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# phys documents (dragged) 30 - κ T =-1 V ± ∂ V ∂ p ²...

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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: κ T =-1 V ± ∂ V ∂ p ² T • The isobaric volume coef±cient: γ p = 1 V ± ∂ V ∂ T ² p • The adiabatic compressibility: κ S =-1 V ± ∂ V ∂ p ² S For an ideal gas follows: γ p = 1 /T , κ T = 1 /p and β V =-1 /V . 8.3 Thermal heat capacity • The speci±c heat at constant X is: C X = T ± ∂ S ∂ T ² X • The speci±c heat at constant pressure: C p = ± ∂ H ∂ T ² p • The speci±c heat at constant volume: C V = ± ∂ U ∂ T ² V...
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## This note was uploaded on 11/16/2010 for the course ENGR 201 taught by Professor Elder during the Spring '10 term at Blinn College.

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