Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from (pi,Vi) to (pf,Vf). With the help of a pV plot compare the work done in the above case with that carried out against a constant pressure pf.


Gibbs free energy is that thermodynamic quantity of a system, the decrease in whose value during a process is equal to the maximum possible useful work that can be obtained from the system.
Mathematically, this results may be derived as follows
The relationship between heat absorbed by a system q, the change in its internal energy, U and the work done by the system is given by the equation of the first law of thermodynamics, therefore,
q=U+Wexpansion+Wnon-expansion........(i)
Under constant pressure condition, the expansion work is given by pV,
q=U+pV+Wnon-expansion(U+pV=H)
=H+Wnon-expansion...............(ii)
For a reversible change taking place at constant temperature,
S=qrevTorqrev=TS...........(iii)
Substituting the value of q from Eq. (iii) in Eq. (ii), we get
TS=H+Wnon-expression
orH-TS=-Wnon-expression.......(iv)
For a change taking place under conditions of constant temperature and pressure,
G=H-TS
Substituting this value in equation (iv), we get
G=-Wnon-expansion............(v)
Thus, free energy change can be taken as a measure of work other than the work of expansion. For most changes, the work expansion can not be converted to other useful work, whereas the non-expansion work is convertible to useful work.
Rearranging equation (v), it may write as
-G=Wnon-expansion=Wuseful
As -G=Wuseful therefore, G has the same units as those of work i.e., joule
G=H-TS
If H=positive and S=positive, then
G will be negative i.e., process will be spontaneous only when TS>H in magnitude, which will be so when temperature is high.