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Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics. Equations of State. Thermodynamic quantities. Internal energy ( U ): the energy of atoms or molecules that does not give macroscopic motion. Temperature ( T ): a measure of the internal energy of a system.

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Thermodynamics and Statistical Mechanics

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  1. Thermodynamics and Statistical Mechanics Equations of State

  2. Thermodynamic quantities • Internal energy (U): the energy of atoms or molecules that does not give macroscopic motion. • Temperature (T): a measure of the internal energy of a system. • Heat (Q): a way to change internal energy, besides work. (Energy in transit.) Thermo & Stat Mech - Spring 2006 Class 2

  3. Laws of Thermodynamics • First law: đQ – đW = dU • Q – W = DU • Energy is conserved Thermo & Stat Mech - Spring 2006 Class 2

  4. Work done by a gas Thermo & Stat Mech - Spring 2006 Class 2

  5. Work done by a gas Thermo & Stat Mech - Spring 2006 Class 2

  6. Work done by a gas Thermo & Stat Mech - Spring 2006 Class 2

  7. Configuration Work • Product of intensive variable times corresponding extensive variable: • đW = xdY • Gas, Liquid, Solid: PdV • Magnetic Material: BdM • Dielectric Material: EdP Thermo & Stat Mech - Spring 2006 Class 2

  8. Equation of State • For an ideal gas: PV = nRT • P = pressure (N/m²)(or Pa) • V = volume (m³) • n = number of moles • T = temperature (K) • R = gas constant (8.31 J/(K·mole)) Thermo & Stat Mech - Spring 2006 Class 2

  9. Ideal gas law Ideal gas law: PV = nRT In terms of molar volume, v = V/n, this becomes: Pv = RT, or P = RT/v Thermo & Stat Mech - Spring 2006 Class 2

  10. Real Substance Thermo & Stat Mech - Spring 2006 Class 2

  11. Real Substance Thermo & Stat Mech - Spring 2006 Class 2

  12. van der Waals equation of state v cannot be decreased indefinitely, so replace v by v – b. Then, Next account for intermolecular attraction which will reduce pressure as molecules are forced closer together. This term is proportional to v-2 Thermo & Stat Mech - Spring 2006 Class 2

  13. van der Waals equation of state This equation has a critical value of T which suggests a phase change. The next slide shows graphs for several values of T . Thermo & Stat Mech - Spring 2006 Class 2

  14. van der Waals equation of state Thermo & Stat Mech - Spring 2006 Class 2

  15. Critical Values Thermo & Stat Mech - Spring 2006 Class 2

  16. van der Waals equation of state This can be expressed in term of dimensionless coordinates, P', v', and T ' with the following Substitutions: Thermo & Stat Mech - Spring 2006 Class 2

  17. van der Waals equation of state • This can also be written, Thermo & Stat Mech - Spring 2006 Class 2

  18. Thermal Expansion • Expansivity or Coefficient of Volume Expansion, b. Thermo & Stat Mech - Spring 2006 Class 2

  19. Thermal Expansion • Usually, b is positive. • An exception is water in the temperature range between 0° C and 4° C. • Range of b is about: b » 10-3 for gasses. • b » 10-5 for solids. Thermo & Stat Mech - Spring 2006 Class 2

  20. Linear Expansion • Coefficient of Linear Expansion, a. Thermo & Stat Mech - Spring 2006 Class 2

  21. Relationship Between a and b Thermo & Stat Mech - Spring 2006 Class 2

  22. Compressibility • Volume also depends on pressure. • Isothermal Compressibility: Thermo & Stat Mech - Spring 2006 Class 2

  23. Bulk Modulus Thermo & Stat Mech - Spring 2006 Class 2

  24. A Little Calculus Thermo & Stat Mech - Spring 2006 Class 2

  25. Cyclical Relation Thermo & Stat Mech - Spring 2006 Class 2

  26. Application • Suppose you need: Thermo & Stat Mech - Spring 2006 Class 2

  27. Application Thermo & Stat Mech - Spring 2006 Class 2

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