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phys documents (dragged) 30 - T =-1 V V p T The isobaric...

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Chapter 8 Thermodynamics 8.1 Mathematical introduction If there exists a relation f ( x,y,z )=0 between 3 variables, one can write: x = x ( y,z ) , y = y ( x,z ) and z = z ( x,y ) . The total differential dz of z is than given by: dz = ± z x ² y dx + ± z y ² x dy By writing this also for dx and dy it can be obtained that ± x y ² z · ± y z ² x · ± z x ² y = - 1 Because dz is a total differential holds ³ dz =0 . A homogeneous function of degree m obeys: ε m F ( x,y,z )= F ( ε x, ε y, ε z ) . For such a function Euler’s theorem applies: mF ( x,y,z )= x F x + y F y + z F z 8.2 Defnitions The isochoric pressure coef±cient: β V = 1 p ± p T ² V The isothermal compressibility:
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Unformatted text preview: T =-1 V V p T The isobaric volume coefcient: p = 1 V V T p The adiabatic compressibility: S =-1 V V p S For an ideal gas follows: p = 1 /T , T = 1 /p and V =-1 /V . 8.3 Thermal heat capacity The specic heat at constant X is: C X = T S T X The specic heat at constant pressure: C p = H T p The specic heat at constant volume: C V = U T V...
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