Equations of State - Thermodynamics and Statistical Mechanics - Lecture Slides, Slides of Thermodynamics

Download Equations of State - Thermodynamics and Statistical Mechanics - Lecture Slides and more Slides Thermodynamics in PDF only on Docsity! Thermodynamics and Statistical Mechanics Equations of State Docsity.com 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.) Docsity.com (a) Work done by a gas Pressure Volume (b) Pressure 0 Volume {c) Docsity.com Pressure Work done by a gas o . a = | = or crt or a 2 2 ao a f Volume 0 Volume 0 (a) (e) Volume (f) Docsity.com Configuration Work •Product of intensive variable times corresponding extensive variable: • đW = xdY •Gas, Liquid, Solid: PdV •Magnetic Material: BdM •Dielectric Material: EdP Docsity.com Real Substance Docsity.com Real Substance cP solid vapor (a) hy Figure 2.4 P-T diagrams for (a) a substance th at contracts on freezing: and (b) a substance that expands on freezing. Docsity.com 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 bv RTP − = Docsity.com Critical Values 227 27 8 3 b aP Rb aT bv C C C = = = Docsity.com van der Waals equation of state ' 3 8 3 1' ' 3' Then, ' ,' ,' 2 Tvv P TTTPPPvvv CCC =      −      + === This can be expressed in term of dimensionless coordinates, P', v', and T ' with the following Substitutions: Docsity.com van der Waals equation of state •This can also be written, 2' 3 1'3 '8' vv TP − − = Docsity.com Linear Expansion •Coefficient of Linear Expansion, α. TXT T XX pT T X X P P ∆=∆      ∂ ∂=∆       ∂ ∂= α α α ),( 1 Docsity.com Relationship Between α and β αβ αα ααα ββ 3 )31()1( )1()1()1(' )1(' 3 = ∆+=∆+= ∆+∆+∆+= = ∆+=∆+=∆+= TVTXYZ TZTYTXV XYZV TVTVVVVV  Docsity.com Compressibility • Volume also depends on pressure. • Isothermal Compressibility: PVP P VV PT P V V T T ∆−=∆      ∂ ∂=∆       ∂ ∂−= κ κκ ),( 1 Docsity.com Cyclical Relation 1 0 −=      ∂ ∂       ∂ ∂       ∂ ∂       ∂ ∂       ∂ ∂−=      ∂ ∂ =      ∂ ∂       ∂ ∂+      ∂ ∂ PVT VTP VTP V T T P P V T P P V T V T P P V T V Docsity.com Application •Suppose you need: VT P       ∂ ∂ 1−=      ∂ ∂       ∂ ∂       ∂ ∂ PVT V T T P P V Docsity.com Application κ β=       ∂ ∂−       ∂ ∂ =       ∂ ∂       ∂ ∂− =       ∂ ∂       ∂ ∂ −=      ∂ ∂ T P T P PT V P V V T V V P V T V V T P VT P 1 1 1 Docsity.com