# State functions in Thermodynamics

Chemical Thermodynamics: state functions

The substance is usually encountered in one of the three main states: gaseous, liquid, or solid. Hence, under various conditions, the substance can exist in different states. In a fixed condition, the substance will always be in one and the same state. For instance, at atmospheric pressure and a temperature of 400 °C, water will exist only in the vapour state but never as a liquid or a solid. In order to determine the concrete physical conditions under which a substance is considered and, thereby, determine unambiguously the state of this substance, convenient characteristics of the state of substance are introduced, the so-called parameters, or properties, of state.

The state of a system is identified by certain observable quantities such as volume, temperature, pressure and density etc. All the quantities that identify the state of a system are called Properties.

A property which depends only on the current state of the system (as defined by T, P, V etc.) is called a state function. This does not depend on the path used to reach a state.A state function depends only on the initial and final conditions while a path function depends on the path taken to reach final condition from the initial condition.For example, a person standing on the roof of a building has a fixed value of potential energy and the potential of person does not depend on whether he has reached to the point by stairs or lift.

Properties are point function or path function:

• Point function- Does not depend on the path taken
• Examples: ∆H (Enthalpy), ∆G (Gibbs free energy),∆A(Helmholtz free energy), ∆S (Entropy) ∆V (Volume), ∆T (Temperature), ∆U (Internal energy)
• Path function- depend on path history
• Examples: W (work), q (heat)

Any property, for example, U is a state function, G is a state function, H is a state function, so, therefore, ∆U, ∆G, ∆H, ∆A, ∆S etc, are exact differentials. And delta (∆)can only be written for a change in state. For example, ∆G integration from an initial state to the final state is equal to G final minus G initial. Alternatively, the work done in changing the state of the system from the same initial state to the same final state may be different under different isothermal or adiabatic conditions.And, for path functions, their derivatives are in exact differentials.In thermodynamic, Internal energy is a state function. Hence, the work needed to move a system from a state of lower internal energy (=UL) to a state of higher internal energy (UH) is (UH) (UL). W = (UH) (UL).

The internal energy of an isolated system (which exchanges neither heat nor mass) is constant. When the state of a system changes then the process is said to occur. The first and last state of the process is the initial and final state respectively. The process gives us the path by which system changes from one state to another. there are some processes are particular State variables are kept constant. Likewise, a process for which the final and initial states are the same is called a cyclic process. For a cyclic process change in a state, function is zero. E.g. U(cyclic process) = 0.