Question

What is Helmholtz free energy and Gibbs free energy?

Answer 1

Hint: Thermodynamic potentials: It is a scalar quantity which represents the thermodynamic state of a system. These are the functions of thermodynamic variables pressure, volume, temperature, and entropy.

Complete answer:
Helmholtz free energy: It is a thermodynamic potential in which the work is measured when the system is closed and volume and temperature of the system is constant.
It can be represented from the following equation:
\[F = U - TS\]
where,
 $F \to $ Helmholtz free energy
$U \to $ Internal energy
$T \to $ Temperature
$S \to $ Entropy
Derivative form of Helmholtz free energy in terms of thermodynamic potential can be represented as follows:
$dF = - PdV - SdT$
Hence it can be written as function of volume and temperature as $F = F(V,T)$
Application of Helmholtz free energy:
Specific heat at constant pressure can be determined as follows:
${C_V} = - T{\left( {\dfrac{{{\partial ^2}F}}{{\partial T}}} \right)_V}$
Gibbs free energy: It is a thermodynamic potential in which the maximum reversible work is measured when pressure and temperature of the system is constant.
It can be represented from the following equation:
\[G = H - TS\]
where,
 $G \to $ Gibbs free energy
$H \to $ Enthalpy
$T \to $ Temperature
$S \to $ Entropy
Derivative form of Gibbs free energy in terms of thermodynamic potential can be represented as follows:
$dG = VdP - SdT$
Hence it can be written as function of pressure and temperature as $G = G(P,T)$
Application of Gibbs free energy:
Can be used to determine spontaneity of the reaction.
Specific heat at constant pressure can be determined as follows:
${C_P} = - T{\left( {\dfrac{{{\partial ^2}G}}{{\partial T}}} \right)_P}$

Note:
Helmholtz energy is sometimes represented with the symbol ‘A’, so need not to get confused. For finding relations between thermodynamic potentials and energies, a thermodynamic square method should be used.