Substitution of a reversible process by the reversible isothermal and reversible adiabatic processes:

Figure 21.1

Let a system be taken from an equilibrium state to another equilibrium state by following the reversible path . Refer to figure 21.1 Let a reversible adiabatic and another reversible be drawn in such a manner that and can be joined by a reversible isotherm.

Also, these reversible adiabatic and reversible isothermal lines are such that the area under is equal to the area under .

Applying the first law for ,

(21.1)

Applying the first law for ,

(21.2)

We know (area under the curves are same)

From Eqn. (21.1) and (21.2)

(21.3)

Since and are zero

(21.4)

Thus, any reversible path may be substituted by a reversible adiabatic, a reversible isotherm and a reversible adiabatic between the same end states such that the heat transferred during the isothermal process is the same as that transferred during the original process.