7.41 textbook

[lilyhui3I]

For 7.41 in the book, the solution error page corrects that C should be the answer but is there a reasoning for that? For C, the lower end of the graph does not touch the axis at all, what does that mean.
Also, the different slope corresponds to the different heat capacities right? Thank you!!

[Chem_Mod]

Please see viewtopic.php?f=2&t=4515 and resubmit your question.

[lilyhui3I]

The following data were collected for a new compound used
in cosmetics: Hfus  10.0 kJ·mol 1, Hvap  20.0 kJ·mol 1; heat
capacities: 30 J·mol 1 for the solid; 60 J·mol 1 for the liquid;
30 J·mol 1 for the gas. Which heating curve below best matches
the data for this compound?

[Niharika Reddy 1D]

I believe it's C instead of B because of the slopes of the heating curve at the different phases. The heat capacity of the liquid is greater than the heat capacities of the solid and gas (double to be exact), so the slope of different states' segments of the heating curve should reflect their heat capacities. Each segment at increasing temperature corresponds to solid, liquid, and gas respectively. The zero-slope segments at a constant temperature correspond to the enthalpy of fusion and enthalpy of vaporization in that order. Since the enthalpy of vaporization is double that of fusion, the segment for enthalpy of vaporization should also be double the length of that for fusion. Going back to the individual states, or the positive-slope line segments, a less steep slope indicates a greater heat capacity, which heating curve C accurately depicts for the liquid. Heating curve B has a less steep slope for the solid and gas, which is not correct since the solid and gas have lower heat capacities than the liquid, which is incorrectly shown to have a steeper slope (indicating lower heat capacity).