Abstract
The quantization thermal excitation isotherms based on the maximum triad spin number (G) of each energy level for metal cluster were derived as a function of temperature by expanding the binomial theorems according to energy levels. From them the quantized geometric mean heat capacity equations are expressed in sequence. Among them the five quantized geometric heat capacity equations, fit the best to the experimental heat capacity data of metal atoms at constant pressure. In the derivations we assume that the triad spin composed of an electron, its proton and its neutron in a metal cluster become a basic unit of thermal excitation. Boltzmann constant (kB) is found to be an average specific heat of an energy level in a metal cluster. And then the constant (kK) is found to be an average specific heat of a photon in a metal cluster. The core triad spin made of free neutrons may exist as the second one additional energy level. The energy levels are grouped according to the forms of four spins throughout two axes. Planck constant is theoretically obtained with the ratio of the internal energy of metal (U) to total isotherm number (N) through Equipartition theorem.
Highlights
The advanced quantized adsorption isotherms derived in the paper [1] fit well to the experimental data which BET isotherm does not fit
The quantization thermal excitation isotherms based on the maximum triad spin number (G) of each energy level for metal cluster were derived as a function of temperature by expanding the binomial theorems according to energy levels
From them the quantized geometric mean heat capacity equations are expressed in sequence
Summary
The advanced quantized adsorption isotherms derived in the paper [1] fit well to the experimental data which BET isotherm does not fit. Using this total isotherm we can manage to quantize the excited particles number in setting up the total. The triad spin made of an electron, its proton and its neutron make the harmonic resonances [4] like Figure 1 In another way the excitation means that the metal photon energy of metals is transferred to the measurement gas and the de-excitation means that the metal photon energy of quantized triad spin grossly reverses measurement gas
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