a given reaction, if you can construct that reaction out of
other reactions, adding them or subtracting them, for which you know the
heat of reaction, then that unknown one will be the sum of those various other
reactions. Standard enthalpy of reactions, unlike
Just a general enthalpy of reaction which is an extensive process it depends on how
much you have a standard enthalpy of reaction is intensive.
It refers to one mole of a certain specified quantity, and such standard
enthalpies are tabulated for defined standard states where definition requires
a choice of convention. And in particular that convention is that
the standard molar enthalpy of formation for a pure element, in its most stable
form, at a given temperature, is defined to have a heat of formation of zero.
And given that definition, looking at the changes in enthalpy as you transform pure
elements into chemical compounds Allows you to define the heat of formation for
those chemical compounds. Given heats of formation and heat
capacities, one can then determine, as long as all of the participants in a
chemical reaction have known heats of formation and heat capacities, One can
determine the enthalpy change for that process, as the heat of formation of the
products minus the heat of formation of the reactant.
That's sufficient if you already have tabulated data for the temperature you're
interested in. If the temperature of interest for the
reaction is not the same as that the heats of formation are tabulated for.
That's when you can use the difference in heat capacities of products versus
reactants to add to that an integrated term from the temperature you know to the
temperature of interest, in order again to determine the heat of reaction at the
final temperature. So a lot of tools that are now in our
toolbox. That allow us to, understand changes in
energy, changes in work, changes in heat and changes in enthalpy.
That wraps up what I think are the most important points in week five.
We're going to move on from the first law of thermodynamics next week.
We're going to address a new state function and a key thermodynamic
property, and that is entropy. I look forward to seeing you then.
Dr. Christopher J. CramerDistinguished McKnight and University Teaching Professor of Chemistry and Chemical Physics
