What function depends only on the present state of a system not on the process used to arrive at that state?

Answer 1

In thermodynamics, a state function, function of state, state quantity, or state variableis a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state (independent of path). 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 a thermodynamic system, irrespective of how the system arrived in that state. In contrast, mechanical work and heat are process quantities because their values depend on the specific transition (or path) between two equilibrium states. The opposite of a state function is a path function. 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, B, T, U, and S are determined when the state of the body is given, and it may be permitted to call themfunctions of the state of the body." A thermodynamic system is described by a number of thermodynamic parameters (e.g. temperature, volume, pressure) which are not necessarily independent. The number of parameters needed to describe the system is the dimension of the state space of the system (). For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system (). 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, as described by the state postulate. 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 and the volume as functions of time from time to . 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 to time we calculate