This problem contains multiple parts, and I will write my initial attempts at solving the problem under it's corresponding section
If we're given that the vapor pressures (described in Atm) of both the liquid and solid phases are as follows:
ln(p_sat) = A - B/T + Dln(T)
We are also given a table of coefficients for the two cases of the Solid-Gas and the Liquid-Gas transition:
[Situation, A, B(K), D;
Solid-Gas, 19.25, 15773, -0.755;
Liquid-Gas, 21.79, 15246, -1.255]
(There are no units given, just those numbers)
And we are expected to determine:
a.) The normal boiling point
- My initial thought was to work with the given equation and solve it for T, assuming p_sat to be 1atm (the normal boiling point) but ran into obvious algebraic difficulty in isolating T, and without introducing the Lambert W function (which I feel is beyond the scope of an introductory thermodynamics course) I'm not entirely sure what the best method to proceed is.
b.) The triple point temperature
- In this case, my initial thought is to find the temperature at which the equation as written for both of the situations. That is, if there is no particular affinity for either the Solid-Gas or the Liquid-Gas transition it makes sense to me that the corresponding temperature would be the triple point.
c.) The difference between the heat capacities of the liquid and the solid
d.) The heat of fusion at the triple point
f.) The slope of the liquid-solid boundary line at the triple point given densities of liquid and solid phases to be 5.66 and 7.14g/cm^3 respectively and if the atomic weight of the metal is 65.4.
Any assistance would be very much appreciated. Even just pointers towards other equations I might be able to bring in.