INTERNATIONAL JOURNAL OF MULTIDISCIPLINARY SCIENCES AND ENGINEERING, VOL. 4, NO. 7, AUGUST 2013 [ISSN: 2045-7057] www.ijmse.org 60 Statistical Thermodynamics Approach to Urinary Analysis Employing Micro-Canonical Ensemble * Chukwuneke J. L., Achebe C.H., Okolie P. C. and Okonkwo U. C. Mechanical Engineering Department, NnamdiAzikiwe University, P.M.B 5025 Awka, Nigeria * jl.chukwuneke@unizik.edu.ng Abstract– This paper presents, the study of urinary analysis using micro-canonical ensemble, which dealt with the study of urine system that was further related to the micro-canonical ensemble of statistical thermodynamics. The goal of statistical thermodynamics is to understand and to interpret measurable macroscopic properties of the absorbance and to establish valid relationships among measureable variables in a statistical manner over samples range. A valid relationship with constant, k B between the absorbance (A abs ) and wavelength (λ) of different samples was obtained. The use of numerical method “Newton Cotes methods” to integrate the absolute values of absorbance (A abs ) and wavelength (λ) was equally employed. This study is necessary to show the relationships among important variables for optimal outputs and longevity of the system. Absolute values of absorbance (A abs ) and wavelength (λ) are 12.32 and 497.143Å, respectively. Keywords– Absorbance, Intensity, Micro-canonical Ensemble, Spectrometer, Statistical thermodynamics, Urine system, Urinary analysis and Wavelength I. INTRODUCTION spectrometer consists of two instruments, namely, a spectrometer for producing light of any selected colour (wavelength), and a photometer for measuring the intensity of light [1]. The instruments are arranged so that liquid in cuvette can be placed between the spectrometer beam and the photometer. The photometer delivers a voltage signal to a play device normally a galvanometer. The signal changes as the amount of light absorbed by the liquid changes [1]. Development of colour is linked to the concentration and can be measured by determining the extent of absorption of light at the appropriate wavelength [1]. A spectrometer is used to measure the intensity of the light entering a sample and the light exiting a sample and compares the two intensities. The information about the two intensities can be expressed as transmittance (the ratio of the intensity of the existing light to the entering light) or percent transmittance (%T). Different materials absorb different wavelengths of light [2], [3]. Therefore, the wavelength of maximum absorption by a material is one of characteristic properties of that material. Many compounds absorb ultraviolet (UV) or Visible (Vis) Light. The amount of radiation absorbed may be measured in a number of ways [3], [4]: Transmittance, T =    (1) % Transmittance,    (2) Absorbance; A =      (3) A =     (4) A =     (5) The %T can be related to the absorbance (A) by the equation below [1], [3]: A = 2 − [log(%T)] (6) The essential task in this application of statistical thermodynamics is to determine the distribution of a given amount of Absorbance over N identical systems. The goal is to understand and to interpret the measurable macroscopic properties of materials in terms of the properties of their constituent particles and the interactions between them. To obtain the absolute Absorbance value of Urine over range of wavelengths. To statistically collect data of absorbance and analyze the system using statistical thermodynamics ensemble. These values obtained are applied to the micro-canonical ensemble with the intent to ultimately establish a relationship between absorbance (A) and the wavelength with a possible constant k, thus defining a mathematical relationship between these parameters. A. Underlying Theory When monochromatic light (light of a specific wavelength) passes through a solution, there is usually a quantitative relationship (Beer’s law) between the solute concentration and the intensity of the transmitted light [1], [2], [4].             (7) Where; I o is the intensity of transmitted light using blank water or pure solvent, I is the intensity of the transmitted light when the sample solvent, L = distance the light passes through the solution, k = constant If the light path is constant, as the case with a spectrometer, Beer’s law may be written as:       (8) Where; K is a new constant, T = transmittance of the solution A