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...

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 dP_m∕dT_m
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 dP_m∕dT_m
is not necessarily constant), we must have