Orphan date February 2009 Expert subject physics date November 2008 Thermodynamic length is a Riemannian metric defined on a manifold of thermodynamic state s. Clarify date November 2008 Category Thermodynamics Physics stub ... more details
Thermodynamics cTopic Thermodynamic system Systems A thermodynamic state is a set of values of properties of a Thermodynamics thermodynamicThermodynamic system system that must be specified to reproduce the system. The individual parameters are known as state variables , state parameters or thermodynamic variables . Once a sufficient set of thermodynamic variables have been specified, values of all other properties of the system are uniquely determined. The number of values required to specify the state depends on the system, and is not always known. State functions Main State function State functions , also called thermodynamic variables , state quantities , or a functions of state describe the momentary condition of a thermodynamic system. Regardless of the path by which a system goes from one state to another i.e., the sequence of intermediate states the total change in any state variable will be the same. This means that the incremental changes in such variables are exact differential s . Examples include entropy , pressure , Thermodynamic temperature temperature , Gas volume volume , etc. Various thermodynamic diagram s have been developed to model the transitions between thermodynamic states. Equilibrium state Systems found in nature are often dynamic and complex, but in many cases their states are amenable to description based on proximity to ideal conditions. One such ideal condition is that of a stable equilibrium state. Based on many observations, thermodynamics postulates that all systems having no effect on the external environment will change in such a way as to approach unique stable equilibrium states. Closed simple system A common example in which the state can be succinctly described is a closed simple system in an equilibrium state. A closed simple system is an ideal system devoid of any internal adiabatic , rigid , or Permeation impermeable boundaries ... stato fa it Stato termodinamico pl Stan termodynamiczny simple Thermodynamic ... more details
Unreferenced date December 2009 Thermodynamics cTopic Thermodynamic system Systems A thermodynamic instrument is any device which facilitates the quantitative measurement of thermodynamic systems . In order for a thermodynamic parameter to be truly defined, a technique for its measurement must be specified. For example, the ultimate definition of temperature is what a thermometer reads . The question follows what is a thermometer? There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system. A thermodynamic reservoir is a system which is so large that it does not appreciably alter its state parameters when brought into contact with the test system. Overview Two general complementary tools are the meter and the reservoir. It is important that these two types of instruments are distinct. A meter does not perform its task accurately if it behaves like a reservoir of the state variable it is trying to measure. If, for example, a thermometer, were to act as a temperature reservoir it would alter the temperature of the system being measured, and the reading would be incorrect. Ideal meters have no effect on the state variables of the system they are measuring. Thermodynamic meters A meter is a thermodynamic system which displays some aspect of its thermodynamic state to the observer ... thermometer described below is just such a meter. In some cases, the thermodynamic parameter is actually ... energy of a system. Some common thermodynamic meters are Thermometer a device which measures temperature ... connected to a thermally isolated system. Thermodynamic reservoirs see also Thermal reservoir A reservoir is a thermodynamic system which controls the state of a system, usually by imposing itself ... be controlled. A reservoir is so large that its thermodynamic state is not appreciably affected by the state ... reflist DEFAULTSORT Thermodynamic Instruments Category Thermodynamics ... more details
Unreferenced date December 2009 In thermodynamics , particularly statistical mechanics , the thermodynamic limit is reached as the number of particles atom s or molecule s in a system, N , approaches infinity. The thermodynamic behavior of a system is asymptotically approximated by the results of statistical mechanics as N tends to infinity, and calculations using the various ensembles used in statistical mechanics converge. The mathematical basis of this result comes from manipulating factorial s arising from Ludwig Boltzmann Boltzmann s formula for the entropy , S k log W by using Stirling s approximation , which is justified only when applied to large numbers. Empirically, the relative size of fluctuations from the average is much bigger from collections of only a few atoms or molecules, and so the probabilistic assumptions of statistical mechanics break down. In some simple cases, and at thermodynamic equilibrium , the results can be shown to be a consequence of the additivity property of statistical independence independent random variable s namely that the variance of the sum is equal to the sum of the variances of the independent variables. In these cases, the physics of such systems close to the thermodynamic limit is governed by the central limit theorem ... at the thermodynamic limit, there are still small detectable fluctuations in physical quantities, but this has ... ity. It is at the thermodynamic limit that the additivity property of macroscopic extensive ... mechanics thermodynamic limit exists, but depends on boundary conditions. For example this happen ... wall boundary conditions. Cases where there is no thermodynamic limit A thermodynamic limit does not exist in all cases. Usually, a model is taken to the thermodynamic limit by increasing .... However, the following two examples demonstrate cases where these approaches do not lead to a thermodynamic ... Thermodynamic Limit Category Fundamental physics concepts Category Statistical mechanics ... more details
File Guggenheim square.svg thumb The thermodynamic square The thermodynamic square also known as the thermodynamic wheel is a mnemonic diagram used to help determine thermodynamic relations. The corners represent common conjugate variables thermodynamics conjugate variables while the sides represent thermodynamic potentials . The placement and relation among the variables serves as a key to recall the relations they constitute. A mnemonic used by students to remember the Maxwell relations in thermodynamics is G ood P hysicists H ave S tudied U nder V ery F ine T eachers , which helps them remember the order of the variables in the square, in clockwise direction. Another mnemonic used here is V alid F acts and T heoretical U nderstanding G enerate S olutions to H ard P roblems , which gives the letter in the normal left to right writing direction. Both times A has to be identified with F , another common symbol for Helmholtz Free Energy. To prevent the need for this switch the following mnemonic is also widely used G ood P hysicists H ave S tudied U nder V ery A mbitious T eachers . Its invention is attributed to Max Born , so it is often referred to as Born square . Use The Thermodynamic square is mostly used to compute the derivative of any thermodynamic potential of interest. Suppose for example one desires to compute the derivative of the Internal energy math U math . The following procedure should be considered Place yourself in the thermodynamic potential of interest, namely math G math , math H math , math U math , math F math . In our example, that would be math U math . The two opposite corners of the potential of interest represent the coefficients of the overall ... to be generalized. The Thermodynamic square can also be used to find the Maxwell Relations. Looking ... books?id aD6TJAuCTVsC&lpg PA59&ots VT00QzdeH&dq Thermodynamic 20square&pg PA59 v onepage&q Thermodynamic 20square&f false Category Thermodynamics physics stub Category Mnemonics de Guggenheim ... more details
In thermodynamics , a thermodynamics Thermodynamic system thermodynamic system is said to be in thermodynamic ... , and chemical equilibrium . The word equilibrium means a state of balance. In a state of thermodynamic ... , and no unbalanced potentials or driving forces , within the system. A system that is in thermodynamic ... equilibrium. Thermodynamics cTopic Thermodynamic system Systems Overview Classical thermodynamics deals with dynamic equilibrium states. The local state of a system at thermodynamic equilibrium ... . To be specific, thermodynamic equilibrium is characterized by the minimum of a thermodynamic ... denoted by the symbol F, but the use of A is preferred by IUPAC 2 . The process that leads to a thermodynamic ... for equilibrium By considering the differential form of thermodynamic potentials , the following ... between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system .... As an example, temperature controls Heat equation heat exchanges . Global thermodynamic equilibrium ... system, while local thermodynamic equilibrium LTE means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium .... In a radiation radiating gas, the photon s being emitted and absorbed by the gas need not be in thermodynamic .... Local thermodynamic equilibrium does not require either local or global stationarity. In other ... are processes that lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium ... Main Quasistatic equilibrium Quasistatic equilibrium is the quasi balanced state of a thermodynamic system near to thermodynamic equilibrium, in some sense. In a quasistatic or equilibrium process, a sufficiently slow transition of a thermodynamic system from one equilibrium state to another ... thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic ... more details
Thermodynamics cTopic Thermodynamic system Systems A thermodynamic process may be defined as the energetic development of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. A state function is a thermodynamic variable which depends only on the current state of the system, not the path taken to reach that state. Conversely a process function does depend on the path. Overview File Stirling Cycle color.png thumb left An example of a series of thermodynamic processes which make up the Stirling cycle A thermodynamic process can be visualized by thermodynamic diagram graphically plotting the changes to the system s state variable s. In the example, four processes are shown. Each process has a well defined start and end point in the pressure volume state space . In this particular example, processes 1 and 3 are isothermal , whereas processes 2 and 4 are isochoric process isochoric . The PV diagram is a particularly useful visualization of a process, because the area under the curve of a process is the amount of work thermodynamics work done by the system during that process. Thus work is considered to be a process variable , as its exact value ... as well as numerous list of thermodynamic properties other properties are considered state variables ... by a boundary that is impermeable to particles. Thermodynamic potentials Any of the thermodynamic potential ... in enthalpy in the system. Polytropic processes main Polytropic process A polytropic process is a thermodynamic ... to accurately characterize processes of certain thermodynamic system system s, notably the compression ... s. Quasistatic process main Quasistatic process A quasistatic process is an idealized model of a thermodynamic ... that are infinitesimally close to thermodynamic equilibrium equilibrium so the system remains in quasistatic ... Thermodynamic processes DEFAULTSORT Thermodynamic Process Category Thermodynamic processes ar ... more details
For a quick reference table of these equations, see Table of thermodynamic equations Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic ... cTopic Equations Introduction One of the fundamental thermodynamic equations is the description of thermodynamic ... of a thermodynamic system and the correlative energetic laws which govern its associated processes. The equilibrium state of a thermodynamic system is described by specifying its state . The state of a thermodynamic system is specified by a number of Intensive and extensive properties extensive ... is known as the first law of thermodynamics . A thermodynamic system is in equilibrium when it is no longer .... A thermodynamic system may be composed of many subsystems which may or may not be insulated from each other with respect to the various extensive quantities. If we have a thermodynamic system in equilibrium in which we relax some of its constraints, it will move to a new equilibrium state. The thermodynamic ... point in a space of thermodynamic parameters. The change in the state of the system can be seen as a path in this state space. This change is called a thermodynamic process . Thermodynamic ... equilibrium state. The concept which governs the path that a thermodynamic system traces in state space ... as an extensive function of all of the extensive thermodynamic parameters. If we have a thermodynamic ... Some of the most common thermodynamic quantities are The conjugate variable pairs are the fundamental state variables used to formulate the thermodynamic functions. cellspacing 5 p Pressure V Volume T Temperature S Entropy Chemical potential N Particle number The most important thermodynamic potential ... G Gibbs free energy Thermodynamic system s are typically affected by the following types of system interactions. The types under consideration are used to classify systems as Thermodynamic system Open system open system s, Thermodynamic system Open system closed system s, and Thermodynamic system ... more details
Thermodynamics cTopic Thermodynamic system Systems A thermodynamic cycle consists of a series of thermodynamic ... variables, eventually returning a thermodynamic system system to its initial state. ref Cite book ... engine . State quantities depend only on the thermodynamic state , and cumulative variation of such properties ... concept in thermodynamics . Thermodynamic cycles often use quasistatic process es to model the workings of actual devices. Heat and work Two primary classes of thermodynamic cycles are power ... to work Image Stirling Cycle.png thumb left 200px Example of P V diagram of a thermodynamic cycle. Because the net variation in state properties during a thermodynamic cycle is zero, it forms ... heat engine 2.svg 200px thumb Heat engine diagram. Main Heat engine Thermodynamic power cycles are the basis ... thermodynamic cycle indicated by the arrows shows that the cycle represents a heat engine. The cycle consists of four states the point shown by crosses and four thermodynamic processes lines . For example the pressure volume mechanical work done in the heat engine cycle, consisting of 4 thermodynamic ... pump cycles Main Heat pump and refrigeration cycle Thermodynamic heat pump cycles are the Mathematical ... and TS diagrams of a Brayton cycle mapped to actual processes of a gas turbine engine Thermodynamic ... up of a series of stages, each of which is itself modelled as an idealized thermodynamic process. Although ... actual volume change. Well known thermodynamic cycles In practice, simple idealized thermodynamic cycles are usually made out of four thermodynamic process es. Any thermodynamic processes may be used ... example thermodynamic cycles and their constituent processes are as follows Table of thermodynamic ... Thermodynamic cycles state uncollapsed References reflist Further reading Halliday, Resnick & Walker ... Law of Thermodynamics . External links Commons category Thermodynamics cycles DEFAULTSORT Thermodynamic Cycle Category Thermodynamic cycles Category Thermodynamics ar ca Cicle ... more details
A thermodynamic potential is a Scalar field scalar function used to represent the thermodynamic state of a physical system system . The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions . One main thermodynamic ... with respect to a defined set of references or datum data . Expressions for all other thermodynamic .... Thermodynamics cTopic Potentials Description and interpretation Five common thermodynamic potentials are ref name Alberty 2001 p1353 Alberty 2001 p1353 ref table of thermodynamic potentials where T temperature ... are all energy potentials, but there are also free entropy entropy potentials . The thermodynamic square ... on the system and the heat given to it. Thermodynamic potentials are very useful when calculating ..., there is a corresponding thermodynamic potential that comes into play. Just as in mechanics ..., the potential will take on an unchanging minimum value. The thermodynamic potentials can also be used to estimate the total amount of energy available from a thermodynamic system under the appropriate ... are important not only for the above mentioned reason, but also because if a thermodynamic potential can be determined as a function of its natural variables, all of the thermodynamic properties of the system ... variables and this is true for no other combination of variables. On the converse, if a thermodynamic ... of the thermodynamic properties of the system. Notice that the set of natural variables for the above ... D math dimensions to the thermodynamic space, then there are math 2 D math unique thermodynamic potentials. For the most simple case, a single phase ideal gas, there will be three dimensions, yielding eight thermodynamic potentials. In statistical mechanics , the relationship between ... is fundamental, and is used to calculate the thermodynamic properties of matters see http clesm.mae.ufl.edu ... for more details. The fundamental equations main Fundamental thermodynamic relation The definitions ... more details
Thermodynamics cTopic List of thermodynamic properties System properties Thermodynamic diagrams are diagrams used by scientists and engineers to represent the thermodynamic states of a material typically fluid and the consequences of manipulating this material. For instance, a temperature entropy diagram Carnot cycle The temperature entropy diagram T S diagram may be used to demonstrate the behavior of a fluid as it is changed by a compressor. Overview Especially in meteorology they are used to analyze the actual state of the atmosphere derived from the measurements of radiosonde s, usually obtained with weather balloons . In such diagrams, temperature and humidity values represented by the dew point are displayed with respect to atmospheric pressure pressure . Thus the diagram gives at a first glance the actual atmospheric stratification and vertical water vapor distribution. Further analysis gives the actual base and top height of cumulus cloud convective clouds or possible instabilities in the stratification. By assuming the energy amount due to solar radiation it is possible to predict the 2 meter m 6.6 Foot length ft temperature, humidity, and wind during the day, the development of the planetary boundary layer boundary layer of the atmosphere, the occurrence and development of clouds and the conditions for soaring flight during the day. The main feature of thermodynamic diagrams ... is proportional to the energy which has been gained or released by the air. Types of thermodynamic ... curve Specific to weather services, there are mainly three different types of thermodynamic diagrams ... transformations. Not a thermodynamic diagram in a strict sense since it does not display the energy .... Characteristics Thermodynamic diagrams usually show a net of five different lines isobar meteorology ... No. 158. ISBN 92 63 10495 6 especially chapter 2.3. External links Commons category Thermodynamic diagrams ... sciences at the University of Wyoming USA Meteorological variables DEFAULTSORT Thermodynamic ... more details
Unreferenced date December 2009 In statistical mechanics , the thermodynamic beta is a physical quantity related to the thermodynamic temperature T of a system. It can be calculated from formula math beta frac1 k mathrm B T ,, math where k sub B sub is the Boltzmann constant . The thermodynamic beta can be viewed as a connection between the statistical interpretation of a physical system and thermodynamics . It is sometimes considered a more fundamental quantity than temperature. Details Statistical interpretation From the statistical point of view, is a numerical quantity relating two macroscopic systems in equilibrium. The exact formulation is as follows. Consider two systems, 1 and 2, in thermal contact, with respective energies E sub 1 sub and E sub 2 sub . We assume E sub 1 sub E sub 2 sub some constant E . The number of Microstate statistical mechanics microstates of each system will be denoted by sub 1 sub and sub 2 sub . Under our assumptions sub i sub depends only on E sub i sub . Thus the number of microstates for the combined system is math Omega Omega 1 E 1 Omega 2 E 2 Omega 1 E 1 Omega 2 E E 1 . , math We will derive from the following fundamental assumption When the combined system reaches equilibrium, the number &Omega is maximized. In other words, the system naturally seeks the maximum number of microstates. Therefore, at equilibrium, math frac d d E 1 Omega Omega 2 E 2 frac d d E 1 Omega 1 E 1 Omega 1 E 1 frac d d E 2 Omega 2 E 2 cdot frac d E 2 d E 1 0. math But E sub 1 sub E sub 2 sub E implies math frac d E 2 d E 1 1. math So math Omega 2 E 2 frac ... of math beta equiv frac d ln Omega d E . math Connection with thermodynamic view On the other hand, when two systems are in equilibrium, they have the same thermodynamic temperature T . Thus intuitively ... . math Comparing with the thermodynamic formula math frac d S d E frac 1 T , math we have math beta ... Ising model DEFAULTSORT Thermodynamic Beta Category Statistical mechanics Category Units of temperature ... more details
Thermodynamic integration is a method used to compare the difference in Thermodynamic free energy free energy between two given states e.g., A and B via sampling state configurations in a molecular dynamics or Metropolis Hastings algorithm Metropolis Monte Carlo simulations. Because the free energy of a system is not simply a function of the phase space coordinates of the system, but is instead related to the canonical partition function Q N,V,T , the free energy difference between two states cannot be calculated directly. In the thermodynamic integration approach, the free energy difference is calculated by defining a thermodynamic path between the states and integrating over enthalpy changes along the path. Such paths can either be real chemical processes or alchemical processes. A good example of the alchemical process is the Kirkwood s coupling parameter method. ref J. G. Kirkwood. Statistical mechanics of fluid mixtures, J. Chem. Phys., 3 300 313,1935 ref Derivation Consider two systems, A and B, with potential energies math U A math and math U B math . The potential energy in either system can be calculated as an ensemble average over configurations sampled from a molecular dynamics or Monte Carlo simulation with proper Boltzmann weighting. Now consider a new potential energy function defined as math U lambda U A lambda U B U A math Here, math lambda math is defined as a coupling parameter with a value between 0 and 1, and thus the potential energy as a function of math lambda math varies from the energy of system A for math lambda 0 math and system B for math lambda 1 math . In the canonical ensemble , the partition function of the system can be written as math Q N, V, T, lambda sum s exp U s lambda kT math In this notation, math U s lambda math is the potential energy of state math s math in the ensemble with potential energy function math U lambda math as defined ... to thermodynamic integration. ref cite doi 10.1021 ct050252w ref See also Free energy ... more details
Refimprove date December 2010 Image system boundary.svg 200px thumb A thermodynamic system is a precisely ... the principles of thermodynamics . All space in the universe outside the thermodynamic system is known ... this boundary. Thermodynamic systems are often classified by specifying the nature of the exchanges that are allowed to occur across its boundary. A thermodynamic system is characterized and defined by a set of thermodynamic parameters associated with the system. The parameters are experimentally measurable ... of thermodynamic parameters necessary to uniquely define a system is called the thermodynamic ... , between its parameters. A system is in thermodynamic equilibrium when the state of the system ... a thermodynamic system as the working substance under study. Thermodynamics cTopic Thermodynamic system Systems Overview Thermodynamics describes the physics of matter using the concept of the thermodynamic ... environment. align right table of thermodynamic systems Isolated systems are completely isolated ... accept limitations on the time frame of a process. History The first to develop the concept of a thermodynamic ... closed surface that encloses or demarcates the volume or region that a thermodynamic system occupies ... year 1998 id ISBN 0 19 856552 6 ref In short, a thermodynamic boundary is a geometrical division between ... W shaft , math The definition of enthalpy , H , permits us to use this thermodynamic potential ... thermodynamic relationship used to compute changes in internal energy, which is expressed ... to completion is considered to be in a state of thermodynamic equilibrium . Truly isolated physical ... does not enter or leave the system. Systems in equilibrium At thermodynamic equilibrium , a system ... to understand than systems which are not in equilibrium. Often, when analyzing a thermodynamic ... to be in a state of thermodynamic equilibrium . The thermodynamic properties of a system in equilibrium ... manner than non equilibrium states. In thermodynamic processes, large departures from equilibrium ... more details
be as generally accessible as possible for the subject matter. Thermodynamics cTopic List of thermodynamic properties System properties Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics . Thermodynamic temperature is an absolute ... comprise the Kinetic energy kinetic energy in a substance. More specifically, the thermodynamic ... in solids. Thermodynamic temperature s null mathematics null point, absolute zero, is the temperature ... as the real world effects that ZPE has on substances can vary as one alters a thermodynamic system ... thermodynamics and its thermodynamic equations equations are founded because they deal with the exchange ... spectrum via a classical thermodynamic operation involving van der Waals forces , Daniel C. Cole, Physical ... Thermodynamic temperature Heat energy at absolute zero Heat energy at absolute zero , below . Throughout the scientific world where measurements are made in International System of Units SI units, thermodynamic ... States U.S. however, measure thermodynamic temperature using the Rankine scale . By http www1.bipm.org ... to represent the thermodynamic temperature as closely as possible throughout its range ... the mass but half the velocity. The thermodynamic temperature of any bulk quantity of a substance ... contributes to the pressure and volume of that gas is a proportional function of thermodynamic temperature ... also relates the thermodynamic temperature of a gas to the mean kinetic energy of an individual particle ... 24 e 23 u J K and is pronounced Kay sub bee T is the thermodynamic temperature in kelvins K Image Maxwell ... and in thermodynamic equilibrium all parts are at a uniform temperature and no heat is going ... motion of atoms and molecules is calculated based on thermodynamic temperature as follows math bar ... particle motion in m s k sub B sub is the Boltzmann constant val 1.3806504 24 e 23 u J K T is the thermodynamic ... local thermodynamic equilibrium LTE phenomena such as combustion , the sublimation chemistry sublimation ... more details
Thermodynamic efficiency limit is the absolute maximum theoretically possible conversion efficiency of sunlight to electricity . Its value is about 86 , which is due to the Carnot cycle Carnot limit , given the temperature of the photon s emitted by the Sun s surface. ref cite web url http www.thenakedscientists.com HTML articles article catching energy from the sun title Catching Energy From the Sun publisher thenakedscientists.com accessdate 2011 07 22 work ref Effect of band gap energy Solar cells operate as quantum energy conversion device s, and are therefore subject to the thermodynamic efficiency limit. Photons with an energy below the band gap of the absorber material cannot generate a electron hole pair , and so their energy is not converted to useful output and only generates heat if absorbed. For photons with an energy above the band gap energy, only a fraction of the energy above the band gap can be converted to useful output. When a photon of greater energy is absorbed, the excess energy above the band gap is converted to kinetic energy of the carrier recombination . The excess ... the solar spectrum into smaller bins where the thermodynamic efficiency limit is higher for each ... year 1983 ref Efficiency limits for different solar cell technologies Thermodynamic efficiency limits ... work ref Thermodynamic efficiency limit for excitonic solar cells File ShockleyQueisserFullCurve.svg ... first3 Michael R. last4 Forrest first4 Stephen R. year 2011 month May title Thermodynamic efficiency ... http jap.aip.org resource 1 japiau v32 i3 p510 s1?isAuthorized no accessdate 2011 07 22 ref Thermodynamic ... higher considering thermodynamic effects. For a solar cell powered by the Sun s unconcentrated ... first3 Hans J. year 1996 title Thermodynamic efficiency limits for semiconductor solar cells with carrier ... 0248 95 00125 5 issn 09270248 url http www.mendeley.com research thermodynamic efficiency limits ... Category Thermodynamic processes ... more details
Thermodynamics cTopic Thermodynamic equations Equations In thermodynamics , Bridgman s thermodynamic equations are a basic set of thermodynamic equations, derived using a method of generating a large number of thermodynamic identities involving a number of thermodynamic quantities. The equations are named after the American physicist Percy Williams Bridgman . See also the exact differential article for general differential relationships . The extensive variables of the system are fundamental. Only the entropy S , the volume thermodynamics volume V and the four most common thermodynamic potentials will be considered. The four most common thermodynamic potentials are Internal energy U Enthalpy H Helmholtz free energy A Gibbs free energy G The first derivatives of the internal energy with respect to its extensive natural variables S and V yields the intensive parameters of the system The pressure P and the temperature T . For a simple system in which the particle number s are constant, the second derivatives of the thermodynamic potentials can all be expressed in terms of only three material properties thermodynamics material properties Heat capacity heat capacity constant pressure C sub P sub Thermal expansion Coefficient of thermal expansion Compressibility Isothermal compressibility sub T sub Bridgman s equations are a series of relationships between all of the above quantities. Introduction Many thermodynamic equations are expressed in terms of partial derivatives. For example, the expression for the heat capacity at constant pressure ... to express many thermodynamic equations. For example from the equations below we have math partial ... P C P c P N math Bridgman s thermodynamic equations Note that Lewis and Randall use F and E for the Gibbs ... V partial T right P math See also Table of thermodynamic equations References reflist cite journal last Bridgman first P.W. authorlink Percy Williams Bridgman title A Complete Collection of Thermodynamic ... more details
Thermodynamics Thermodynamic databases contain information about List of thermodynamic properties thermodynamic properties for substances, the most important being enthalpy , entropy , and Gibbs free energy . Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature dependent values for one mole of substance ... condition for pressure are in use. Thermodynamic data Thermodynamic data is usually presented ..., one kg . A thermodynamic datafile is a set of equation parameters from which the numerical data values ... must be defined for the value to have any meaning. The state of aggregation for thermodynamic purposes ... indefinitely. Thermodynamic functions that refer to conditions in the normal standard state are designated with a small superscript . The relationship between certain physical and thermodynamic properties ... difficult to measure the absolute amount of any thermodynamic quantity involving the internal energy ... own typical temperature at which it begins to become important in thermodynamic reactions. It is therefore ... thermodynamic databases such as for steam, the reference temperature is 273.15 K 0 C . The Heat capacity ... and the compound. Entropy and Gibbs energy The entropy of a system is another thermodynamic ... states. Hence, the main functional application of Gibbs energy from a thermodynamic database is its ... of thermochemical databases may contain some additional thermodynamic functions. For example ... constant K sub eq sub is often listed, which is calculated from the defining thermodynamic equation. div align center math log 10 left K eq right Delta G circ form 19.1448T math div Thermodynamic databases A thermodynamic database consists of sets of critically evaluated values for the major thermodynamic ... for calculating reaction properties and displaying the data as charts. Thermodynamic data comes ... consistency requires that all values of the thermodynamic functions are correctly calculated ... more details
Refimprove date September 2009 Thermodynamic pump testing is a form of pump testing where only the temperature rise and power consumed need to be measured to find the efficiency of a pump. This is measured by means of temperature and pressure probes fitted to tapping points on the pump s inlet and outlet. Flow rate is derived from the pump efficiency measurement and electrical power supplied to the pump. ref US Patent 4781064 ref ref http www.aems.co.uk yates flow meters.aspx ref ref http www.pumpmonitor.com P22 Pump Efficiency And Flow Meter.php ref ref http www.riventa.co.uk ref The thermodynamic method was developed in the 1960s at the University of Glasgow and the University of Strathclyde in Scotland, and the National Engineering Laboratory in France Electricite de France and Austin Whillier Chamber of Mines, Johannesburg, South Africa and his paper titled pump efficiency determination from temperature measurements as published in the October 1967 edition of The South African Mechanical Engineer. ref ftp 140.98.193.80 uploads pes PowerAfrica2007 PowerAfrica 32 cattaeae.pdf.pdf ref This method is capable to undertake a calibration check on the flow meter on each pump and provides a precise flow measurement to enhance leakage detection and allows for accurate calculation of performance, especially for non revenue water . When calculating pump efficiency, highly accurate measuring equipment should be used to get the most accurate reading, resulting in maximum efficiency. For example, the temperature rise is very small only hundredths of a kelvin , so very sensitive, stable thermocouple s must be used to accurately measure the rise. Properly installed and maintained pumps for water can be around 70 90 efficient, while less cared for pumps can be less efficient due to wear on the impeller and general back leakage through over large clearances. The alternative to the thermodynamic .... Thermodynamic pump testing can be incorporated with Integrated Geographical Information System ... more details
Main Intensive and extensive properties class wikitable style text align center Thermodynamic physical property properties and their characteristics Property Symbol Units Intensive and extensive properties Extensive? Intensive and extensive properties Intensive? Conjugate variables thermodynamics Conjugate Thermodynamic potential Potential? State function State br qty. ? Process function Process br qty. ? style text align left activity chemistry Activity math a math spaced ndash aye aye style text align left Altitude m aye aye style text align left Chemical potential math mu i math kJ mol aye Particle br number aye style text align left Compressibility small adiabatic small math beta S math , math kappa math Pa sup 1 sup aye aye style text align left Compressibility small isothermal small math beta T math , math kappa math Pa sup 1 sup aye aye style text align left Cryoscopic constant ref Citation last Aylward first Gordon author link Gordon Aylward last2 Findlay first2 Tristan author2 link Tristan Findlay title SI Chemical Data 5th ed. place Sweden publisher John Wiley & Sons year 2002 edition 5 pages 202 isbn 0 470 80044 5 ref math K f math K kg mol style text align left Density math rho math kg m sup 3 sup aye aye style text align left Ebullioscopic constant math K b math style text align left Enthalpy math H math J aye aye aye style text align left s 3 Specific enthalpy math h math J kg aye aye style text align left thermodynamic entropy Entropy math S math J K aye Temperature aye small Free entropy entropic small aye style text align left s 3 Specific entropy math s math J kg K aye aye style text align left Fugacity math f math N m aye aye style text align left Gas constant ... br potential style text align left Pressure math p math Pa aye Volume aye style text align left Thermodynamic ... s Thermodynamic databases for pure substances Thermodynamic variable References reflist DEFAULTSORT List Of Thermodynamic Properties Category Physics lists Thermodynamic properties fa ... more details
A thermodynamic process path is the path or series of states through which a system passes from an initial equilibrium state to a final equilibrium state ref Thermodynamics Third Edition , Kenneth Wark, McGraw Hill Inc, 1977, ISBN 0 07 068280 1 ref and can be viewed graphically on a pressure volume P V , pressure temperature P T , and temperature entropy T s diagrams. ref Fundamentals of Engineering Thermodynamics Seventh Edition , Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey, John Wiley & Sons, Inc., 2011, ISBN 13 978 0470 49590 2 ref File Gax expanding doing work on a piston in a cylinder.jpg thumb Figure 1 There are an infinite number of possible paths from an initial point to an end point in a thermodynamic process process . In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path. ref Philip E. Bloomfield, William A. Steele, Thermodynamic processes, in AccessScience, McGraw Hill Companies, 2008, http www.accessscience.com ref Consider a gas in cylinder with a free floating piston resting on top of a volume of gas v1 at a temperature T1 . If the gas is heated so that the temperature of the gas goes up to T2 while the piston is allowed to rise to V2 as in Figure 1 , then the pressure is kept the same in this process due to the free floating piston being allowed to rise making the process an isobaric process or constant pressure process. This Process Path is a straight horizontal line from state one to state two on a P V diagram. File P V diagram, Isobaric Process.jpg thumb Figure 2 It is often valuable to calculate the work done in a process. The work done in a process is the area beneath the process path on a P V diagram. Figure 2 If the process is isobaric, then the work thermodynamics work done on the piston is easily calculated. For example, if the gas expands slowly against the piston, the work done by the gas to raise the piston is the force ... more details
Expert subject Engineering date October 2008 For more elaboration on these equations see thermodynamic equations . For list of mathematical notation used in these equations see mathematical notation . The following page is a concise list of common thermodynamic equations and quantities Variables main List of thermodynamic properties Thermodynamic symbols Equations The equations in this article are classified by subject. Entropy math S k B ln Omega math , where math k B math is the Boltzmann constant , and math Omega math denotes the volume of macrostate in the phase space or otherwise called thermodynamic probability. math dS frac delta Q T math , for reversible processes only Quantum Properties math U N k B T 2 left frac partial ln Z partial T right V math math S frac U T N S frac U T N k B ln Z N k ln N Nk math Indistinguishable Particles where N is number of particles, Z is the partition function statistical mechanics partition function , h is Planck s constant , I is moment of inertia , Z sub t sub is Z sub translation sub , Z sub v sub is Z sub vibration sub , Z sub r sub is Z sub rotation sub br math Z t frac 2 pi m k B T frac 3 2 V h 3 math br math Z v frac 1 1 e frac h omega 2 pi k B T math br math Z r frac 2 I k B T sigma frac h 2 pi 2 math br where math sigma 1 math , heteronuclear math sigma 2 math , homonuclear Quasistatic process Quasi static and Reversible process thermodynamics reversible processes math dQ C p dT l v d v dU PdV TdS math Heat capacity at constant pressure math C p left partial Q rev over partial T right p left partial U over partial T right p p ... V left partial U over partial T right V T left partial S over partial T right V math Thermodynamic potential s and related concepts table of thermodynamic potentials See also Maxwell relations Fundamental thermodynamic relation Compressibility at constant temperature math K T 1 over V left partial ... Thermodynamic equations Equations Antoine equation Bejan number Bowen ratio Bridgman s thermodynamic ... more details
File Maxwell thermodynamic surface.png thumb 300px right Historic photograph of Maxwell s plaster model taken by James Pickands II, and published in 1942 . ref name Rukeyser Muriel Rukeyser 1942 , Willard Gibbs American Genius reprinted by Ox Bow Press, ISBN 0918024579 , p. 203. ref Maxwell s thermodynamic surface is an 1874 sculpture ref name letters James Clerk Maxwell and P. M. Harman 2002 , http books.google.com books?id JbNK9lRLHPEC&pg PA148 The Scientific Letters and Papers of James Clerk Maxwell, Volume 3 1874 1879 , Cambridge University Press, ISBN 0521256275, p. 148 I have just finished a clay model of a fancy surface, showing the solid, liquid, and gaseous states, and the continuity of liquid and gaseous states. letter to Thomas Andrews scientist Thomas Andrews , November, 1874 ref made by Scottish physicist James Clerk Maxwell 1831 1879 . This model provides a three dimensional three dimensional plot of the various states of a fictitious substance with water like properties. ref name onheat James Clerk Maxwell, Elizabeth Garber, Stephen G. Brush, and C. W. Francis Everitt 1995 , http books.google.com books?id hA oIDR0eXkC&pg PA248 Maxwell on heat and statistical mechanics on avoiding all personal enquiries of molecules , Lehigh University Press, ISBN 093422334, p. 248 I ... of the model Gibbs papers defined what Gibbs called the thermodynamic surface, which expressed ... with complete historical accuracy. For example, the thermodynamic surface represented by the sculpture ... name onheat Related models Maxwell s model was not the first plaster model of a thermodynamic surface ... Maxwell s work by constructing their own plaster thermodynamic surface models. ref name knaw ... ESM4714 methods Gibbs.html Thermodynamic Case Study Gibbs Thermodynamic Graphical Method at Virginia Tech s Laboratory for Scientific Visual Analysis http www.eoht.info page Maxwell E2 80 99s thermodynamic surface Maxwell s thermodynamic surface at the Encyclopedia of Human Thermodynamics Category ... more details
A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of Gibbs free energy G values to determine unknown and experimentally inaccessible values. ref Cite journal doi 10.1021 ar00156a004 volume 21 issue 12 pages 456 463 last Bordwell first Frederick G. title Equilibrium acidities in dimethyl sulfoxide solution journal Accounts of Chemical Research date 1988 12 01 unused data DUPLICATE DATA doi 10.1021 ar00156a004 ref ref Cite journal doi 10.1021 ic961297y volume 36 issue 10 pages 2069 2078 last Gardner pmid 11669825 first Kimberly A. coauthors Linda L. Kuehnert, James M. Mayer title Hydrogen Atom Abstraction by Permanganate Oxidations of Arylalkanes in Organic Solvents journal Inorganic Chemistry date 1997 05 01 unused data DUPLICATE DATA doi 10.1021 ic961297y ref Overview Analogous to Hess s Law which deal with the summation of enthalpy H values, Bordwell thermodynamic cycles deal with the summation of Gibbs free energy G values. Free energies used in these systems are most often determined from Chemical equilibrium equilibriums and redox potential s, both of which correlate with free energy. This is with the caveat that redox scales are not absolute and thus it is important that all electrons are evaluated in redox pairs. This removes the offset of a given reference potential, otherwise the values are reported as potentials V against that reference. Its also worth recognizing that the values of the pK sub a sub system are just moderately transformed K sub eq sub values. When working with equilibrium energy values such as G and E sub 1 2 sub values it common to employ a naught symbol. The naught has a two component definition. The first more common component is that it refers to the physical conditions being at standard state. The second more significant component is that energy refers to an equilibrium energy even if there is a conditionally ... Reflist Category Thermodynamic cycles ... more details
Thermodynamics cTopic Thermodynamic potential Potentials The thermodynamic free energy is the amount of Work thermodynamics work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system minus the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a system multiplied by the temperature of the system. Like the internal energy, the free energy is a thermodynamic state function . Overview Free energy is that portion of any first law of thermodynamics first law energy that is available to perform thermodynamic work thermodynamics work i.e. , work mediated by thermal energy . Free energy is subject to Irreversibility irreversible loss in the course of such work. ref Stoner, Clinton D. 2000 . Inquiries into the Nature ... functions are Legendre transformation s of the internal energy . For Thermodynamic process processes ... of the partition function statistical mechanics Relation to thermodynamic variables partition ... earlier Helmholtz free energy is defined as F U &minus TS , where U is the internal energy, T is the thermodynamic ... functions depend on the often suppressed chemical compound composition , as do all proper thermodynamic potentials extensive quantity extensive functions , including the internal energy. table of thermodynamic ..., do on each other as they pass or transform from one step of or thermodynamic state state ... of the Thermodynamic Properties of Substances by Means of Surfaces , in which he introduced the preliminary ... the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded ... 0 when refers to the variation produced by any variations in the thermodynamic state state of the parts ... speaking world. See also Exergy Merle Randall References Reflist DEFAULTSORT Thermodynamic Free Energy Category Energy in physics Category Thermodynamic free energy Category State functions ... more details
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