1 / 27

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.

molimo
Download Presentation

Thermodynamics and Statistical Mechanics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related