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Published byEllen Jeppesen Modified over 5 years ago
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Perfect gas: PV = nRT = NkT (equation of state) only in equilibrium!
Closed system: n constant (dn = 0) only two independent variables
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Amadeo Avogadro di Quaregna e Cerreto
J/mol K J/K Amadeo Avogadro di Quaregna e Cerreto
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Total differential of a state function: Internal energy for U=U(P,V)
First law: Closed system => Characteristic Eq. T follows from the equationof state
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Total differential of a state function: Internal energy for U=U(P,V)
(SG: appendix A) Closed system => T follows from the equationof state Choose P and V as independent variables
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dP is not the most convenient variable for dU
Total differential of a state function: Internal energy for U=U(P,V) Closed system => T follows from the equationof state dP is not the most convenient variable for dU
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Introduce new energy function: Enthalpy H
(SG: page 4) Enthalpy H Consequence: heat capacity differs for U and H
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Total differential of a state function: Internal energy for U=U(P,V)
Closed system => T follows from the equationof state Choose P and V as independent variables
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Constant V has no use in characteristic eq.
Total differential of a state function: Internal energy for U=U(P,V) Closed system => T follows from the equationof state Constant V has no use in characteristic eq.
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Introduce Helmholtz free energy and Gibbs free energy
(SG: page 6-7) Helmholtz free energy A Gibbs free energy G defined via the enthalpy H
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} Total differential of a state function:
Choose appropriate energy function } For a choice S and V : For a choice S and P : Characteristic equations For a choice V and T : For a choice P and T : Choice of P and V is possible but very inconvenient [PV] = J and [ST] = J, so choose S,V or S,P or V,T or P,T Choice of eg. T and P for H is tedious (exercise 4) but possible and can be advantageous
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Total differential of a state function: Gibbs free energy
Closed system => V follows from the equationof state Process: (P1,V1,T1,n1) => (P2,V2,T2,n1)
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Total differential of a state function: Gibbs free energy
Closed system => V follows from the equationof state
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Total differential of a state function: Gibbs free energy
Closed system => V follows from the equationof state
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Total differential of a state function: Gibbs free energy
G state function
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Total differential of a state function: Gibbs free energy
G state function dG exact differential
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Total differential of a state function: Gibbs free energy
Closed system => Any change in G Total differential of G Characteristic (fundamental) equation of G
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Exact differential of a state function: Maxwell relation
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General properties of a differentiable function: f(x,y)
Euler chain relation
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