사용자:StarLight/작업실3

상태함수(영어: state function)란 열역학에서 계의 어떤 물리량의 변화가 경로에 관계 없이 항상 초기 상태와 나중 상태로만 결정되는 물리량을 말한다. 예로써, 내부에너지, 엔탈피, 엔트로피와 같은 물리량들이 있다. 상태함수는 또한 계의 평형상태를 기술하는 양이다. 때문에 일과 열같은 물리량은 상태의 전이 과정을 기술하는 물리량이기 때문에 상태함수가 아니다.

History

It is likely that the term “functions of state” was used in a loose sense during the 1850s and 60s by those such as Rudolf Clausius, William Rankine, Peter Tait, William Thomson, and it is clear that by the 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.”

Overview

열역학적 계는 몇개의 온도, [부피]], 압력등의 몇몇 열역학적 매개변수들에 의해 기술되게 된다. 여기서

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.

계가 갑자기 변하지 않고, 연속적으로 변하는 경우,

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

W(t_{0},t_{1})=\int _{\textrm {state0}}^{\textrm {state1}}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 $VdP$ over the path. We would have:

\Phi (t_{0},t_{1})=\int _{t_{0}}^{t_{1}}P{\frac {dV}{dt}}\,dt+\int _{t_{0}}^{t_{1}}V{\frac {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 $PV$ is therefore a state function of the system.

By way of notation, we will specify the use of d to denote an exact differential. In other words, the integral of $d\Phi$ will be equal to $\Phi (t_{1})-\Phi (t_{0})$ . The symbol δ will be reserved for an inexact differential, which cannot be integrated without full knowledge of the path. For example $\delta W=PdV$ 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 $PV$ 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.

예

다음은 상태함수라 알려져 있는 물리량을 나열한 것이다.