# Thermodynamic Potential

Introduction to Thermodynamic Potential:The thermodynamic state of a homogeneous system may be represented by certain specific thermodynamic variables such as pressure P and volume V and temperature T and the entropy S.

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Out of these four variables any two are independent and when they are known the others may be determined. Thus there are only two independent variables and the remaining may be considered as their functions.Relation between the variables of thermodynamicsThere exists certain relation between these thermodynamic variables.

The first and second law of thermodynamics provides the following two relations:dQ = dU + P dVand dQ = T dSCombining these two relations we getT dS = dU + P dVor dU = T dS – P dVAbove equation express the change in internal energy of the system in terms of four thermodynamic variables P and V and T and S.

However for a complete knowledge of the system certain other relations are required and for this purpose the functions of the variables P and V and T and S are used and these functions are called the thermodynamic potential or the thermodynamic functions.Relation between the variables of thermodynamics

Relation between the variables of thermodynamicsPrinciples in Thermodynamic PotentialsThere are four principal thermodynamic potentials which are as follows:Internal energy or intrinsic energy: When a system apparently shows no mechanical energy but is still capable of doing work then it is said to possess internal energy or intrinsic energy and it is denoted as U.

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Helmholtz function: The combined first and the second law of thermodynamics yieldsdU = T dS – dWIf we consider the process in which the system undergoes is at constant temperature thenT dS = d (TS)Thus we may writed (U – TS) = - dWor dF = - dWwhere the function F = U – TSis called the Helmholtz function.Gibbs function: Gibbs function of a system is given byG = U – TS + PVEnthalpy: Enthalpy is a property of the system and is of particular significance and it is given byH = U + PV