Thermodynamics Of Materials Pdfkeyclever

  • Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics.
  • Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics.

Photo showing gas bubbles form and collapse when a liquid is energized by ultrasound. (Courtesy of K.S. Suslick and K. J. Kolbeck, University of Illinois; National Science Foundation.)

'Thermodynamics of Materials' introduces the basic underlying principles of thermodynamics as well as their applicability to the behavior of all classes of materials, while providing an integrated approach from macro- (or classical) thermodynamics to meso- and nanothermodynamics, and microscopic (or statistical) thermodynamics.

Instructor(s)

Prof. W. Craig Carter

MIT Course Number

3.00

As Taught In

Key

Fall 2002

Level

Undergraduate

Some Description

Instructor(s)

Prof.

As Taught In

Spring 2002

Course Number

2.24

Level

Undergraduate/Graduate

Features

Lecture Notes, Student Work

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Thermodynamics Of Materials

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Course Description

Course Features

Course Description

Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics. Develops graphical constructions that are essential for the interpretation of phase diagrams. Treatment includes electrochemical equilibria and surface thermodynamics. Introduces aspects of statistical thermodynamics as they relate to macroscopic equilibrium phenomena.

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(Redirected from Material property (thermodynamics))
Thermodynamics
  • Equilibrium / Non-equilibrium
State
Processes
Cycles
Process functions
Functions of state
  • Temperature / Entropy (introduction)
  • Pressure / Volume
  • Chemical potential / Particle number
Specific heat capacityc={displaystyle c=}
T{displaystyle T}S{displaystyle partial S}
N{displaystyle N}T{displaystyle partial T}
Compressibilityβ={displaystyle beta =-}
1{displaystyle 1}V{displaystyle partial V}
V{displaystyle V}p{displaystyle partial p}
Thermal expansionα={displaystyle alpha =}
1{displaystyle 1}V{displaystyle partial V}
V{displaystyle V}T{displaystyle partial T}
  • Internal energy
    U(S,V){displaystyle U(S,V)}
  • Enthalpy
    H(S,p)=U+pV{displaystyle H(S,p)=U+pV}
  • Helmholtz free energy
    A(T,V)=UTS{displaystyle A(T,V)=U-TS}
  • Gibbs free energy
    G(T,p)=HTS{displaystyle G(T,p)=H-TS}
History
Philosophy
Theories
Key publications
  • 'An Experimental Enquiry
    Concerning ... Heat'
  • 'Reflections on the
    Motive Power of Fire'
Timelines
  • Art
  • Education

The thermodynamic properties of materials are intensive thermodynamic parameters which are specific to a given material. Each is directly related to a second order differential of a thermodynamic potential. Examples for a simple 1-component system are:

  • Compressibility (or its inverse, the bulk modulus)
  • Isothermal compressibility
βT=1V(VP)T=1V2GP2{displaystyle beta _{T}=-{frac {1}{V}}left({frac {partial V}{partial P}}right)_{T}quad =-{frac {1}{V}},{frac {partial ^{2}G}{partial P^{2}}}}
  • Adiabatic compressibility
Thermodynamics of materials pdf key clever math
βS=1V(VP)S=1V2HP2{displaystyle beta _{S}=-{frac {1}{V}}left({frac {partial V}{partial P}}right)_{S}quad =-{frac {1}{V}},{frac {partial ^{2}H}{partial P^{2}}}}
Thermodynamics Of Materials PdfkeycleverThermodynamics Of Materials Pdfkeyclever
  • Specific heat (Note - the extensive analog is the heat capacity)
  • Specific heat at constant pressure
cP=TN(ST)P=TN2GT2{displaystyle c_{P}={frac {T}{N}}left({frac {partial S}{partial T}}right)_{P}quad =-{frac {T}{N}},{frac {partial ^{2}G}{partial T^{2}}}}
  • Specific heat at constant volume
cV=TN(ST)V=TN2AT2{displaystyle c_{V}={frac {T}{N}}left({frac {partial S}{partial T}}right)_{V}quad =-{frac {T}{N}},{frac {partial ^{2}A}{partial T^{2}}}}
  • Coefficient of thermal expansion
α=1V(VT)P=1V2GPT{displaystyle alpha ={frac {1}{V}}left({frac {partial V}{partial T}}right)_{P}quad ={frac {1}{V}},{frac {partial ^{2}G}{partial Ppartial T}}}

where P is pressure, V is volume, T is temperature, S is entropy, and N is the number of particles.

For a single component system, only three second derivatives are needed in order to derive all others, and so only three material properties are needed to derive all others. For a single component system, the 'standard' three parameters are the isothermal compressibility βT{displaystyle beta _{T}}, the specific heat at constant pressure cP{displaystyle c_{P}}, and the coefficient of thermal expansion α{displaystyle alpha }.

For example, the following equations are true:

cP=cV+TVα2NβT{displaystyle c_{P}=c_{V}+{frac {TValpha ^{2}}{Nbeta _{T}}}}
βT=βS+TVα2NcP{displaystyle beta _{T}=beta _{S}+{frac {TValpha ^{2}}{Nc_{P}}}}

The three 'standard' properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure.

Thermodynamics

See also[edit]

Thermodynamics Of Materials Pdf Key Clever Essay

  • Specific heat of melting (Enthalpy of fusion)
  • Specific heat of vaporization (Enthalpy of vaporization)

External links[edit]

  • The Dortmund Data Bank is a factual data bank for thermodynamic and thermophysical data.

References[edit]

Thermodynamics Of Materials Pdf Key Clever Answers

  • Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). New York: John Wiley & Sons. ISBN0-471-86256-8.
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