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 mg. Note that this integral represents the

melon sliceshaped 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