## What Is An Equation Of State

There are two types of equations of state, or EOS. In general, they are thermodynamic relationships between three properties of a pure {one-component) substance. In discussing the fundamental meaning of equations of state, it is useful to eliminate the quantity of the substance in order to deal only with intensive properties <see Section 1.6.2). Extensive properties can be converted to intensive properties by dividing the formed by the quantity of the substance, (e.g., on a per-mole basis v = V/n, u = U/n).

The volumetric EOS refers to the relationship of the p-v-T properties of a gas. Solids and liquids are also described by p-v-T equations of state, although the quantitative forms are very different from those applicable to gases.

In functional form, the volumetric EOS can be written as v =fip,T), or v(p,T) for short. This form indicates that the specific volume (or molar volume) is expressed as a function of pressure and temperature. However, the EOS can be equally well written as pOOD or T(p,v). Because pressure and temperature are usually specified in an experiment or in a process, the form v(p,T) is most commonly employed.

The EOS relating v, p, and T provides no information about the other thermodynamic properties, in particular about the internal energy u and the entropy s. However, according to the phase rule (Section 1.12), specifying any two properties of a pure substance fixes all properties. Nonetheless, the EOS in the form p(T,V), for example, gives no hint about the functions w(7>), s(T,v\ or of the remaining auxilliary properties h,f, and g (see Section 1.6.1). Knowledge of (7ยป requires information about the substance beyond that contained in its p-v-T relationship. Functional relationships such as w(7>) are sometimes called thermal equations of state. Two gases, helium and nitrogen for example, may follow the ideal -gas law with reasonable accuracy, but show significantly different u(T,v) behavior.

## Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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