NationMaster - Encyclopedia: State function

In thermodynamics, a state function, or state quantity, is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. A state function describes the equilibrium state of a system. For example, internal energy, enthalpy and entropy are state quantities because they describe quantitatively an equilibrium state of thermodynamic systems. At the same time, mechanical work and heat are process quantities because they describe quantitatively the transition between equilibrium states of thermodynamic systems. Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... A physical quantity is either a quantity within physics that can be measured (e. ... This article needs to be cleaned up to conform to a higher standard of quality. ... (LTE is an acronym for the progressive-instrumental rock band Liquid Tension Experiment) In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann distribution. ... System (from the Latin (systÄ“ma), and this from the Greek (sustÄ“ma)) is an assemblage of entity/objects, real or abstract, comprising a whole with each and every component/element interacting or related to at least one other component/element. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as Î” or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant conditions. ... see also: Entropy (disambiguation) Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... In thermodynamics, a thermodynamic system is defined as that part of the universe that is under consideration. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... A process function (or a process quantity) is a physical quantity that describes the transition of a system from an equilibrium state to another equilibrium state. ...

1 History
2 Overview
3 Examples
4 See also

History

Although it is likely that the term “functions of state” was used in a loose sense during the 1850s and 60s by those as Rudolf Clausius, William Rankine, Peter Tait, William Thomson, it is clear that by 1870s the term had acquired a use of its own. In 1873, for example, Willard Gibbs, in his paper “Graphical Methods in the Thermodynamics of Fluids”, states: “The quantities V, P, T, U, and S are determined when the state of the body is given, and it may be permitted to call them functions of the state of the body.” Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 â€“ August 24, 1888), was a German physicist and mathematician. ... William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. ... Peter Tait Peter Guthrie Tait (April 28, 1831 - July 4, 1901) was a Scottish physicist. ... There have been a number of people named William Thomson: William Thomson, 1st Baron Kelvin, usually known as Lord Kelvin, was a 19th century British physicist. ... Josiah Willard Gibbs (February 11, 1839 â€“ April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ...

Overview

A thermodynamic system is described by a number of thermodynamic parameters (e.g. temperature, volume, pressure). The number of parameters needed to describe the system is the dimension of the state space of the system ( $D$ ). For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system ( $D = 2$ ). In this example, any system is uniquely specified by two parameters, such as pressure and volume, or perhaps pressure and temperature. These choices are equivalent. They are simply different coordinate systems in the two-dimensional thermodynamic state space. An analogous statement holds for higher dimensional spaces. Fig. ... Volume is how much space a thing has. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... In computer science, a state space is a description of a configuration of states used as a simple model of machines. ... In physics and chemistry, monatomic is a combination of the words mono and atomic, and means single atom. ...

When a system changes state continuously, it traces out a "path" in the state space. The path can be specified by noting the values of the state parameters as the system traces out the path, perhaps as a function of time, or some other external variable. For example, we might have the pressure $P (t)$ and the volume $V (t)$ as functions of time from time $t 0$ to $t 1$ . This will specify a path in our two dimensional state space example. We can now form all sorts of functions of time which we may integrate over the path. For example if we wish to calculate the work done by the system from time $t 0$ to time $t 1$ we calculate Work (abbreviated W) is the energy transferred in applying force over a distance. ...

$W(t_0,t_1)=int_{textrm{state 0}}^{textrm{state 1}}P,dV=int_{t_0}^{t_1}P(t)frac{dV(t)}{dt},dt$

It is clear that in order to calculate the work W in the above integral, we will have to know the functions $P (t)$ and $V (t)$ at each time $t$ , over the entire path. A state function is a function of the parameters of the system which only depends upon the parameters' values at the endpoints of the path. For example, suppose we wish to calculate the work plus the integral of $V d P$ over the path. We would have:

$Phi(t_0,t_1)= int_{t_0}^{t_1}Pfrac{dV}{dt},dt +int_{t_0}^{t_1}Vfrac{dP}{dt},dt = int_{t_0}^{t_1} frac{d(PV)}{dt},dt=P(t_1)V(t_1)-P(t_0)V(t_0)$

It can be seen that the integrand can be expressed as the exact differential of the function $P (t) V (t)$ and that therefore, the integral can be expressed as the difference in the value of $P (t) V (t)$ at the end points of the integration. The product $P V$ is therefore a state function of the system. An function defined as an exact differential is independent of the path of integration. ...

By way of notation, we will specify the use of d to denote an exact differential. In other words, the integral of $d Φ$ will be equal to $Φ(t 1) - Φ(t 0)$ . The symbol δ will be reserved for an inexact differential, which cannot be integrated without full knowledge of the path. For example $δ W = P d V$ will be used to denote an infinitesimal increment of work.

It is best to think of state functions as quantities or properties of a thermodynamic system, while non-state functions represent a process during which the state functions change. For example, the state function $P V$ is proportional to the internal energy of an ideal gas, but the work $W$ is the amount of energy transferred as the system performs work. Internal energy is identifiable, it is a particular form of energy. Work is the amount of energy that has changed its form or location.

Examples

The following are a few examples of state functions:

Fig. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as Î” or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant conditions. ... see also: Entropy (disambiguation) Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... It has been suggested that this article or section be merged into Helmholtz energy. ... In thermodynamics, the Gibbs energy or Gibbs energy function is the energy portion of a thermodynamic system available to do work. ... Fugacity is a measure of the tendency of a substance to prefer one phase (liquid, solid, gas) over another. ... The refractive index (or index of refraction) of a material is the factor by which the phase velocity of electromagnetic radiation is slowed in that material, relative to its velocity in a vacuum. ... The pitch drop experiment at the University of Queensland. ... In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat. ... Density, or volumic mass (ISO 31), is a measure of mass per given unit volume. ...

Encyclopedia > State function

Contents

History

Overview

Examples

See also