Determination of Entropy and Specific Heat of Hydrogen from Partition Functions of Elementary Particles

Elementary particles are atomic or sub-atomic particles that make up all kinds of matter. They are classified into two main groups, namely: bosons and fermions. In other words, bosons and fermions are found in all states of matter, viz: solids, liquids and gases. Fermions are constituents of matter while bosons are force carriers. Bosons are particles that transmit interactions or the constituents of radiation. The main objective of this paper is to derive and integrate the intermolecular partition function into the general partition function of the elementary gases. The application of the partition function so formulated in the determination of the thermodynamic states of the elementary particles and its validity can eventually be addressed. The partition function of a system is the ratio of the total number of particles in the system to the number of particles in the lowest energy state of that system. Thus, it is dimensionless. Partition function is very important in the analyses of thermodynamic systems. Once an expression for the partition function of a system is known, then the thermodynamic functions appertaining to the system; entropy, specific heat capacity, Helmholtz free energy, internal energy, etc can be determined. Many have been neglecting the effects of intermolecular interactions while calculating the overall partition function of interacting systems. This article considered the common way of determining partition function, z without considering intermolecular interaction effects and compared it with z determined by taking cognizance of the effects of intermolecular interactions. A comparison of the two was made, and the result analyzed. An overview of the various z’s in the old way was presented and a new one called inter-particle interaction partition function was derived using the Schrodinger equation. . To validate the work, the entropies and specific heats of hydrogen were compared with published data by two-way ANOVA.  It was determined that the values were significantly different as expected. This work has established that intermolecular interactio

Modeling and simulation of belt bucket elevator head shaft for safe life operation

Abstract This research paper presents a step by step conceptual design and life prediction approach for the design, modeling and simulation of head shaft of a belt bucket elevator, to be used for conveying grains to a height of 33.5 m and at the rate of 200 tons/h. output. For this elevator system, the force and torque acting on the head shaft as well as the bending moment were calculated. Furthermore, the diameter of each cross section of the shaft was determined taking into consideration the geometric and fatigue stress concentration factors, due to shoulders which contribute significantly to most fatigue failures of shafts. The stress induced on the shaft by the force and the factor of safety for each cross section of the shaft was calculated using the DE-Goodman criterion. The model of the shaft was created from the calculated diameters and subjected to static and fatigue analysis using SolidWorks FEA. The results were validated by comparing the values from the FEA and the calculated values for stress and factor of safety of the critical section of the shaft, which showed an equivalent value. The FEA gave a fatigue load factor greater than one, which signifies that the shaft will not go into failure mode within the infinite life cycle of the shaft. The value of the fatigue strength obtained from FEA was higher than the value for the maximum von misses stress of the shaft, this result shows that the head shaft will sustain the loading stresses over a finite life prediction. This research is significant because the stress induced forces on the head shaft from each component of the elevator system were properly identified and analyzed so as to obtain precise results for life prediction