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.

Thermodynamics isn’t just a good idea, it’s the law!

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.

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.

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”.

…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?

Thermodynamics First 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

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!

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 =  H products -  H reactants Enthalpy – Heat of Reaction

The Universe System Surroundings Consider a chemical reaction (system).

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 = (+)

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 = (-)

The Second Law You can’t break even….the house always takes it’s cut. This all has to do with something called entropy.

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.

The answer is entropy. So, what’s the question? Why do things happen the way they do, and not in reverse?

Glassware breaks spontaneously when it hits the floor. Yet you can’t drop broken glass and have it form a graduated cylinder.

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

A sugar cube dissolves spontaneously in hot coffee, but dissolved sugar never precipitates out to form a sugar cube?

x

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.

Solids Liquids Solutions Gases Increasing Entropy Fewer Particles More Particles

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.

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

What does it mean that for some process we find that  S universe is negative?

This means that the process is not spontaneous in the direction described. Rather, the process is spontaneous in the opposite direction.

Heat Flow Energy (heat) flows from the warm swimmer to the cold ocean, never from the cold ocean to the warm swimmer.

Dave’s Hand John’s Hand 2.6 million to one What are the odds?

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.

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.

The more microstates a macrostate can have, the higher its entropy.

Hey, wake up loser. The law of entropy says you’re probably going to get junk.

I Microstates Consider a tank with 4 air molecules.

I II Microstates

I II III Microstates This is the most likely

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.

Probably Not!

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!

In this house we obey the laws of thermodynamics.

“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

Entropy is given the symbol S  S  =  n p S  products -  n r S  reactants Two factors determine the spontaneity of a reaction … 1. Heat of Reaction - Enthalpy 2. Disorder - Entropy

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

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.

 S o =  n p  S products -  n r  S reactants To Calculate the Change of Entropy (  S o )

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.

But what if they contradict each other in predicting spontaneity?

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  - T  S  Gibb’s Free Energy

 G  =  H  - T  S  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

Gibb’s Free Energy Can be calculated two ways…  G  =  H  - T  S   G  =  n p  G  products -  n r  G  reactants OR

Consider Melting Ice… H 2 O (solid) + Heat  H 2 O (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.

Example Consider Freezing Water… H 2 O (liquid)  H 2 O (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)

 The reaction will occur spontaneously at some temperature T and below. This temperature is of course 0 o C.

Another Example… Will the following reaction occur spontaneously at room temp (25 o C)? CH 4 (g) + 2O 2 (g)  CO 2 (g) + 2H 2 O (g)

1. Calculate  S  S =  n p  S products -  n r  S reactants CH 4 + 2O 2  CO 2 + 2H 2 O (gas)  S = [  S(CO 2 ) + 2  S(H 2 O)] – [  S(CH 4 ) + 2  S(O 2 )]  S = [ (213.6) + 2 (188.7)] – [ (186.2) + 2 (205)]  S = -5.2 joules/K mole

Next, calculate  H  H = [  H(CO 2 ) + 2  H(H 2 O)] – [  H(CH 4 ) + 2  H(O 2 )]  H = [(-395.3) + 2(-241.8)] – [(-74.86) + 2(0)]  H = kJ/mole = -804,000 J/mole Note: Be careful about the units.  H =  n p  H products -  n r  H reactants

Now, Calculate  G  G =  H - T  S = -804,000 – (298k)(-5.2) = -802,450 J/mole = -802 kJ/mole

Or, Calculate  G another way  G =  n p  G products -  n r  G reactants  G = [  G(CO 2 ) + 2  G(H 2 O)] – [  G(CH 4 ) + 2  G(O 2 )]  G = [(-394.4) +2(-228.6)] – [(-50.8) + 2(0)]  G = kJ

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.

Gibbs Free Energy ΔG o = ΔH o -TΔS o The “o” superscript indicates all substances are in their standard states – that is, at standard conditions (25 o C, 1 atm pressure) ΔG = ΔH -TΔS

OK, what if it’s not at standard conditions? Lets consider pressure…. ΔG = ΔG o + RT ln(P) Where R is the gas constant… R = J/K·mol

ΔG = ΔG o + RT ln(P) From this… ΔG = ΔG o + RT ln(Q) Where Q is the reaction quotient. See sec. 16.7

Now, lets consider the reaction when it’s at equilibrium…. At equilibrium…… Q = k where k is the equilibrium constant ΔG = 0 ΔG = ΔG o + RT ln(Q)

Now, lets consider the reaction when it’s at equilibrium…. At equilibrium…… Q = k where k is the equilibrium constant ΔG = 0 ΔG = ΔG o + RT ln(Q) 0

Now, lets consider the reaction when it’s at equilibrium…. At equilibrium…… Q = k where k is the equilibrium constant ΔG = 0 ΔG = ΔG o + RT ln(Q) 0 ΔG o = -RT ln(k) k

ΔG o = ΔH o -TΔS o

This is a linear equation with the form y = mx + b y = mx+ b

y = mx+ b 1/T ln(k)

This is a linear equation with the form y = mx + b y = mx+ b 1/T ln(k) Slope

This is a linear equation with the form y = mx + b y = mx+ b 1/T ln(k) Y intercept Slope