Thermodynamic Potentials, Physics tutorial

Thermodynamic Potentials:

The four (4) thermodynamic potentials are:

  • internal energy U
  • enthalpy H
  • Helmholtz free energy A
  • Gibbs free energy G.

Depending on the thermodynamic constraints on the system, it is always suitable to use the particular thermodynamic potential to explain the system. For instance Helmholtz free energy A can be utilized to explain the system in which temperature and volume are held constant. Equilibrium condition for system is dA=0. Gibbs free energy G can be utilized to explain equilibrium between phases (as two phases share same pressure and temperature).

Internal Energy U:

Internal energy U of the system is the state function i.e. it depends on state of the system. First law of thermodynamics provides the insight in internal energy of the system. Change in internal energy U of system DU, according to first law of thermodynamics is

ΔU = Q - W

And the differential form is

dU = dQ - dW

Work done on a system may include the irreversible component dWI (like stirring with a paddle, or forcing the electric current through a resistor) and some reversible components dWR. Irreversible component of work is dissipated as heat and is identical to adding heat to system. So we can write dS = (dQ + dWI)/T and this provides dQ = TdS - dWI. Reversible component of work may consist of work done in compressing system (PdV), but there may also be other types of work. Generally expression for each of these forms of reversible work is of the form XdY, where X is the intensive state variable and Y is extensive state variable. All of these forms of non dissipative work can together be known as configuration work. Thus, total work done on system is of form

dW = dWI - PdV + ΣXdY

so, the first law of thermodynamics takes the form

dU = dQ + dWI - PdV + ΣXdY

This is a kind of complete form of first law taking into consideration all possible forms of work. Using equation if the particular system is held at constant volume, then no PdV work of expansion or compression is done. And if no other sort of work is done (either non- PdV reversible work or irreversible work dWI), then increase in internal energy of this system is just equal to heat added to system.

Thus, internal energy U can be utilized to describe the system in which heat is transferred (either in or out) and / or work is done on or by system.

Enthalpy H:

Enthalpy is a heat energy exchange which occurs during chemical reactions. It has symbol H and is estimated in kJ/mol, or kilojoules per mole. Energy exchanged with surrounding environment at constant pressure is known as enthalpy change of a reaction. To estimate change, standard conditions are utilized, including the pressure of 1 atmosphere and temperature of 298 Kelvin (77°F or 25°C).

When reaction is giving off heat, it is termed as exothermic. In this case, enthalpy change is negative, as reaction is going from high energy to low energy because of the loss of heat energy to its surroundings. If energy flows from surrounding environment into the system, or heat is being taken in, it is termed as endothermic. In this case, change is positive as system is gaining energy in form of heat.

Enthalpy Formula is given by

Enthalpy change = heat of the reaction

ΔH = H2 - H1

Helmholtz Free Energy A:

The Helmholtz free energy A is stated as:

A = U - TS

Its differential form is:

dA = dU - TdS - SdT

But dU = dQ + dWI - PdV + ΣXdY so equation becomes:

dA = -SdT - PdV + ΣXdY so equation becomes:

dA = -SdT - PdV + ΣXdY

This Equation defines that in the isothermal process (i.e. when dT = 0), increase in Helmholtz function of a system is equal to all reversible work (-PdV + ΣXdY) done on system. On the other hand, if the machine does any reversible work at constant temperature, Helmholtz function decreases, and decrease in Helmholtz function is equal (if temperature is constant) to reversible work (of all types) done by system.

Gibbs free energy G:

Gibbs function is express as

PG =U - TS + V

It can also be stated as

G = H - TS and as:

G = A + PV

Its differential from equation is:

dG = dH - TdS - SdT,

By solving equation we get:

dG = -SdT + VdP + ΣXdY

This equation can be utilized to explain the system which goes through constant temperature and constant pressure processes. Example of the process of this type is phase change of pure substance which generally occurs at constant temperature and pressure. Therefore, Gibbs free function is very helpful in describing the process which involves change of phase.

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