Thermodynamic cycleA thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine.
Retardation factorIn chromatography, the retardation factor (R) is the fraction of an analyte in the mobile phase of a chromatographic system. In planar chromatography in particular, the retardation factor RF is defined as the ratio of the distance traveled by the center of a spot to the distance traveled by the solvent front. Ideally, the values for RF are equivalent to the R values used in column chromatography. Although the term retention factor is sometimes used synonymously with retardation factor in regard to planar chromatography the term is not defined in this context.
Kinetic theory of gasesThe kinetic theory of gases is a simple, historically significant classical model of the thermodynamic behavior of gases, with which many principal concepts of thermodynamics were established. The model describes a gas as a large number of identical submicroscopic particles (atoms or molecules), all of which are in constant, rapid, random motion. Their size is assumed to be much smaller than the average distance between the particles. The particles undergo random elastic collisions between themselves and with the enclosing walls of the container.
Maxwell–Boltzmann distributionIn physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment.
Binomial theoremIn elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example, for n = 4, The coefficient a in the term of axbyc is known as the binomial coefficient or (the two have the same value).
Binomial coefficientIn mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the multiplicative formula which using factorial notation can be compactly expressed as For example, the fourth power of 1 + x is and the binomial coefficient is the coefficient of the x2 term.
Column chromatographyColumn chromatography in chemistry is a chromatography method used to isolate a single chemical compound from a mixture. Chromatography is able to separate substances based on differential adsorption of compounds to the adsorbent; compounds move through the column at different rates, allowing them to be separated into fractions. The technique is widely applicable, as many different adsorbents (normal phase, reversed phase, or otherwise) can be used with a wide range of solvents.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Separation processA separation process is a method that converts a mixture or a solution of chemical substances into two or more distinct product mixtures, a scientific process of separating two or more substance in order to obtain purity. At least one product mixture from the separation is enriched in one or more of the source mixture's constituents. In some cases, a separation may fully divide the mixture into pure constituents. Separations exploit differences in chemical properties or physical properties (such as size, shape, mass, density, or chemical affinity) between the constituents of a mixture.
Joint probability distributionGiven two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).
Binomial distributionIn probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.
Beta-binomial distributionIn probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution.
