General Statements of the First Law

With definitions of work w and heat q established, we proceed to formal statement(s) of the first law of thermodynamics (cf. IL-5 Table 2.1). Although the first law is sometimes stated colloquially as Energy is conserved (or, somewhat more satisfactorily, Energy is conserved if heat is taken into account ), a proper statement requires the introduction of a new quantity, internal energy U, that can be distinguished from energy as used in the mechanical framework  

First Law (IL-5) There exists a macroscopic state property U ( internal energy ) whose change, in a process A — B involving only the absorption of heat q or performance of work w on the system, is given by 

However, the change in state property U must be independent of the path from A to B, (At/A B)adiabatic = (At/A- B)diaihemiab so we deduce from (3.38a, b) that 7 adiabatic Wdiathermab as stated in (3.36). 

The essential content of the first law is that dU =dq +dw is the (exact) differential of a state property, and hence independent of the path from A to B. The path integral over dU from A to B therefore depends only on the values of internal energy (UA, UB) at the two endpoints 

As stated above, the first law refers only to closed systems that allow no exchange of mass with the surroundings. To obtain an alternative expression of the first law in words, we might therefore consider the entire universe (which perforce has no surroundings) as the system, which leads to the somewhat melodramatic pronouncement  

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The statement of the first law given in Eq. (3-12) applies, for example, to cases in which only pV work is considered. A more general and precise statement of the first law is... 

The statement of the first law of thermodynamics defines the internal energy and asserts as a generalization of experiment fact that it is a state function. The second law of thermodynamics establishes the entropy as a state function, but in a less direct way. 

The second law of thermodynamics, like the first, represents a generalization of the results of a large number of experiments. In Sec. 4-1 we present two equivalent physical statements of the second law. In Sec. 4-2 we present the mathematical statement of the second law and determine how a criterion for equilibrium can be set up, making use of the mathematical statement. In Sec. 4-3 the mathematical statement of the second law is shown to be equivalent to the physical statements. The argument proceeds by demonstrating that Caratheodory s principle can be derived from the physical statements. 

The first law of thermodynamics is concerned with the conservation of energy. In its most general form, it is written as the following statement ... 

The first law of thermodynamics is the most general statement of this law of conservation of energy no exception to this law is known. The law of conservation of energy is a generalization from experience and is not derivable from any other principle. 

In terms of the methodology of scientific concepts, the first law of thermodynamics and the second law of thermodynamics are basic statements that cannot be proved further. These laws play a similar fundamental role as axioms in mathematics. Unlike axioms in mathematics the basic laws of thermodynamics like other basic laws in natural sciences, e.g., MaxwelFs equations, are based on observations. These observations are generalized. The result of these observations is extended to a basic law, also addressed as a postulate. 

Summary. The First Law was postulated as a simple general statement on performing work by a system exclusively upon the absorption of heat. Such a general statement was demonstrated to lead to the proof of equivalency between heat and work and to the proof of existence of the internal energy and its balance (with heat and work). 

Kepler s principal contribution is summarized in his laws of planetary motion. Originally derived semiempir-ically, by solving for the detailed motion of the planets (especially Mars) Ifom Tycho s observations, these laws embody the basic properties of two-body orbits. The first law is that the planetary orbits describe conic sections of various eccentricities and semimajor axes. Closed, that is to say periodic, orbits are circles or ellipses. Aperiodic orbits are parabolas or hyperbolas. The second law states that a planet will sweep out equal areas of arc in equal times. This is also a statement, as was later demonstrated by Newton and his successors, of the conservation of angular momentum. The third law, which is the main dynamical result, is also called the Harmonic Law. It states that the orbital period of a planet, P, is related to its distance from the central body (in the specific case of the solar system as a whole, the sun), a, by a. In more general form, speaking ahistorically, this can be stated as G M -h Af2) = a S2, where G is the gravitational constant, 2 = 2n/P is the orbital frequency, and M and M2 are the masses of the two bodies. Kepler s specific form of the law holds when the period is measured in years and the distance is scaled to the semimajor axis of the earth s orbit, the astronomical unit (AU). 

We would like to generalize our experience with the directionality of nature (and the limits of reversibility) into a quantitative statement that allows us to do calculations and draw conclusions about what is possible, what is not possible, and whether we are close to or far away from the idealization represented by a reversible process. Indeed, it would be nice if we had a thermodynamic property (i.e., a state function) which would help us to quantify directionality, just as internal energy, it, was central in quantifying the conservation of energy (the first law of thermodynamics). It turns out the thermodynamic property entropy, s, allows us to accomplish this goal. 

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