Equivalence statements

There are many equivalent statements of the second law, some of which involve statements about heat engines and perpetual motion machines of the second kind that appear superficially quite different from equation (A2.T21). They will not be dealt with here, but two variant fonns of equation (A2.T21) may be noted in... 

Equivalence statement—Assigns two or more variable names to the same memory location... 

We can find alternate, but equivalent, statements that define p,. Starting with... 

In the coarse grained representation the equivalent statement to Eq. (3.71) in the steady state reads ... 

Because the times it takes for the same amount of two substances to effuse through a small hole are inversely proportional to the rates at which they effuse, an equivalent statement is... 

If a result is quoted as having an uncertainty of 1 standard deviation, an equivalent statement would be the 68.3% confidence limits are given by Xmean 1 Sjc, the reason being that the area under a normal distribution curve between z = -1.0 to z = 1.0 is 0.683. Now, confidence limits on the 68% level are not very useful for decision making because in one-third of all... 

A major advantage of fluorescence as a sensing property stems from the sensitivity to the precise local environment of the intensity, i.e., quantum yield (excited state lifetime (xf), and peak wavelength (Xmax). In particular, it is the local electric field strength and direction that determine whether the fluorescence will be red or blue shifted and whether an electron acceptor will or will not quench the fluorescence. An equivalent statement, but more practical, is that these quantities depend primarily on the change in average electrostatic potential (volts) experienced by the electrons during an electronic transition (See Appendix for a brief tutorial on electric fields and potentials as pertains to electrochromism). The reason this is more practical is that even at the molecular scale, the instantaneous electric... 

An equivalent statement is that no row of the coefficient matrix (j8) can be formed as a linear combination of the other rows. Since the matrix s determinant is nonzero when and only when this statement is true, we need only evaluate the determinant of (/ ) to demonstrate that a new basis B is valid. In practice, this test can be accomplished using a linear algebra package, or implicitly by testing for error conditions produced while inverting the matrix, since a square matrix has an inverse if and only if its determinant is not zero. 

As the superheat-limit temperature of light hydrocarbons can be closely approximated as 0.89 times the critical temperature, an equivalent statement would be... 

Numerous equivalent statements of the second law exist. We will begin with the following statement proposed by Clausius ... 

The reaction proceeds through the oxidation of the hydrocarbon to the alcohols, which are subsequently oxidized to ketones. This sequence is indicated by the fact that with increasing conversion, the selectivity for ketones increases at the expense of that for alcohols. The absence of isomerization products was confirmed by the formation of only 2-hexanone when 2-hexanol was the reactant the equivalent statement pertains to the 3-compounds (Parton et al., 1991). 

As the second form of the criterion shows, an equivalent statement is that the curvature of the free energy along the direction 5p vanishes. Equation (50) can also be written as... 

Formally, percent by weight to volume is defined as grams of solute per 100 mL of solution. There are two mathematically equivalent statements of this definition ... 

The last four are some of many equivalent statements of the Second Law of Thermodynamics. Unlike internal energy (U) or enthalpy (//), entropy has its absolute value. 

The Tg of linear polymers such as polyimides is heavily dependent on, and increases with, the molecular weight. The equivalent statement can also be said about crosslinked networks, where the glass transition temperature is dependent on the network crosslink density [111-117]. 

It is only a small step from here to the equivalent statement, known as the Nyquist theorem, for current noise of thermal fluctuations in a circuit with resistance R.4... 

The CIPM-MRA is a transparent process to underpin measurement capability claims of signatories to the meter convention. Key comparisons are organized for NMIs or designated laboratories to demonstrate the equivalence of their measurements in view of mutual acceptance of national standards and reference measurements. Their reported results and the equivalence statements of the measurements are included in the Appendix B of the CIPM-MRA, which can support the CMCs in Appendix C of the CIPM-MRA. Once reported there is no possibility of withdrawal of measurement results. Conversely, in a CCQM pilot study results could be withdrawn, but participation does not result in equivalence statements in Appendix B of the CIPM MRA. Therefore, participation in CCQM pilot studies was recently extended to invited expert laboratories. The results of both CCQM key comparisons and pilot studies are published in the Technical Supplement of Metrologia [24], The IRMM assists the CIPM to support the MRA by making... 

The above concepts may be summarized in four equivalent statements. Let F be a thermodynamic function of state then the following holds ... 

Fixed-Point-Free Motions. These include translations, screw rotations, and glide reflections. Because the primitive translation vector, Eq. 1.2, joins any two lattice points, an equivalent statement is that Eq. 1.2 represents the operation of translational symmetry bringing one lattice point into coincidence with another. However, we must choose the basis vectors (a, b, c) so as to include all lattice points, thus defining a... 

There were some contradictions in Carnot s work—a result of his reliance on the caloric theory—that were subsequently cleared up by Clausius. Clausius accepted Carnot s proposition that some heat must be thrown away when converting heat to work as a law of nature, something that cannot be proved or derived from something else, but as far as we have ever been able to tell describes the way the world works. He called it the second law of thermodynamics and then sought to recast it in a different, more general, form that did not apply to heat engines alone. He showed that an equivalent statement of the... 

Consider a pin measuring 2.85 cm in length. What is its length in inches To solve this problem, we must use the equivalence statement... 

To convert from one unit to another, use the equivalence statement that relates the two units. 

Unit factor an equivalence statement between units used for converting from one unit to another (A2.2)... 

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