```Organization: Auburn University Engineering
From: henley@eng.auburn.edu (James Paul Henley)

o What is Thermodynamics?
o What are the First and Second Laws of Thermodynamics?
o How are the Laws of Thermodynamics applied to various systems?
o Does Snowflake formation violate the Second Law of Thermodynamics?
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```
o What is Thermodynamics?

"Thermodynamics is defined as the study of energy, its forms and transformations, and the interactions of energy with matter." [1, p.5]

Energy can exist in a number of forms, electrical energy, chemical energy, potential energy, kinetic energy, PV energy, mechanical energy, etc. In order to apply the laws of thermodynamics mathematically, which is the only way to "prove" anything, you must have a definition of energy that is consistent with the laws of Thermo. The Laws of Thermo describe the Laws by which transformations in energy must abide. They have never been shown false, and they have been demonstrated so thoroughly, that they are not considered theories, but laws. The field of engineering is based largely on these laws, and in most fields of engineering*, proposed processes must first be shown to satisfy these laws to merit furthur consideration. In chemical engineering, they are necessary criteria for chemical reaction equilibria.

* At Auburn University, all departments in the Engineering School except Computer Science require their students to take EGR 201 - Introductory Thermodynamics. Applications of the Laws of Thermodynamics can be demonstrated in every field of engineering represented, including Agricultural Engineering.

W : Work - Energy transfer due to a force acting against a resistance. In most general sense, work can be described as change.

Q : Heat Transfer - one of three different types of energy transfer:

1) Conduction
2) Convection

Enthalpy is a convenient property defined in terms of internal energy, pressure, and volume:

```   H = U + PV

H : enthalpy
U : internal energy
P : pressure
V : volume
```
Gibbs energy is a measure of the amount of energy available to do work (ie. to effect a change) in chemical processes. To determine Gibbs energy we take the enthalpy, and subtract out the disordered energy, ie. the energy that is not available to do work:
```   G = H - TS

G : Gibbs free energy
S : entropy
T : temperature
```
So, what is entropy?

Entropy is a measure of the disorder of the energy of a system. Ordered energy is available to do work, disordered energy is not. So, mathematically we see that entropy*temperature is the amount of disordered energy at that temperature.

One criterion for chemical equilibruim in a closed system is that the total Gibbs free enery must be at a minimum, which means that entropy must be at a maximum.

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o What are the First and Second Laws of Thermodynamics?

The first law is generally stated in terms of a closed system, also called a control mass. So an auxiliary law is the conservation of mass:

THE LAW OF THE CONSERVATION OF MASS

"The mass of a control mass never changes." [1, p.120]

THE FIRST LAW OF THERMODYNAMICS

For a Closed system (control mass)

"A change of the total energy (kinetic, potential, and internal) is equal to the work done on the control mass plus the heat transfer to the control mass." [1, p.121]

"Although energy assumes many forms, the total quantity of energy is constant, and when energy dissapears in one form, it appears simultaneously in other forms." [2, p.22]

E2 - E1 = 1Q2 + 1W2

E2 : energy of the system at state 1
E1 : energy of the system at state 2

```   1Q2: the net heat transfer into the system in going from
state 1 to state 2

1W2: the net work done on the system in going from state 1
to state 2
```
[1, p.121]

"Equililibrium is a word denoting a static condition, the absence of change. In thermodynamics it is taken to mean not only the absence of change, but the absence of any tendency toward change on a macroscopic scale. Thus a system at equilibrium is one which exists under such conditions that there is no tendency for a change in state to occur." [2, p.37]

For an Open system: (control volume)

rate of change of energy = energy flow rate in - energy flow rate out

Control Volume : A system fixed in space which permits mass to cross the system boundaries. [1, p.130]

```.     .      .     .
d~Ecv/d~t = Ein - Eout + Qcv + W

d~ : partial derivative

Ecv : Total energy of the control volume
.    .
Ein, Eout : Energy flow rate in and out, across crossing boundaries (Energy
.           flux at crossing boundaries)
Qcv : Net rate of heat transfer into system across inside boudaries.  (heat
.           flux)
W  : Net rate of work done on system by surroundings  (power)

[1, p.133]
```
Steady State: Implies that conditions at all points in the [system]* are constant with time. For this to be the case, all rates must be constant, and there must be no accumulation of material or energy within the [system] over the period of time considered. [2, 30]

* lit. apparatus. For a control volume analysis, each component of the apparatus is considered an open system (control volume). The apparatus as a whole is actually a closed system. A point in the system would be represented by a particular location in the apparatus.

For a cyclical process in a closed system, a point in the system would be represented by a periodic time in the cycle.

Pseudo steady state is a condition in which it is convenient to assume steady state for portions of a non-steady state system.

THE SECOND LAW OF THERMODYNAMICS:

"The entropy S, an extensive* equilibrium property, must always increase or remain constant for an isolated system**. [1, p.187]

dSi >= 0

dSi : change in entropy of an isolated system**

* The units of extensive entropy are energy divided by temperature. The units of the intensive property would be energy divided by temperature and mass, or divided by temperature and moles.

In SI units:

```   S (the extensive property) has units:    J/K
s (the intensive property) has units:   J/(kg K)  or J/(kg mole  K)
```
** An isolated system is one in which there is no mass or energy transfer across system boundaries. (see How do the Laws...Apply to Various Systems)

In terms of a non-isolated system:

```   dSsys + dSsur >= 0  or alternately: dSu >= 0

dSsys : change in entropy of system
dSsur : change in entropy of surroundings
dSu   : change in entropy of universe
```
Entropy generation within a system is due to friction. In the absence of any friction, then the net entropy change is 0. Friction here includes things like electical resistance, resistance to heat transfer, resistance to chemical reactions (inverse of rate constant), mechanical friction, air resistance, etc.

For any real process, there is friction. Entropy is transferred with heat transfer, and the direction of entropy transfer is the same as that of heat transfer. So, any time heat is transferred into the system, the entropy of the system increases. Any time heat is transferred out of the system, the entropy of the system decreases. Heat transfer out is the only means of decreasing system entropy of a closed system. For an open system, entropy can be transferred out with energy transfer out, and with mass transfer out.

So, any real process increases the entropy of the system + surroundings, but whether the entropy of the system itself increases or decreases is dependent on the heat transfer.

Since for an isolated system, there is no heat transfer, there is no means of reducing the entropy of the system. Which means that for any real process in an isolated system, the entropy of the system increases, and the energy available to do work decreases.

Equilibrium, the state in which all properties stop changing, is defined by the second law as is the state of maximum entropy, that is, there is no more energy available to do work, and no capacity for change.

In terms of cyclic process:

"It is impossible by a cyclic process to convert the heat absorbed by a system completely into work." [2, p.139]

"The word cyclic requires that the system be restored periodically to its original state." [2, p.139]

In terms of a cyclic process, there are two implications here:

1) Some of the heat in the system is unavailable to do work in restoring the system to its original state.

2) In order to achieve a steady state cycle, there must necessarily be some energy lost, ie. not available to do work. This would mean a continuous input and output of energy is necessary to drive a continuous cycle.

Attempts have been made to invent devices called perpetual motion machines. There are two classes of perpetual motion machines called PMM1 and PMM2.

PMM1 - "A perpetual motion machine of the first kind is a continuously operating device that produces a continuous supply of energy without receiving energy input." [1, p.159]

PMM2 - "An engine that, operating continously, will produce no effect other than the extraction of heat from a single reservoir, and the performance of an equivalent amount of work." [1, p.246]

A PMM1 violates the First Law because it has more energy output than input.

A PMM2 violates the Second Law, because it allows a complete conversion of heat energy into work. In order to operate, an engine must have a heat sink. In a steady state cycle, entropy generation must be offset by heat transfer to the heat sink. This is why it is impossible to convert all of the heat input into work - some of that heat must necessarily be lost to the heat sink.

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o How are the Laws of Thermodynamics applied to various systems?

System - that part of the universe set apart for examination. [1, p.33]

Surroundings - that part of the universe which strongly interacts with the system under study. [1, p.33] Universe - the totality of matter that exists. [1, p.33]

This definition does not include energy that exists apart from matter. For example, radiation in space. Pure energy, apart from matter, is not measureable. This is somewhat like the uncertainty principle. In order to measure energy, you must first allow it to interact with matter, and then you measure the effect on the matter. But once you have done that, it is no longer pure energy, so you can't be certain that what you are measuring is accurate for pure energy. For example, the speed of light. We must depend on the interaction of light with matter to measure the speed, but in so doing, we are no longer measuring light *apart from* matter, but rather measuring the effect of light *on* matter. By this definition of the universe, pure energy exists in another dimension - outside of the space-time continuum that we call the universe. It is only when energy interacts with matter that it enters the universe. This gives us a clue about the nature of entropy - anytime energy interacts with matter, some of that energy is transferred to the matter, and some of that energy becomes disordered.

(note to RobD - Is matter the ten thousand things of which Lao Tzu spoke? And is pure energy the Tao? )

System Boundary - the surface that separates the system from its surroundings. [1, p.34] Inside Boundary - the part of the boundary impervious to mass flow. [1, p.35]

Crossing Boundary - the part of the boundary at which mass enters and leaves the system. [1, p.35]

Closed system, or Control Mass, which means that the mass of the system is constant, and mass is not allowed to cross the system boundaries.

Open System - a system in which mass is allowed to cross the system boundaries.

In actuality, there are very few truly closed systems. Take a balloon - we know that the air inside is slowly diffusing through the walls of the balloon, and given sufficient time the balloon will deflate. What we have to do is make an approximation. If we are studying effects of heat transfer on the properties in the balloon, then the rate of mass transfer across the boundaries is negligible, and we can use a closed system as a good approximation.

Take the earth - we know that gas molecules can occasionally escape into space, meteors occasionally shower down into the atmosphere, and space missions leave the earth. So in the strictest sense, the earth is an open system. But if we study the rate of overall energy transfer, and compare that with the rate of transfer due to matter entering and leaving, then for all practical purposes the earth is currently a closed system, because the effect on the overall energy balance is negligible. If we take the upper reaches of the atmosphere as the system boundary, then we can also say that the system has a fixed boundary. In effect, we are really saying that a balloon is a model of the earth - for the purpose of thermodynamic analyses.

Two different forms of the Laws of Thermo are used for open and for closed systems. One consideration in an open system is the fact that energy can be transferred across the system boundaries due to intrinsic energy of the mass that is transferred.

There are a number of different types of closed systems:

Diabatic - allowing heat transfer across sytem boundaries Adiabatic - not allowing heat transfer across system boundaries. (insulated thermally)

Insulated System (electrically) - a System in which electrical work cannot cross the system boundaries

Rigid System - a System in which the boundaries are fixed, ie. not allowing mechanical work to cross the system boundaries.

Isolated system - a closed system that allows neither mass nor energy transfer across system boundaries.

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o Does Snowflake formation violate the Second Law of Thermodynamics?

A forming snowflake is an open system. There is mass transfer across the boundary. If snowflake formation causes a reduction in the entropy of the snowflake, then, by the second law, the entropy change of the surroundings must increase.

What about the order of the snowflake? A snowflake indeed appears to have a high degree of order, but remember, we are talking about ordered energy. Ordered energy is energy that is available to do work. Once a snowflake forms, it doesn't do any work, it just slowly drifts down to the ground and then just sits there, melts, or sublimates. A snowflake has a pattern, but that pattern is static, and is *not* ordered energy available to do work. Snow has a remarkable ability to resist change. Unmelted snowflakes will not readily bond to each other, snow has a very poor ballistic coefficient which prevents snowflakes from accumulating any significant kinetic energy when they fall. Snow does not readily absorb radiation or heat energy. Snow is chemically inert compared to water in other states. At the macroscopic level, since snowflakes are unique, we would have to say that the pattern of snowflakes is highly disordered - otherwise we should see large numbers of identical patterns.

 _Fundamentals_of_Engineering_Thermodynamics_, Howell and Buckius, McGraw-Hill, 1987

 _Introduction_to_Chemical_Engineering_Thermodynamics_, _Fourth_Edition_, Smith and van Ness, McGraw-Hill, 1987

 _Classical_Thermodynamics_of_Nonelectrolyte_Solutions_, van Ness and Abbott, McGraw-Hill, 1982

James P. Henley Jr.
Chemical Engineering Dept.
Auburn University
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Ilye Prigogine, who won the nobel prize in chemistry in 1977 proved all that is required to create order in a non-equilibrium system is an influx of energy. 