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Statistical Thermodynamics Justification of Some Commonly Used Expressions for the Excess Gibbs Energy
Published in Juan H. Vera, Grazyna Wilczek-Vera, Classical Thermodynamics of Fluid Systems, 2016
Juan H. Vera, Grazyna Wilczek-Vera
We observe that Wang transferred the temperature dependence of the partition function from the exponential term used in Guggenheim’s formulation, Equation 26.35, to the temperature dependence of the interaction parameters. Guggenheim’s formulation needed the exponential term; otherwise, Equation 26.37 would not have had any adjustable parameter to represent energetic interactions. In Wang’s formulation, these energy interactions are represented by the parameters characterizing the interactions of groups. According to Equation 24.14, the chemical potential is obtained by differentiation of the logarithmic form of Equation 26.62 with respect to ni at a constant volume and constant number of moles of all other compounds different from i, so we write the logarithm of Equation 26.65 as lnFα=∑k=1Gαk2ln∑l=1Gαl2τlk−∑k=1Gαk2ln∑l=1Gαl2
Suspended load monitoring for sustainable hydropower development
Published in Silke Wieprecht, Stefan Haun, Karolin Weber, Markus Noack, Kristina Terheiden, River Sedimentation, 2016
M. Guerrero, A. Antonini, N. Rüther, S. Stokseth
It is worth noting that much of the existing literature regarding the use of ADCPs to assess the concentration of suspended sediment, reports a logarithmic form of the sonar equation, including the target strength or an equivalent decibel expression of the backscattering strength that is ten times the common logarithm of ks2Ms. This is because echo intensity levels, E, recorded by the ADCP are proportional to the received sound intensity in a dB scale, IdB. In this case the sonar equation recasts in a logarithmic form (Equation 2) where the unknown constant C represents the instrumental parameters and the environmental noise level, E0, which was assumed not variable and well below the measured echo intensity level, i.e., kc(E − E0) greater than 10 dB. The conversion factor kc between measured echo level and sound intensity in dB typically ranged close to 0.45 dB/counts and it was assumed not variable for a given ADCP. () IdB=kc⋅E−C=10log(ks2⋅Ms)−20log(rψ)−40log(e)⋅α⋅r
Design development and performance evaluation of photovoltaic/thermal (PV/T) hybrid solar dryer for drying of ber (Zizyphus mauritiana) fruit
Published in Cogent Engineering, 2018
Surendra Poonia, A.K. Singh, Dilip Jain
where Deff is the effective diffusivity coefficient (m2/s), r is the half thickness of the samples (m), n is the positive integer and t is the drying time (s). For long drying times (setting n = 1), Saravacos and Raouzeos (1986) demonstrated that Eq. (12) could be further simplified to a straight-line equation and can be expressed in a logarithmic form by taking the natural logarithm of both sides.
Quantitative analysis of impact factors and scenario prediction of energy related carbon emissions at county level
Published in International Journal of Green Energy, 2022
Where I indicates the environmental impact; a is the model coefficient; b, c, and d are the exponents of population size (P), affluence degree (A), and technology level (T); e is the error. Then apply the natural logarithm to both sides of Equation (2) and obtain the logarithmic form shown in Equation (3).
Study of the rheological properties of clayey suspensions: an interest in the field of landfills
Published in European Journal of Environmental and Civil Engineering, 2023
Hamma Fabien Yonli, Anne Pantet, David Yemboini Kader Toguyeni
For the yield stress, the chosen value is the lowest stress (stress value at 5.34 s−1); for n and k, a representation of the Herschel-Bulkley equation in logarithmic form allows to choose the initial value of n as the slope of the curve and the logarithm of initial k like the y-intercept.