Kirchoff’s equations

Kinetic, energy, 24 theory of dissipation, 87 theory of gases, 515 theory of solids, 517 theories in thermodynamics, 513 Kirchoff s equation for effect of temperature, 112, 259 equations for vapour-pressure, 179, 190, 192, 390, 412 Konowalow s theorem, 385, 407 vapour-pressure curves, 382... 

There are two important relationships in thermochemistry which are very useful in the calculation of enthalpies of reactions. These are known as Hess s law and Kirchoff s equation. 

This equation is the well-known Kirchoff s equation that is more often used in the integrated form, which is... 

Now the equations derived from Kirchoff s first law are essentially material balances around each of (N — 1) vertices. As an alternative, balances could also be drawn up around groups of such vertices. Is there a special way of grouping the vertices, which will yield a particularly advantageous formulation Also, as we have noted, the selection of cycles is not unique, but the cycles must be independent. How can we generate an independent set of cycles Are some of these independent sets more fundamental than others If so, how many fundamental sets are there To answer these questions we must explore further the properties of a graph. 

Equation (4.10) is the differential form of Kirchoff s law. In the integral form, it becomes... 

E being the heat content before, and E that after the change). But this equation is of course wrong correctly it must read (Kirchoff s Law)... 

Thus, for a constant field, the flux of current density through a closed surface is always zero, that is, the amount of charge arriving in a volume during a given time period is exactly equal to the amount of charge that leaves that volume in the same period. Let us note that the last equation in set 1.136 is the well-known Kirchoff s law for currents. 

Equation 9.114 leads to Kirchoff s Law which states that the absorptivity, or fraction of incident radiation absorbed, and the emissivity of a surface are equal. If two bodies A and B of areas Ai and A2 are in a large enclosure from which no energy is lost, then the energy absorbed by A from the enclosure is Aia 7 where / is the rate at which energy is falling on unit area of A and ai is the absorptivity. The energy given out by A is 1 A] and, at equilibrium, these two quantities will be equal or ... 

For a grey body, the emissivity and the absorptivity are, by definition, independent of temperature and hence equation 9.115 may be applied more generally showing that, where one radiation property (a, r or e) is specified for an opaque body, the other two may be obtained from equations 9.115 and 9.124. Kirchoff s Law explains why a cavity with a small aperture approximates to a black body in that radiation entering is subjected to repeated internal absorption and reflection so that only a negligible amount of the ineident radiation escapes through the aperture. In this way, a = e = 1 and, at T K, the emissive power of the aperture is... 

The solution of Equation (23.16) throughout the network was achieved by solving simultaneously the one-dimensional equation for each pore, assuming that at the nodes of the network no adsorption or reaction takes place. The node material balance can be expressed by an equation similar to Kirchoff s law as... 

The equivalent circuit, which is essentially a resistive network, provides a set of simultaneous equations derived by applying Kirchoff s node and loop laws. Thus, at a node, the algebraic sum of electric currents flowing in and out is zero, and in a closed circuit of network, the sum of the ohmic voltages (with respect to the direction of the current) is equal to the sum of the voltage sources. These equations, expressed in... 

The Rankine-Kirchoff equation can be simplified further, as described by Mackay et al. [104], The authors assumed that the change in both heat capacities is 0, so the entropy of vaporization is given by Trouton s rule,... 

For the majority of fluxes evaluated, the standard deviation, s, and the average percent variation, A%, is lower for the Kirchoff-Rankine fitted equation vs. the Arrhenius Equation, indicating a better fit of the experimental data. The difference is most pronounced for those fluxes where the nonlinearity of the experimental nTi vs. 1/T data is greatest. 

The Hagen-Poiseuille law is mathematically analogous to the Ohm s Law. In addition, the conservation of mass (or flow for incompressible fluid) of fluid is analogous to the law of conservation of charge and current in electrical systems. This analogy allows for the use of Kirchoffs equations for calculation of the distribution of the volumetric flow of liquid between channels in a microfluidic network once we know the resistances of all the channels in the network and the pressures at the inlet and outlet, we can calculate the speed of flow in any part of the network (Fig. 1). 

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