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Thermodynamics filled in class notes_Part_2

# Thermodynamics filled in class notes_Part_2 - 11 v P T = T...

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Unformatted text preview: 11 v P T = T 1 v 2 v 1 12 12 2 1 âˆ« w = P dv 12 1 2 s T âˆ« q = T ds 12 1 2 u - u = q - w v 2 v 1 s 2 s 1 T P T v v 1 v 2 2 T = T 1 v 1 v 2 2 1 2 P P 1 P 2 P T = T 1 2 2 T = T 1 1 P 2 P 1 2 1 2 1 2 1 2 Figure 1.1: Sketch of isothermal thermodynamic process. On an isochore, v is constant, so dv = 0. So on an isochore, we have Tds = c v dT, on an isochore . (1.4) or, using the partial derivative notation, âˆ‚T âˆ‚s vextendsingle vextendsingle vextendsingle vextendsingle v = T c v . (1.5) Next recall the definition of enthalpy, h : h = u + Pv. (1.6) We can differentiate Eq. (1.6) to get dh = du + Pdv + vdP. (1.7) Substitute Eq. (1.7) into the Gibbs equation, (1.1), to eliminate du in favor of dh to get Tds = dh âˆ’ Pdv âˆ’ vdP bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright = du + Pdv, (1.8) = dh âˆ’ vdP. (1.9) CC BY-NC-ND. 18 November 2011, J. M. Powers. 12 CHAPTER 1. REVIEW v P s T q = w cycle cycle Figure 1.2: Sketch of thermodynamic cycle....
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Thermodynamics filled in class notes_Part_2 - 11 v P T = T...

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