Question
what is free energy? Prove that ∆G = ∆H – T∆S.
Solution
Free energy is a thermodynamic quantity and refers to the capacity of the system to do useful work. It may be defined as the amount of energy available from a system that can be put into useful work. Mathematically, free energy (G) is defined by the relation:
G = H - TS ...(1)
where H is the heat content. T is absolute temperature and S is the entropy of the system.
H = U + PV
The change in free energy (∆G) during the process may be expressed as:
If the process is carried out at constant pressure and constant temperature, then
Substituting the values in (3), we have,
But at constant temperature and constant pressure.
Hence,
This equation (4) is known as Gibb's Helmholtz equation.
G = H - TS ...(1)
where H is the heat content. T is absolute temperature and S is the entropy of the system.
H = U + PV
The change in free energy (∆G) during the process may be expressed as:
If the process is carried out at constant pressure and constant temperature, then
Substituting the values in (3), we have,
But at constant temperature and constant pressure.
Hence,
This equation (4) is known as Gibb's Helmholtz equation.
