Consider the process executed by a single-component system as its state m moves along the edge of…

Consider the process executed by a single-component system
as its state m moves along the edge of the dome from state f to state g. As
indicated in Fig. P6.10, the initial and final temperature in this process is
T0. Prove that if dPm_dTm is practically constant,

in which the line integral appearing on the left side
follows the edge of the dome, f –m–g. Note that this integral represents the
melon slice–shaped area trapped between the dome and the T = T0
base. Show also that, in general (i.e., when dPm_dTm
is not necessarily constant), we must have