Closed system Maxwell relations

The Maxwell relations (5.49a-d) are easy to rederive from the fundamental differential forms (5.46a-d). However, these relations are used so frequently that it is useful to employ a simple mnemonic device to recall their exact forms as needed. Sidebar 5.7 describes the thermodynamic magic square, which provides such a mnemonic for Maxwell relations and other fundamental relationships of simple (closed, single-component) systems. 

These four relations are known as the Maxwell relations, and are useful in terms of converting one set of variables to another. They are limited to closed systems, as indicated by the constancy of the mole numbers of the components. 

Table 1.14 Total differentials of the state functions and the Maxwell relations for closed systems of a homogeneous fluid of constant composition...

Abstract Thermodynamic energy functions are related to six variables such as volume, pressure, temperature, entropy, chemical potential and amount of substance. They are rather cumbersome and perplexing to undergraduates who start to leam their relations. With a story and the two-dimensional Cartesian coordinate system, most of thermodynamic relations could be obtained in addition to the Maxwell relations for a reversible change in a closed system only in the presence of pressure-volume work and heat. 

For closed systems (dXi = 0), applying the reciprocity relation ( 2.2.6) to equations (14.28)-(14.31) results in the set of Maxwell s equations, which are often useful in manipulating thermodynamic equations. These are... 

Table 1.4 Total Differentials of the State Functions and the Maxwell Relations for Closed Systems of a Homogeneous Fluid of Constant Composition...

Maxwell relations (again valid for a closed system with C=l, P=l, and dw =0) ... 

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