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Thermodynamics = Thermo + Dynamics
Classical “Thermo”:
empirical derivation of the laws
(this course)
Statistical “Thermo”:
theoretical derivations via statistical quantum mechanics
(if you “dare” to go there in the future …)
Laws of Thermodynaics:
0th, 1st, 2nd, and 3rd Laws
2 © Prof. Zvi C. Koren 21.07.10
Thermodynamics, is it an “easy” subject?From: http://www.journaloftheoretics.com/Articles/2-3/tane-pub.htm
It is well known that while being very efficient in practice, the thermodynamic
tool remains difficult to understand from the theoretical point of view.
It is also well known that the difficulties encountered are not mathematical, but
rather conceptual, and that they are perceived by those who have to learn
thermodynamics as well as by those who have to teach it.
The reality of the conceptual difficulty is openly and rapidly evocated rather than
cancelled as a forbidden subject.
One of the best examples is that given by the following opinion of the great
physicist Arnold Sommerfeld about thermodynamics:
"The first time I studied the subject, I thought I understood it except for a few minor points.
The second time, I thought I didn't understand it except for a few minor points.
The third time, I knew I didn't understand it, but it did not matter, since I could use it effectively."
Arnold Johannes Wilhelm Sommerfeld Born: 5 Dec 1868 in Königsberg, Prussia (now Kaliningrad, Russia)
Died: 26 April 1951 in Munich, Germany 3 © Prof. Zvi C. Koren 21.07.10
1. What is the maximum amount of work that can be performed by an
engine?
2. Which processes are spontaneous, and which need to be “kicked”
into action?
3. Which battery system is the most efficient?
What can “Thermo” do for us?
Etc., etc., etc. …
4 © Prof. Zvi C. Koren 21.07.10
Thermodynamics = Thermo + Dynamics
U
U (or E) = Internal Energy
What is meant by “internal” energy?
U is connected to the important (relevant) processes.
Total Energy = Internal Energy + External Energy
U (or E) f(position, velocity)
For example, if a chemical rxn occurs in a beaker, which is in a
moving train, or on somebody’s head or on the ground (different
potential energies due to height, position) what are we really
interested in?
5 © Prof. Zvi C. Koren 21.07.10
Forms of Energy
Kinetic Energy(Energy of Motion)
Mechanical(macroscopic objects in motion)
Thermal(submicroscopic motions of atoms, molecules, and ions)
Electrical(movement of electrons through a conductor)
Radiant(electromagnetic radiation –photons – propagating through space)
Potential Energy(Energy of Position)
Gravitational(objects held in a certain position against the force of gravity)
Electrostatic(positive and negative charges held in close proximity)
Chemical(energy attractions of electrons and nuclei in molecules)
6 © Prof. Zvi C. Koren 21.07.10
Interconversions of Kinetic Energy
Electrical
Mechanical
Thermal
Radiant
Generator
Steam
Engine
HeatLamp
Heater
LightBulb
SunlightSolarCell
Stirrer
7 © Prof. Zvi C. Koren 21.07.10
Interconversions of Kinetic & Potential Energies
Mechanical
Kinetic Energy Potential Energy
Thermal
Electrical
Radiant
Gravitational
Electrostatic
Chemical
ElevatorWaterwheel
Fallingmeteor
Staticcling
Lightning
Car engine
Wood
burning
Battery
Fireworks
Spaceshuttle
8 © Prof. Zvi C. Koren 21.07.10
Energy Units
SI unit = Joule (J)
1 J = 1 kg·m2/s2 = 1 V·C = 1 Pa·m3
1 cal 4.184 J (exactly), cal = calorie
1 BTU = 1054.35 J, BTU = British Thermal Unit
1 kW·h = 3.6x106 J, kWh = kilowatt hour
1 L·atm = 101.325 J (exactly)
1 cal = energy needed to raise the temperature of 1 g of water by 1oC.
1 “dietary calorie” is 1 Cal (“big calorie”) = 1 kcal.
Values & Units of R, Gas Constant:
0.0821 L·atm/mol·K
1.99 cal/mol·K
8.31 J/mol·K
James Prescott Joule (1818 - 1889)
English physicist
9 © Prof. Zvi C. Koren 21.07.10
System & Surroundings
NO thermal or,
e.g., mechanical
links to the outside
world
Closed with respect
to matter, but there
are thermal and,
e.g., mechanical
links to the outside
world
Open to everything
10 © Prof. Zvi C. Koren 21.07.10
State Functions
State Variables:P, V, T, n
properties that depend only on the state itself and not on the “history” of that state
Examples
Thermodynamic Properties:U (or E) = Internal EnergyH = EnthalpyS = EntropyG = Gibbs Free EnergyA = Helmholtz Free Energy
Path Functionsproperties that depend on the process – the way the change is brought about
Examplesw (or W) = work (compression, expansion, stirring, electrical, …)q (or Q) = heat
Heat is heat!!! But work could be many things!12 © Prof. Zvi C. Koren 21.07.10
The Existence of Temperature
&
The Zeroth (0th) Law of Thermodynamics
A
B C
Thermal
Equilibrium
Thermal
Equilibrium
Thermal
Equilibrium
That is, they’re all at the same T
13 © Prof. Zvi C. Koren 21.07.10
First Law of Thermodynamics
Infinitesimal changes (differential form): dU = đq + đw
Finite changes (integral form): U = q + w
dx = exact differential = (מסויים)דיפרנציאל שלםđx = inexact differential (“dee-slash”) or x
The system does not “know” whether q and/or w were used to change its energy, U. We can tell, but the system is “blind”.
Heat and work are equivalent ways of changing a system’s energy.The system is like a “bank”: It accepts deposits in either “currency”,
but stores its reserves as internal energy.
two methods of changing the energy of a system
For example, as Lord Rumford noticed while working in a cannon
factory, drilling into metal increased the temp, as if it was heated.
Thus, w can have a similar affect as q in raising the U.
Benjamin Thompson Rumford (1753-1814)
14 © Prof. Zvi C. Koren 21.07.10
System
State 1 State 2
(P1,V1,T1,n1) (P2,V2,T2,n2) :גַדלים מדידים
q
w
U = U2 - U1
U1 U2
(תחילי וסופי)תלוי במצבי הקצה
U = q + w
Schematic of Energy Changes in a System
15 © Prof. Zvi C. Koren 21.07.10
U = q + w
2. The equation is NOT any of the following:
U is a state function
q and w are path functions
U = q + w
or
U = q + w
Notes about :
3. q & w are algebraic quantities (+ or –):
A positive quantity is one that increases U, so:
q = +, heat absorbed by system from surroundings: endothermic process
–, heat released by system to surroundings: exothermic process
w = +, work done on the system by the surroundings (e.g., compression)
–, work done by the system on the surroundings (e.g., expansion)
4. While q & w are path-dependent, their sum is “amazingly” invariant.
Other examples? (length of a vector, Hess’s Law, etc.)
1. First Law is for a closed system (closed to material, but open to q and w)
16 © Prof. Zvi C. Koren 21.07.10
Δxxxdx if
f
i
j
j
x
1
Back to First Law – Differential Form
& The Meaning of dx and đx :
dU = đq + đw
State i State fqtotal
đq1 đq2 đq3 …
= x1+x2+x3+ ··· = xi
f
i
f
dU = đq + đw dU = đq + đw U = q + w
Differential Form Integral Form
đx =(BIG x)
i
f
đx (đq, đw)dx (dU)
inexact differential exact differential
infinitesimal QUANTITY of x
đx = little bit of x: x1 đx1, etc.
infinitesimal CHANGE in x (between close states)
đx = x dx = xi
f
17 © Prof. Zvi C. Koren 21.07.10
How can we tell
whether a differential is exact (dz) or inexact (đz)?If “z” is a state function, where z=z(x,y), then:
dyy
zdx
x
zdz
xy
partialderivative
totaldifferential
xy y
zN
x
zMNdyMdxdz
& ,
xy
z
x
z
yy
M
xyx
2
yx
z
y
z
xx
N
yxy
2
order of
differentiation
is irrelevant
aldifferentiexact an is then , and if So, dzx
N
y
MNdyMdxdz
yx
and z is a state function!!! (The reverse is also true.)18 © Prof. Zvi C. Koren 21.07.10
More Two-Way Mathematical “Streets”
For State & Path functions:
(cycle integral מסלול סגור) 0 dx(Why?)
constantdx f
i
f
i
đx f(integration path)
dx is an exact differential x is a state function (property)
If then
then If
đx is an inexact differential x is a path function (property)
x is a state function (property)
x is a path function (property)
x is a state function (property)
19 © Prof. Zvi C. Koren 21.07.10Additional Problems on Exactness
For an isolated sysytem (sys + surr), U is saved and dU = 0:
Why is U a State Function?
Energy (and mass) cannot be created or destroyed:
“Law of Conservation of Energy (and mass)”Why? Because!!! (Perpetual motion or perpetuum mobile machines do not exist.)
1 2
U = q + w
qa,wa;Ua
qb,wb;Ub
Ua = –Ub, otherwise we WILL be able to create or destroy energy
qa vs. qb, wa vs. wb, Ua vs. Ub ?
U is a State Function
dU = 0
20 © Prof. Zvi C. Koren 21.07.10
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