On The Theory of Time dilation in Chemical Kinetics

The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasiequilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius Equation, of the collision frequency and of the Eyring and Marcus equations renders the rate law also Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction. Lorentz transformation of the half-life equation explains time dilation of the half life period of chemical reactions and proves special theory of relativity and presents theory of relativistic chemical kinetics in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine are considered as numerical examples.Comment: 34 pages, 1 figures, 2 table

Quantum Mechanics of Insitu Synthesis of Inorganic Nanoparticles with in Anionic Microgels

In this work, we discuss the quantum mechanics of many-body systems i.e. hybrid microgel consisting of negatively charged anionic microgels possessing thick sheath of water molecules solvating its protruding anionic moieties and nanoparticle captivated with in it. Thermodynamic feasibility of synthesis of particular nanoparticle with in the microgel is dependent upon the magnitude of interaction between nanoparticle, water molecules and microgel relative to sum of magnitude of self-interaction between counterions and interaction between counterions and microgel. Nanoparticles synthesized with in the microgels have thick electronic cloud that oscillates under the influence of net interaction potential of charged anionic moieties and solvent water molecules. Hamiltonian describing energy of oscillating electronic cloud wrapped around nanoparticle is mathematically derived to be equal to product of integral of electron density and its position vector overall space multiplied with net electric force acting on the oscillating electronic cloud of nanoparticle.Comment: 11 pages, 2 figures,mathematical modelling of use of microgel as nano-reacto

Effect of strength of gravitational field on electrode processes

Gravitational transformation of free energy dictates cell potential to be lower near the vicinity of massive planet which results in the slower oxidation and reduction of ions at their respective electrodes, in lower gravitational field. The newly formulated gravitational transformations formulates decrease in the electrode potential, cell potential and electrochemical rate constants at lower gravitational field, this is due to greater flux of gravitons escaping in to higher dimensions at lower gravitational fields than at higher gravitational fields

Investigating viscous damping using a webcam

We describe an experiment involving a mass oscillating in a viscous fluid and analyze viscous damping of harmonic motion. The mechanical oscillator is tracked using a simple webcam and an image processing algorithm records the position of the geometrical center as a function of time. Interesting information can be extracted from the displacement-time graphs, in particular for the underdamped case. For example, we use these oscillations to determine the viscosity of the fluid. Our mean value of 1.08 \pm 0.07 mPa s for distilled water is in good agreement with the accepted value at 20\circC. This experiment has been successfully employed in the freshman lab setting.Comment: 13 pages, 5 figure

Price-setting for Residential Water: Estimation of Water Demand in Lahore

The Water and Sewerage Agency (WASA) of Lahore is facing soaring demand and rising costs. But while massive investments are made to augment supply, tariffs remain low and are not adjusted in line with growing expenses. This has resulted not only in heavy and increasingly unsustainable reliance on loans and subsidies, but also in consumers undervaluing the resource, resulting in its inefficient utilisation. In this scenario, water tariffs badly need to be reformed. This study explores the potential of a pricing policy to regulate residential water demand in order to achieve the objectives of cost recovery, efficient water use, and equitable allocation of water resources. To this end, a demand function is estimated using household level data about water consumption and socio-economic characteristics of 156 households supplied by WASA, Lahore, for the period 2004-2006. Under block-rate tariffs the price variable is endogenously determined and a system of simultaneous equations emerges, solved here using two-stage least squares method. The estimated model explains 57 percent variation in water demand. The study finds water demand to be inelastic to price and, considering WASA’s exceedingly low tariffs, recommends up to 50 percent increase in the current tariff structure. Further computations show that a 50 percent increase will not endanger lifeline water supply. However, tariff increases may not be felt uniformly across all income groups, and absence of income data remains a limitation of this study. The study also recommends linking the non-volumetric part of tariffs to wealth-determined variables, such as property value and income.Water Demand; Price-setting

Estimation of willingness to pay for improvement in dirnking water quality: a study of wasa, lahore

This study examines the existing water quality of Lahore and measures domestic household's willingness to pay for improvement in water quality services. To this end, a Tobit model is estimated by conducting a contingent valuation survey about household perceptions in six towns of Lahore. The results show that the factors affecting household's willingness to pay are coping costs that a household pay for ensuring quality of water.The study also finds the education level of head of family is an important factor in determining the willingness to pay for improved water services. It is recommended that by ensuring the supply and quality to the household additional revenue of 4.22 million rupees could be earned by the authority.Willingness to Pay, Tobit, Drinking Water Quality