# INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS GASKELL PDF

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## Introduction to the Thermodynamics of Materials

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Actions Shares. Some important effects are chemical reactions such as oxidation , formation of solutions, phase transformations. In other words, the changes in the matter are more interesting than the heat and work effects. The system is any collection of objects that we choose to analyze. The surroudings is the rest of the universe, but in more practical terms is the environment of the system. Our interest is in understanding the system. The system and surroundings interact be exchanging heat and work.

The surroundings can supply heat to the system or do work on the system. Alternatively, the system may give off heat supply heat to the surroundings or do work on the surroundings. Some examples of material science type systems are a metalllic alloy in a crucible, a multi-component, multiphase ceramic, a blend of polymer molecules, a semiconductor alloy, or a mixutre of gases in a container.

In material science, our main interest in such systems is the equilibrium state of the system, will the components react, will they mix or phase separate, will there by phase transitions, and how will they respond to externally applied stimuli such as pressure, temperature, stress, strain, electrical field, or magnetic filed.

Thermodynamics is concerned only with the equilibrium state of matter and not in the rate at which matter reaches the equlibrium state.

Early thermodynamics was on heat thermo and work dynamics effects. In heat engines with gases and liquids, equilibrium is often reached very fast and the rate of reaching equilibrium is very fast. For example, a polymer glass well below its glass transition is a non-equilibrium structure.

A detailed thermodynamic analysis of glass polymers a difficult problem would predict that the polymer should exist in a different state than it actually does. At sufficient low temperatures, the polymer, however, will remain in the non-equilibrium glassy state; the equilibrium state will not be realized on any practical time scale.

The state of a system can be defined by specifying the masses, velocities, positions, and all modes of motion e. Such a state is called the microscopic state of the system. Given the microscopic state, we could deduce all the properties of the system. Normally, however, we do not have such detailed knowledge because there will always be a large number of particles e.

Fortunately such detailed knowlege is not required. Instead, it is possible to define a macroscopic state of the system by specifying only a few macroscopic and measurable variables such as pressure, volume, and temperature. It is found that when only a few of these variables are fixed, the entire state of the system is also fixed. Thus, the thermodynamic state of a system is uniquely fixed when a small number of macroscopic, independent variables are fixed.

For example, consider a gas or a liquid of constant composition such as a pure gas or liquid.

The three key variables are pressure, P, temperature, T, and volume, V. It has been observed that when P and T are fixed that V always has a unique value.

Once P and T are known, V and all other properties in this simple example are determined. P, V, and T are all known as state variables; they only depend on the current state and not the path the system took to reach the current state. Notes on Gaskell Text 7 The use of P and T as the independent variables is simply a matter of choice and is done usually because P and T are easy to control and measure.

## 9585_3bdf.pdf - Introduction to the thermodynamics of...

It would be equally acceptable to define V and T as the independent variables and define the system by an equation of state for pressure: Other systems require more variables, but the number required is always relatively small. The volume of the system will depend not only on P and T, but also on which gases are present. As above, this new equation of state could be done instead as an equation for P in terms of V, T, and composition: Pressure or volume are all that are needed to define mechanical stimuli on a gas or a liquid.

For solids, however, the matter might experience various states of stress and strain.

## David R. Gaskell INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, FOURTH EDITION

For a pure solid, the natural variables are temperature, stress s instead of P , and strain e instead of V. Unlike P and V which are scalar quantities, stress and strain are tensors with 6 independent coordinates. If the material is not a pure material, such as a composite material, the stress-strain relations will also depend on the compositions of the material and typically on the geometry of the structure.

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For interactions of matter with other stimuli suich as electric or magnetic fields, the equations of state will also depend on the intensity of those fields. Thus, in summary, the thermodynamic state can also be expressed as an equation of state that is a function of a relatively small number of variables.

The simplest examples involve only two variables.

More complicated systems require more variables. Thus equations of state follow the rules of mutlivariable mathematics. In thermodynamics, we are often concered with how something changes as we change the independent variables. A general analysis of such a problem can be written down purely in mathematical terms. This Mathematica notation will be used throughout these notes which were prepared in a Mathematica notebook.

Many input expressions are followed be semicolons which simple supresses uninteresting Mathematica output. Any change in volume due to a change in T and P can be calculated by integrating dV: In thermodynamics we are usually dealing with physical quantities. In general, the partial derviatives for the total differentials themselves often have physical significance. In other words, they often correspond to measurable quanties.

Sometimes the physical significance is not clear. In such problems, the partial derivative is defined as having having physical significance or it becomes a new thermodynamic quantity. One good example to be encountered later in this course is chemical potential. For example V is a state variable. It depends only on the independent variables P, T, and perhaps others and not on the path taken to get to the variables.

There are many thermodynamic state variables and they are very important in thermodynamics. There are some thermodynamic quantities that are not state variables. The two most important are heat and work. The heat supplied to a system or the work done by a system depend on the path taken between states and thus by definition, heat and work are not state variables.

The previous sections define equations of state for matter. Equilibrium is the state of the system when the variable reaches the value it should have as defined by the equation of state. For example, a pure gas has an equation of state V[P,T]. Equilibrium is reached when after changing P and T to some new values, the volume becomes equal to the V[P,T] defined by the equation of state. All systems naturally proceed towards equilibrium. They are driven there by natural tendencies to minimize energy and to maximize entropy.

These concepts will be discussed later. Although all systems tend towards equilibrium, thermodynamics says nothing about the rate at which they will reach equilibrium. Some systems, particularly condensed solids as encountered in material science, may not approach equilibrium on a pratical time scale.

Boyle found that at constant T that V is inversely proportional to P. These are the units of work or energy. When R was first measured, P was measured in atm and V in liters; thus P V or work or energy has units liter-atm. SI units for energy is Joules. The first law of thermodynamics connects the two energy units and allows one to relate heat and work energy or to relate calories and Joules.

Extensive variables depend on the size of the system such as volume or mass. Intensive variables do not depend on the size such as pressure and temperature. Extensive variables can be changed into intensive variables by dividing them by the mass or number of moles.

Such intensive variables are often called specific or molar quantities. For example, the volume per mole or molar volume is an intensive variable of a system.

Similarly, mass is an extensive property, by mass per unit volume or density is an intensive property. Systems are characterized by the number of components and the type of phase diagrams depend on the number of components. Examples are one-component unary , two-component binary , three-component ternary , four- component quarternary , etc.. In each zone, one state is the most stable state.

On lines, two phases can coexist. At triple points, three phases can coexist. Example of unary is water phase diagram. Unary diagrams usually use two variables like P and T.

Binary diagrams add composition as a third variable. Binary diagrams are usually for one variable T, P, or V together with the composition variable.

The complete phase space is 3D. Thus, 2D binary plots are sections of the 3D curves. Zones can be single phase solutions or two-phase regions. The relative proportions of phases in two- phase regions are given by the lever rule. Choice of components is arbitrary. First law connected heat and work and clarified conservation of energy in all systems. The key new energy term that developed from the first law is internal energy.

Internal energy often has a nice physical significance; sometimes, it significance is less apparant. The DGsimp agrees with the book, but the DG in the book is different.

Some books have 9 problems that correctly correspond to the 9 solutions.

Other books probably early printings of the thrid edition are missing the problem that goes with the first solution and have an extra problem that has no solution. These notes give the solutions to the 8 problems in common to all books.

Some books have them as 7. Notes on Gaskell Text 41 Problem 7. Once the vapor-liquid equilibrium is reached at constant volume, the P and T will remain on the transition curve but the vapor pressure will change with temperature.Heat Treatm. The total change in enthalpy can be written two ways as: First, we have to use the methods of Chapter 6 to find the enthalpy required to heat 1 mole of Cu and 1 mole of Ag from K to K.

The third section Reactions and Transformations can be used in other courses of the curriculum that deal with oxidation, energy, and phase transformations.

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Harry Potter. Rajulapati, University of Hyderabad, India. This extra work is not needed because in all cases, DU can be calculated directly from the same information used to first get DH. If you pay by the mole, you would prefer the ideal gas because it would be cheaper.

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If you pay by the container, you would prefer the van der Waals gas because you would get more moles per dollar.