NMR In nuclear magnetic resonance (NMR), various relaxations are the properties that it measures. Chemical relaxation methods In chemical kinetics, relaxation methods are used for the measurement of very fast reaction rates. A system initially at equilibrium is perturbed by a rapid change in a parameter such as the temperature (most commonly), the pressure, the electric field or the pH of the solvent. The return to equilibrium is then observed, usually by spectroscopic means, and the relaxation time measured. In combination with the chemical equilibrium constant of the system, this enables the determination of the rate constants for the forward and reverse reactions. Monomolecular first-order reversible reaction A monomolecular, first order reversible reaction which is close to equilibrium can be visualized by the following symbolic structure: A <=> B In other words, reactant A and product B are forming into one another based on reaction rate constants k and k'. To solve for the concentration of A, recognize that the forward reaction (A ->[{k}] B) causes the concentration of A to decrease over time, whereas the reverse reaction (B ->[{k'}] A) causes the concentration of A to increase over time. Therefore, , where brackets around A and B indicate concentrations. If we say that at , and applying the law of conservation of mass, we can say that at any time, the sum of the concentrations of A and B must be equal to the concentration of , assuming the volume into which A and B are dissolved does not change: Substituting this value for [B] in terms of [A]0 and [A](t) yields which becomes the separable differential equation This equation can be solved by substitution to yield In atmospheric sciences Desaturation of clouds Consider a supersaturated portion of a cloud. Then shut off the updrafts, entrainment, and any other vapor sources/sinks and things that would induce the growth of the particles (ice or water). Then wait for this supersaturation to reduce and become just saturation (relative humidity = 100%), which is the equilibrium state. The time it takes for the supersaturation to dissipate is called relaxation time. It will happen as ice crystals or liquid water content grow within the cloud and will thus consume the contained moisture. The dynamics of relaxation are very important in cloud physics for accurate mathematical modelling. In water clouds where the concentrations are larger (hundreds per cm3) and the temperatures are warmer (thus