cH12 - Thermo Relations

# cH12 - Thermo Relations - Partial Differential Relations...

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Partial Differential Relations The order of differentiation is immaterial for properties since they are continuous point functions and have exact differentials. Thus, Reciprocity relation Cyclic relation Demonstration of the reciprocity relation for the

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THE MAXWELL RELATIONS The equations that relate the partial derivatives of properties P , v , T , and s of a simple compressible system to each other are called the Maxwell relations . They are obtained from the four Gibbs equations by exploiting the exactness of the differentials of thermodynamic properties. Helmholtz function Gibbs function Maxwell relations Maxwell relations are extremely valuable in thermodynamics because they provide a means of determining the change in entropy, which cannot be measured directly, by simply measuring the changes in properties P , v , and T . These Maxwell relations are limited to simple compressible systems.
Maxwell Relations Means of determining changes in entropy Limited to simple compressible systems s v T v s P T P T P s P v s v T T v s v P s P T v = - = = = - M M

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Problem solving Using the Maxwell relations, determine a relation for ( s / P ) T for a gas whose equation of state is P ( v - b ) = RT . Analysis This equation of state can be expressed as Then, From the fourth Maxwell relation P R T P = v P R - = - = P T T P s v b P RT + = v
Clapeyron Equation Liquid-vapor and solid-vapor phase change- simplified forms. For liquid-vapor phase change, at low

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## This note was uploaded on 10/27/2008 for the course MEM 410 taught by Professor Husanu during the Summer '08 term at Drexel.

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cH12 - Thermo Relations - Partial Differential Relations...

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