Geochemistry
DM Sherman, University of Bristol
2008/2009
Thermodynamics
Part 1: The First Law, Heat and Work
Geochemistry
DM Sherman, University of Bristol
Energy
There are two kinds of energy:
• Kinetic energy (energy of motion)
• Potential energy (energy due to a force field)
The unit of energy is the Joule = 1 N•m = 1 VC
Thermal energy (heat) is kinetic energy of many atoms.
Atomic and molecular kinetic energy can take on several
forms: translational, vibrational and rotational. Even a
solid crystal has kinetic energy at T > 0!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Some fundamentals..
The system = that bit of the universe that we are
interested in.
The surroundings = the rest of the universe.
An open system can exchange matter with its
surroundings; a closed system cannot.
An isolated system cannot exchange heat or work
with the surroundings.
Some fundamentals (cont.)..
Extensive properties require looking at the system
as a whole (e.g., mass).
Intensive properties are well-defined by each small
region of the system (e.g., density, pressure,
temperature).
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Some fundamentals (cont.)..
Reversible processes happen by the successive
application of infinitesimal (dX) changes. Must occur
slowly, no friction and no finite temperature
differences.
Irreversible processes result from finite changes (Δ
X) in state variables.
The Zeroth Law of Thermodynamics
Two systems in thermal equilibrium will have the same
temperature.
In all of our calculations, we will be using the Kelvin
scale T (K) = T (ºC) + 273.15.
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Geochemistry
DM Sherman, University of Bristol
2008/2009
The First Law of Thermodynamics
dU = dQ + dW
Where
U = the internal energy of the system,
!
dQ = the heat added to the system from the
surroundings.
dW = the work done on the system by the
surroundings.
Types of Work
Work = Force x distance
dW = Fdx
1. Compressional work:
!
dW = "PdV
Where P is the external pressure, V is the volume of the
system. This is the work done on the system by the
surroundings.
!
When the system is compressed by the surroundings,
dV < O and dW > O.
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Types of Work (cont.)
2. Gravitational (mechanical) work:
dW = "Mgdh
where g is the gravitational acceleration and dh is the
change in height and M is mass.
!
3. Changing the surface area by fracturing or
recrystallization:
dW = "dA
where γ is the surface tension and dA is the change
in surface area.
!
Evaluation of Compressional Work
Compressional work is
dW = "PdV
so that
V
W = # "PdV
V0
The work done from V1P1 to V2P2 depends on the path
taken:
!
!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Evaluation of Compressional Work
Isobaric work: P is constant, then W = -PΔV.
Isochoric work: V is constant, then W = 0
Isothermal work: along a path P(V) where T is
constant. We need an equation of state.
The Ideal Gas Law
No. of moles
R = 8.31 J/mole-K
Volume
Pressure
PV = nRT
Temperature (Kelvin !)
Pressure and volume units must be consistent with nRT.
1bar " 1cm3 "
105 Pa
1N
1J
1m3
" 2 "
"
= 0.1J
bar
m Pa Nm (100cm)3
!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Evaluation of Isothermal Work (cont.)
For an ideal gas,
PV = nRT
so that
V=
nRT
P
Differentiating V with respect to P gives,
!
dV = "
nRT
dP
P2
!
so that
!
"PdV =
nRT
dP
P
!
Evaluation of Isothermal Work (cont.)
We can evaluate the work by integrating:
V
P
nRT
P
dP = nRT ln
P0
P0 P
W = # "PdV = #
V0
!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Evaluation of Isothermal Work (cont.)
Example: Calculate the work done in compressing 1
mole of a gas from 1 bar to 100 bar at 298 K. Assume
the gas is ideal (PV=nRT so that dV= (-nRT/P2)dP).
$ Pf '
nRT
dP
=
nRT
ln
& )
P2
% P0 (
$
J '
= (1 mol)&8.31
)(298 K)(ln100. /1.00)
mol " K (
%
= 1.14x10 4 J
" # PP PdV = # PP P
f
f
0
0
!
Evaluation of Isothermal Work (cont.)
Sometimes, the work is only defined by the volume
change..
Example: Calculate the work done in compressing 1
mole of a gas by 25 % at 298 K. Assume the gas is
ideal (PV=nRT).
$ 0.75V0 '
nRT
dV = nRT ln&
)
V
% V0 (
$
J '
= "(1 mol)&8.3145
)(298 K)(ln0.75)
mol " K (
%
" #VV PdV = " #VV
f
0
f
=
712.81 J
!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Heat vs. Work
The kinetic energies of atoms in a solid, liquid or gas
are quantized into many levels.
Adding heat changes
the population of
energy levels
Doing work changes
the energies of the
levels.
Evaluation of Heat
Heat is also a path-dependent quantity. We can
calculate the heat change if we specify a path (e.g.,
constant V or constant P).
The heat capacity Cv (constant V) or Cp (constant P)
reflects the number of energy levels available to the
system.
T
Q = " Cv dT
(Heat added at constant V)
T0
T
!
Q = " Cp dT
(Heat added at constant P)
T0
!
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Heat Capacities
Substance
Water (H2O)
Cp at 298 K, 1 bar
(J/mole-K)
75.19
Quartz (SiO2)
44.59
Calcite (CaCO3)
83.47
Iron (Fe)
24.98
Microcline (KAlSi3O8)
202.4
Forsterite (Mg2SiO4)
117.9
Enthalpy
Enthalpy (H) is defined as
H = U + PV
If we take the differential of H, we get
dH = dU + PdV+ VdP
Since dU = dQ - PdV then
dH = dQ + VdP
At constant P, therefore, dH = dQ.
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Enthalpy (cont.)
It follows that we can write
T
H(T) = H(T0 ) + " Cp dT
T0
The enthalpy of a
!substance can be
measured using
calorimetry. The bomb
calorimeter measures heat
change at constant V.
Enthalpy and Chemical Reactions
Hess’ Law: The enthalpy change of a chemical reaction is
the difference between the formation enthalpies of the
products and the formation enthalpies of the reactants.
It doesn’t matter how the reaction occured! Enthalpy is a
state function and evaluation of ΔH is path-independent.
C (graphite) + O2(g) → CO2(g)
ΔH = -391.51 kJ/mole
-(C (diamond) + O2(g) → CO2(g)
ΔH = -395.40 kJ/mole)
C (graphite) → C (diamond)
ΔH = 1.89 kJ/mole
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Geochemistry
DM Sherman, University of Bristol
2008/2009
Summary and Reading
Understand the concepts:
•First Law
•Compressional Work
•State Function
•Enthalpy
Suggested Reading:
Thermodynamics and Chemical Equilibrium
(http://www.chem1.com/acad/webtext/thermeq/)
Energy, Entropy and Fundamental Thermodynamic
Concepts (White, Chapter 2)
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