Ncert Exercises & Solutions

Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from $(p_{i}, V_{i})$ to $(p_{f}, V_{f})$ . With the help of a pV plot compare the work done in the above case with that carried out against a constant pressure $p_{f}$ .

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 + W_{expansion} + W_{non - expansion} . . . . . . . . (i)

Under constant pressure condition, the expansion work is given by

p ∆ V

∴ q = ∆ U + p ∆ V + W_{non - expansion} (∵ ∆ U + p ∆ V = ∆ H)

= ∆ H + W_{non - expansion} . . . . . . . . . . . . . . . (ii)

For a reversible change taking place at constant temperature,

∆ S = \frac{q_{rev}}{T} or q_{rev} = T ∆ S . . . . . . . . . . . (iii)

Substituting the value of q from Eq. (iii) in Eq. (ii), we get

T ∆ S = ∆ H + W_{non - expression}

or ∆ H - T ∆ S = - W_{non - expression} . . . . . . . (iv)

For a change taking place under conditions of constant temperature and pressure,

∆ G = ∆ H - T ∆ S

Substituting this value in equation (iv), we get

∆ G = - W_{non - 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 = W_{non - expansion} = W_{useful}

- ∆ G = W_{useful}

therefore,

∆ G

has the same units as those of work i.e., joule

∆ G = ∆ H - T ∆ S

∆ H =

positive and

∆ S =

positive, then

∆ G

will be negative i.e., process will be spontaneous only when

T ∆ S > ∆ H

in magnitude, which will be so when temperature is high.