the field of thermodynamics studies the behavior of energy (heat) flow. from this study, a number of...
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The field of thermodynamics studies the behavior of energy (heat) flow. From this study, a number of physical laws have been established.
The laws of thermodynamics describe some of the fundamental truths observed in our Universe.
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Thermodynamics isn’t just a good idea, it’s the law!
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A way to think about thermodynamics, is to liken it to gambling. The Universe is the Great Casino.
You have to understand, that no matter what, in the long run, the house is going to win.
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1. You can’t win. You can’t get something for nothing.
2. You can’t break even. The house always wins!
3. You can’t get out of the game.
These are the rules:
In the end, you’re going to lose….no matter what.
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Every time you place a bet…the house takes it’s share.
You can’t make any new money,….the amount of money is fixed, and finite. Kind of like “table stakes”.
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…and so first there was the second law, then there came
the first law, which was followed 80 years later by the zeroth law, and then
finally the third law, which may not actually be a law at all. So, what confuses you?
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ThermodynamicsFirst Law: The energy of the universe is
constant. Energy can be neither created nor destroyed, so while energy can be converted to another form, the total energy remains constant.
This is merely a statement of conservation of energy.
Energy In Energy Out
Any Isolated System
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Electric Motor
Electric Generator
Mechanical Work Out
For a long time, people tried to design and build Perpetual Motion Machines
Cool. I’m going to be rich!
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The enthalpy of a substance is a measure of the energy that is released or absorbed by the substance when bonds are broken and formed during a reaction.
When bonds are formed, energy is released. In order to break bonds, energy must be absorbed.
H = Hproducts - Hreactants
Enthalpy – Heat of Reaction
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The Universe
System
Surroundings
Consider a chemical reaction (system).
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The Universe
System
Surroundings
Heat
When heat leaves the system, the reaction is said to be exothermic. (H = -)
Energy of the surroundings goes
up. H = (+)
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The Universe
System
Surroundings
Heat
When heat enters the system, the reaction is said to be endothermic. (H = +)
Energy of the surroundings
goes down. H = (-)
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The Second Law
You can’t break even….the house always takes it’s cut.
This all has to do with something called entropy.
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The time has come the Walrus said, to speak of many things. Of shoes, and ships, and sealing
wax. Of Entropy, Enthalpy, and Free
Energy.
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The answer is entropy.
So, what’s the question?
Why do things happen the way they do, and not in reverse?
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Glassware breaks spontaneously when it hits the floor. Yet you can’t drop broken glass and have it form a graduated cylinder.
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Why is it that….
A parked new car left to itself will become junk over time…..
The junk car will never become like new over time
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A sugar cube dissolves spontaneously in hot coffee, but dissolved sugar never precipitates out to form a sugar cube?
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x
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Entropy
A measure of the disorder of a system.
Systems tend to change from a state of low entropy to a state of higher entropy. That is to say, if left to themselves, systems tend to increase their entropy.
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Solids Liquids Solutions Gases
Increasing Entropy
Fewer Particles More Particles
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The second law can be stated in many forms…
Heat can never pass spontaneously from a cold to a hot body. As a result of this fact, natural processes that involve energy transfer must have one direction, and all natural processes are irreversible.
If you do work, if you use energy, if you convert it from one form to another, you will lose some of it. No machine can be 100% efficient. This lost energy goes to increasing the disorder of the Universe.
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The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.
S universe = S system + S surroundings
For a spontaneous process:
S universe > 0
For an equilibrium process:
S universe = 0
The Second Law of Thermodynamics
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What does it mean that for some process we find that S universe
is negative?
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This means that the process is not spontaneous in the direction described. Rather, the process is
spontaneous in the opposite direction.
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Heat Flo
w
Energy (heat) flows from the warm swimmer to the cold ocean, never from the cold ocean to the warm swimmer.
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Dave’s Hand
John’s Hand
2.6 million to one
2.6 million to one
What are the odds?
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Johns hand is one of a very select group of hands called a straight flush. Out of the 2.6 million possible hands, there are only 40 straight flushes.
Dave has junk. There are over a million hands that are junk.
In other words, there are very few combinations of five cards that form a straight flush, and very many combinations that result in junk.
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John’s Hand 7 8 9 10 J Straight Flush
Dave’s Hand 4 8 7 3 K Junk
Microstate Macrostate
Entropy is defined in terms of microstates and macrostates.
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The more microstates a macrostate can
have, the higher its entropy.
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Hey, wake up loser. The law of entropy says
you’re probably going to get junk.
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I
Microstates
Consider a tank with 4 air molecules.
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I
II
Microstates
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I
II
III
Microstates
This is the most likely
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And so it is with air molecules. Considering the extremely large number of molecules in a house
for example, the odds are overwhelmingly high that the
molecules will spread out evenly.
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Probably Not!
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So, next time you’re thirsty, go ahead,
wander into the kitchen and get yourself a drink
of water. There’ll be plenty of air to breath when you get there.
Probably!
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In this house we obey the laws of
thermodynamics.
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“If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations.
If it is found to be contradicted by observations – well, these experimentalists do bungle things sometimes.
But if your theory is found to be against the second law of thermodynamics I can give you no hope. There is nothing for you do do but collapse in deepest humiliation”
Sir Arthur Eddington - 1928
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Entropy is given the symbol SS = npSproducts - nrSreactants
Two factors determine the spontaneity of a reaction…
1. Heat of Reaction - Enthalpy
2. Disorder - Entropy
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Two factors determine the spontaneity of reactions…
1. Heat content - - - Enthalpy
Reactions with a (-) H tend to be spontaneous.
2. Disorder - - - Entropy
Reactions with a (+) S tend to be spontaneous
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Typically, the entropy is expected to increase for processes in which…
Liquids or solutions are formed from solids
Gases are formed from either solids or liquids.
The number of molecules increases during a chemical reaction.
The temperature of a substance is increased.
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So = np S products - nrS reactants
To Calculate the Change of Entropy (So)
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Cool, we now have two separate means to predict
spontaneity.
Enthalpy, for which -H means the process tends to be
spontaneous, -and-
Entropy, for which +S means the process tends to be
spontaneous.
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But what if they contradict each
other in predicting spontaneity?
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Combines the concepts of enthalpy and entropy in predicting spontaneity of a reaction.
Defined as the maximum amount of energy that can be taken out of a reaction to do useful work.
G = H - TS
Gibb’s Free Energy
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G = H - TS
If G is (+) the reaction is not spontaneous
If G is (-) the reaction is spontaneous
If G is (0) the reaction is at equilibrium
T is in Kelvin
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Gibb’s Free Energy
Can be calculated two ways…
G = H - TS
G = np Gproducts - nr Greactants
OR
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Consider Melting Ice…
H2O (solid) + Heat H2O (liquid)
H = (+) Endothermic
S = (+) entropy increases
G = H – T S= (+) – T(+)
Must be < 0 to occur
The reaction will occur spontaneously at some temperature T and above.
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Example Consider Freezing Water…
H2O (liquid) H2O (solid) + Heat
H = (-) Reaction is exothermic
S = (-) Entropy decreases going from a liquid to a solid
G = H - T S
At some temperature T and below, the S becomes larger, making G (-)
(This favors spontaneity)
(This favors non-spontaneity)
= (-H) – T(-S)
= (-H) + T(S)
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The reaction will occur spontaneously at some temperature T and below. This temperature is of course 0o C.
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Another Example…
Will the following reaction occur spontaneously at room temp (25oC)?
CH4(g) + 2O2(g) CO2(g) + 2H2O (g)
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1. Calculate S
S = npSproducts - nrSreactants
CH4 + 2O2 CO2 + 2H2O (gas)
S = [S(CO2) + 2S(H2O)] – [S(CH4) + 2S(O2)]S = [ (213.6) + 2 (188.7)] – [ (186.2) + 2 (205)]
S = -5.2 joules/K mole
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Next, calculate H
H = [H(CO2) + 2H(H2O)] – [H(CH4) + 2H(O2)]H = [(-395.3) + 2(-241.8)] – [(-74.86) + 2(0)]
H = - 804.0 kJ/mole = -804,000 J/mole
Note: Be careful about the units.
H = npH products - nrH reactants
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Now, Calculate G
G = H - T S
= -804,000 – (298k)(-5.2)
= -802,450 J/mole = -802 kJ/mole
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Or, Calculate G another way
G = npGproducts - nrGreactants
G = [G(CO2) + 2G(H2O)] – [G(CH4) + 2G(O2)]
G = [(-394.4) +2(-228.6)] – [(-50.8) + 2(0)]
G = -800.8 kJ
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The other laws…
The Third Law: It isn’t possible to reach absolute zero temperature. It is important to understand that all motion does not cease at this temperature, rather this is the lowest temperature that energy can be extracted from the substance.
The Zeroth Law: If A is in thermal equilibrium with C, and B is also in thermal equilibrium with C, then A is in thermal equilibrium with B. This establishes temperature as the fundamental variable in thermodynamics.
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Gibbs Free Energy
ΔGo = ΔHo -TΔSo
The “o” superscript indicates all substances are in their standard states – that is, at standard conditions (25oC, 1 atm pressure)
ΔG = ΔH -TΔS
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OK, what if it’s not at standard conditions?
Lets consider pressure….
ΔG = ΔGo + RT ln(P)
Where R is the gas constant…
R = 8.3145 J/K·mol
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ΔG = ΔGo + RT ln(P)From this…
ΔG = ΔGo + RT ln(Q)
Where Q is the reaction quotient.
See sec. 16.7
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Now, lets consider the reaction when it’s at equilibrium….
At equilibrium……
Q = k where k is the equilibrium constant
ΔG = 0
ΔG = ΔGo + RT ln(Q)
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Now, lets consider the reaction when it’s at equilibrium….
At equilibrium……
Q = k where k is the equilibrium constant
ΔG = 0
ΔG = ΔGo + RT ln(Q)
0
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Now, lets consider the reaction when it’s at equilibrium….
At equilibrium……
Q = k where k is the equilibrium constant
ΔG = 0
ΔG = ΔGo + RT ln(Q)
0
ΔGo = -RT ln(k)
k
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ΔGo = -RT ln(k)ooo STHkRTG )ln(
ΔGo = ΔHo -TΔSo
RT
ST
RT
Hk
oo
)ln(
R
S
TR
Hk
oo
1)ln(
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R
S
TR
Hk
oo
1)ln(
This is a linear equation with the form y = mx + b
y = m x + b
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R
S
TR
Hk
oo
1)ln(
This is a linear equation with the form y = mx + b
y = m x + b
1/T
ln(k)
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R
S
TR
Hk
oo
1)ln(
This is a linear equation with the form y = mx + b
y = m x + b
1/T
ln(k)
Slope
R
H o
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R
S
TR
Hk
oo
1)ln(
This is a linear equation with the form y = mx + b
y = m x + b
1/T
ln(k)
Y intercept
R
SoSlope
R
H o