Temperature A map of global long term monthly average surface air temperatures in Mollweide projection. A temperature is a numerical measure of hot and cold. Its measurement is by detection of heat radiation or particle velocity or kinetic energy, or by the bulk behavior of a thermometric material. It may be calibrated in any of various temperature scales, Celsius, Fahrenheit, Kelvin, etc. The fundamental physical definition of temperature is provided by thermodynamics. Measurements with a small thermometer, or by detection of heat radiation, can show that the temperature of a body of material can vary from time to time and from place to place within it. Within a body that exchanges no energy or matter with its surroundings, temperature tends to become spatially uniform as time passes. The kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic systems. Thermal vibration of a segment of proteinalpha helix. Use in science[edit] Temperature scales[edit]
Enthalpy Enthalpy is a defined thermodynamic potential, designated by the letter "H", that consists of the internal energy of the system (U) plus the product of pressure (P) and volume (V) of the system:[1] Since enthalpy, H, consists of internal energy, U, plus the product of pressure (P) and the volume (V) of the system, which are all functions of the state of the thermodynamic system, enthalpy is a state function. The unit of measurement for enthalpy in the International System of Units (SI) is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie. The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer. The total enthalpy, H, of a system cannot be measured directly. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy and Gibbs energy. Origins[edit] or
Entropy (information theory) 2 bits of entropy. A single toss of a fair coin has an entropy of one bit. A series of two fair coin tosses has an entropy of two bits. The number of fair coin tosses is its entropy in bits. This random selection between two outcomes in a sequence over time, whether the outcomes are equally probable or not, is often referred to as a Bernoulli process. The entropy of such a process is given by the binary entropy function. This definition of "entropy" was introduced by Claude E. Entropy is a measure of unpredictability of information content. Now consider the example of a coin toss. English text has fairly low entropy. If a compression scheme is lossless—that is, you can always recover the entire original message by decompressing—then a compressed message has the same quantity of information as the original, but communicated in fewer characters. Shannon's theorem also implies that no lossless compression scheme can compress all messages. . The average uncertainty , with
Acceleration For example, an object such as a car that starts from standstill, then travels in a straight line at increasing speed, is accelerating in the direction of travel. If the car changes direction at constant speedometer reading, there is strictly speaking an acceleration although it is often not so described; passengers in the car will experience a force pushing them back into their seats in linear acceleration, and a sideways force on changing direction. If the speed of the car decreases, it is sometimes called deceleration; mathematically it is simply acceleration in the opposite direction to that of motion.[4] Definition and properties[edit] Acceleration is the rate of change of velocity. Mathematically, instantaneous acceleration—acceleration over an infinitesimal interval of time—is the rate of change of velocity over time: Average acceleration over a period of time is the change in velocity divided by the duration of the period Tangential and centripetal acceleration[edit] where = time.
Conjugate variables (thermodynamics) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs. For a mechanical system, a small increment of energy is the product of a force times a small displacement. A similar situation exists in thermodynamics. The thermodynamic square can be used as a tool to recall and derive some of the thermodynamic potentials based on conjugate variables. In the above description, the product of two conjugate variables yields an energy. Just as a small increment of energy in a mechanical system is the product of a force times a small displacement, so an increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" which, when unbalanced, cause certain generalized "displacements" to occur, with their product being the energy transferred as a result. is:
Entropy Figure 1: In a naive analogy, energy in a physical system may be compared to water in lakes, rivers and the sea. Only the water that is above the sea level can be used to do work (e.g. propagate a turbine). Entropy represents the water contained in the sea. In classical physics, the entropy of a physical system is proportional to the quantity of energy no longer available to do physical work. History The term entropy was coined in 1865 [Cl] by the German physicist Rudolf Clausius from Greek en- = in + trope = a turning (point). The Austrian physicist Ludwig Boltzmann [B] and the American scientist Willard Gibbs [G] put entropy into the probabilistic setup of statistical mechanics (around 1875). The concept of entropy in dynamical systems was introduced by Andrei Kolmogorov [K] and made precise by Yakov Sinai [Si] in what is now known as the Kolmogorov-Sinai entropy. The formulation of Maxwell's paradox by James C. Entropy in physics Thermodynamical entropy - macroscopic approach References
Velocity If there is a change in speed, direction, or both, then the object has a changing velocity and is said to be undergoing an acceleration. Constant velocity vs acceleration[edit] To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path (the object's path does not curve). Thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Distinction between speed and velocity[edit] Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving.[1] If a car is said to travel at 60 km/h, its speed has been specified. Equation of motion[edit] The average velocity during a time interval is described by the formula: at time and is: , then: can be used.
Boltzmann constant The Boltzmann constant (kB or k), named after Ludwig Boltzmann, is a physical constant relating energy at the individual particle level with temperature. It is the gas constant R divided by the Avogadro constant NA: It has the same dimension (energy divided by temperature) as entropy. Bridge from macroscopic to microscopic physics[edit] where R is the gas constant (8.314 4621(75) J K−1 mol−1[1]). The left-hand side of the equation is a macroscopic amount of pressure-volume energy representing the state of the bulk gas. Role in the equipartition of energy[edit] Given a thermodynamic system at an absolute temperature T, the thermal energy carried by each microscopic "degree of freedom" in the system is on the order of magnitude of kBT/2 (i. e., about 2.07×10−21 J, or 0.013 eV, at room temperature). Application to simple gas thermodynamics[edit] Kinetic theory gives the average pressure p for an ideal gas as Substituting that the average translational kinetic energy is gives History[edit]
8. Reductio ad Absurdum – A Concise Introduction to Logic 8.1 A historical example In his book, The Two New Sciences,[10] Galileo Galilea (1564-1642) gives several arguments meant to demonstrate that there can be no such thing as actual infinities or actual infinitesimals. One of his arguments can be reconstructed in the following way. He also proposes that we take as a premise that there is an actual infinity of the squares of the natural numbers. Now, Galileo reasons, note that these two groups (today we would call them “sets”) have the same size. If we can associate every natural number with one and only one square number, and if we can associate every square number with one and only one natural number, then these sets must be the same size. But wait a moment, Galileo says. We have reached two conclusions: the set of the natural numbers and the set of the square numbers are the same size; and, the set of the natural numbers and the set of the square numbers are not the same size. 8.2 Indirect proofs (P→(QvR)) This argument looks valid.
Momentum Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude by its own weight Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. Newtonian mechanics[edit] Momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as vector quantities. Single particle[edit] The momentum of a particle is traditionally represented by the letter p. The units of momentum are the product of the units of mass and velocity. Many particles[edit] This is known as Euler's first law.[2][3] Conservation[edit]