Elements of Thermodynamics

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Maxwell’s relations are for conjugate quantities. Relations between non-conjugate quantities are possible 1 = 0 ⎟⎟ ⎟⎟ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎜⎜ ⎜⎜ ⎝⎝ ⎛⎛ + − ⎟⎟ ⎟⎟ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎜⎜ ⎜⎜ ⎝⎝ ⎛⎛ − + ⎟⎟ ⎟⎟ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎜⎜ ⎜⎜ ⎝⎝ ⎛⎛ + = + = + = ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ Z X Z Y Y X X Y Y X Z X Z Y X Y Y X Z Y X Y Z X Y X Y X Z Z Y X Z Z X Z Y Z Z dZ dX dZ dZ dX dX dZ dX dY dZ dY dX
⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ =− ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ ⎟⎟ ⎠⎠ ⎞⎞ ⎜⎜ ⎝⎝ ⎛⎛ ∂ ∂ = − = T P P V T V X Z Z Y Y X X Y Y X V T Y X Z Z P Z 1 1 useful relations example If f(P,V,T)=0 then
Page 1 and 2: Elements of Thermodynamics Indispen
Page 3 and 4: We distinguish extensive (size depe
Page 5 and 6: Consider a system of n extensive qu
Page 7 and 8: Conjugate quantities are related by
Page 9 and 10: Thermodynamic potentials The energy
Page 11 and 12: Energy can be expressed using vario
Page 13 and 14: These expressions allow us to defin
Page 15: dU = TdS − PdV # dU = % ∂U $
Page 20 and 21: In general, the heterogeneity depen
Page 22 and 23: In general, of course, rocks are no
Page 24 and 25: (b) Deformation is parallel to laye

Elements of Thermodynamics

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