Lecture 1 Plan of the Course The Geochemical Toolbox Thermodynamics Kinetics Aquatic systems Trace elements amp magmatic systems Isotopes Radiogenic Stable The Big Picture Cosmochemistry ID: 585961
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Slide1
Thermodynamics, Systems, Equilibrium & Energy
Lecture 1Slide2
Plan of the Course
The Geochemical ToolboxThermodynamics
Kinetics
Aquatic systems
Trace elements & magmatic systems
Isotopes
Radiogenic
Stable
The Big Picture: Cosmochemistry
Formation of the elements
Formation of the Earth and the Solar System
Chemistry of the EarthSlide3
Other Info
Grading: 40% Problem Sets (6 to 8),20
%
Prelim, 40
% Final Exam
http
://www.geo.cornell.edu/geology/classes/geo455/EAS455.htmlOffice: 4112 SneeOffice Hours: no formal office hours – drop by anytime.
Text: White
:
Geochemistry
,
Wiley
-Blackwell, ISBN 978-0-470-65668-6 Slide4
Thermodynamics
Thermodynamics is the study of energy & its transformations.
Chemical changes involve energy; by “following the energy”, we can predict the ‘equilibrium’ state of a system and therefore the outcome of reactions.
For example, we can predict the minerals that will crystallize from a cooling magma.
We can predict that as the concentration of atmospheric CO
2
increases, so does that of the ocean and the calcium carbonate shells of oysters and skeletons of corals will become more soluble.(This at first seems counter-intuitive, and has to do with a decrease in ocean pH).Thermodynamics uses a macroscopic approach.
We can use it without knowledge of atoms or molecules.We will occasionally consider the microscopic viewpoint
using statistical mechanics when
our understanding can be enhanced by doing
so.Slide5
Thermodynamics and Kinetics
The equilibrium state of a system is independent of any previous state. So, for example, if we do a partial melting experiment with rock, it should not matter if we start with a solid and partially melt it or with a melt and partially crystallize it, or whether we partially dissolve calcium carbonate or partially precipitate it.
Kinetics
is the study of rates and mechanisms of reaction.
Kinetics
concerns itself with the pathway to
equilibrium; thermodynamics does not. Very often, equilibrium in the Earth is not achieved, or achieved only very slowly, which naturally limits the usefulness of thermodynamics. Slide6
‘The System’
A thermodynamic
system
is
the
part of the universe we are considering. Everything else is referred to as the
surroundings. We are free to define the ‘system’ anyway we chose. However, how we define it may determine whether we can successfully apply thermodynamics.
Four
Kinds
of
SystemsSlide7
Equilibrium
The
equilibrium state
is the one toward which a system will change in the absence of
constraints
.
It is time invariant on the macroscopic scale, but not necessarily on the microscopic one.Slide8
Equilibrium & Thermodynamics
Conundrum: strictly speaking, we can apply thermodynamics only to the equilibrium state. If
a reaction is proceeding, then the system is out of equilibrium and thermodynamic analysis cannot be
applied!
Solution:
we imagine
reversible processes in which systems are only infinitesimally out of equilibrium. In contrast, natural processes can proceed only in one direction and are irreversible.We might also imagine
local equilibrium where even if the whole system (e.g. the ocean or magma and crystals) is out of equilibrium, we can imagine a part of it is in equilibrium (rim of the crystal).Slide9
Fundamental Variables
Pressure: PForce/unit area
Volume; V
Temperature: T
Energy: U
Work:
Wwe are mainly concerned with P-V work: pressure integrated over volume changeWork done by a system is negativeHeat: QEntropy: S – more on that in next lectureSlide10
Work, Heat, and Energy
Work is done by moving a mass,
M
, over some distance against a force (
eg
., gravity)
Where
Note that the minus sign occurs because work done by a system is negative, work done on a system is positive.Heat is thermal energy that results from collective random motion of atoms or molecules in a system (including rotational and vibrational motions); related to kinetic energy, particularly with respect to translational motions of molecules in a gas.Slide11
System International (S.I.) Units
Pressure: Pascals
, Pa ( Newton/m
2
= kg-sec
2
/m)Other: atmospheres ~ bars ≈ 0.1 MPaVolume: m3Other: cm3, liter 1m
3 = 106 = 103 l(note: liter is the standard unit in aquatic chemistry)
Temperature: Kelvins (K)
Other; ˚C; 1K = 1˚C, 0˚C = 273.16 K
Energy: Joules, J (kg-m
2
/sec
2
)
Other: calories 1J = 4.184 cal.
Entropy: J/K
Mass: mole, N (also
mol
); amount, in grams, of an element equal to its atomic weight (e.g., 1
mol
C = 12g or 0.012 kg).Slide12
Extensive vs. Intensive variables
Extensive variables are ones that depend on the mass of the
system, intensive ones do not.
Which of the following are extensive?
Pressure
Volume
TemperatureEnergyWork
HeatMolesWe can convert extensive variables to intensive ones by dividing on extensive variable by another.
Molar
volume:
Density: V/MSlide13
State Variables and Equations of State
State variables depend only on the state of the system, not on the path taken. Not all the variables listed above are state variables.
Equations of state express the relationship between state variables, e.g.
PV=NRT
Tells us, for a given number of moles, now temperature, volume, and pressure of an ideal gas relate to each other; i.e., if we heat the gas, what happens to volume and pressure?Slide14
Ideal Gas Law
PV = NRT
Ideal gas law grew out of Boyle’s (1627-1691) experiments with gases and was formalized by
Émile
Clapeyron in 1834.
Fine as an approximation, but doesn’t work with real gases.
An ideal gas is one in which:The molecules occupy no volume
The only interactions between molecules are elastic collisions.When might a gas most behave ideally?Van der Waals EquationThe
b
term corrects for the finite volume of molecules while the
a
term corrects for their interactions.
This is still often a poor approximation to the behavior of real gases. Two geochemically important gases, water vapor and CO
2
show particularly complex P-T-V behavior.
R: Gas constant: simply converts units. (We’ll see it is the molar equivalent of
Boltzmann’s
constant, which has atomic units).Slide15
General Equation of State
Obviously, there is no one solution to the ideal gas law, but we can imagine a couple of special cases:
Hold pressure constant
Isothermal compressibility (
β
): change in volume with change in pressure at constant temperature
per unit volume: β≡ -1
/V(∂V/∂P)
T
Hold temperature constant
Coefficient of thermal expansion
(
α
): change in volume with change in temperature at constant pressure
per
unit volume
1/V(
∂V/
∂T
)
P
.
We can write a general equation relating V, T & P:
dV
= ∂V/∂T
)
P
dT
+
(
∂V/∂P
)
T
dP
dV
= Vα
dT
+
Vβ
dP
These equations are general and apply to all substances. The difference is that
α
and
β
have simple solutions for ideal gases (
NR/P and 1/T, respectively), while they are more complex functions for real substances.Slide16
Temperature
Temperature is a measure of the average internal kinetic energy of a system.
How do we measure it?
Since the volume of an ideal gas is a simple function of
T
at constant
P, we can use it to construct a thermometer.We can arbitrarily define a scale such thatV =
V0(1+γτ)Where
τ
is our measure of temperature. If so, we might have negative
τ
.
But note
V
cannot be negative, so there must be
a
minimum value of
τ
: an absolute minimum to temperature.
The absolute minimum of
T
occurs where the volume of an ideal gas is 0.
Use the absolute scale (K) in all thermodynamic calculations
.Slide17
Zeroth Law
Two bodies in thermal equilibrium have the same temperature.
Two bodies in equilibrium with a third body are
in
equilibrium with
each
other.Slide18
The Three E’s
Energy, Entropy and EnthalpySlide19
The First Law
Statements:
Energy is conserved in all transformations
Heat and work are equivalent (the sum of the two is always the same).
Change in energy of a system is independent of the path taken.
Mathematically:
ΔU = Q +WThe First Law implies that energy change is path independent and thus that energy is a state variable. Heat and work are not.State variables have exact differentials (heat and work do not).
(we are mainly concerned with energy changes, not absolute amounts).(Of course, the First Law ultimately fails because energy can be created out of mass. This turns out to be important because this energy source powers not only the Sun (and hence many processes at the surface of the Earth), it also powers, in part, the Earth’s interior and geologic processes such as plate tectonics. That need not concern us until much later in the course.)Slide20
State Functions & Path Independence
State functions are path independent and have
exact
differentials.
Think about an internal combustion engine. Chemical energy is released by burning gas. Some of that energy goes into heat and some to work. There is no fixed rule about how much goes to each – it depends on your engine design (engineers work to increase the amount going into work).
Therefore, heat and work cannot be state functions.
However, no matter how you design the engine, the sum of heat and work for a given amount of (fully) combusted gasoline is the same.Energy is path independent and a state function.Slide21
State Functions & Exact Differentials
State functions have exact differentials.
(These are not new, they are the kind you have learned about in calculus).
This means we can obtain (in principle anyway) an exact solution if we differentiate them (or integrate the differentials).
Exact differentials have the property that the cross differentials are equal (in other words, if we differentiate by two separate variables, the order doesn’t matter).
Again, this is what you learn in calculus.
Consider dV = (∂
V/∂T)PdT + (∂V/∂P)
T
dP
If V is a state function, then (∂V
2
/
∂
T∂P
)=
(∂V
2
/
∂P∂T
)
This is not true of non-state functions like work and heat.Slide22
Work
Is Work done by an ideal gas a state
function?
Work is:
dW
= -PdVExpanding the dV term, we have
Substituting for (∂V/∂T)P
and
(∂
V/
∂P
)
T