Equation with variables into a line graph

In a "divide and conquer" strategy, which parts do you need help with? Here are the steps I would expect to see:

1) Enter equation coefficients.
2) Enter a column of temperatures covering the desired range. Note that to accurately show the phase changes, you will need two entries for those temperatures.
3) Enter a formula adjacent to the temperatures that computes enthalpy. I note that you are giving the equation for heat capacity Cp=(dH/dT)constantP, so you will need to take the antiderivative of your Cp function and compute a suitable "initial condition" so that H=0 at your desired reference condition.
4) Copy that formula (or formulas) down the enthalpy column.
5) Select T and H columns -> Insert Chart -> Scatter chart -> desired subtype (lines without markers??). Pay attention here so that you don't get a line chart. Make sure you get a scatter chart.
5a) If Excel gets the data series wrong (as it often does for me), then go into the Select Data dialog and fix Excel's mistakes.
6) Format chart as desired.

With the process broken down like that, where do you get stuck?

I am not sure how to input the equation into the graph without having data points.

You are thinking of some other kind of charting program. When you want to create a chart in a spreadsheet, you compute the individual data points, and then chart those data points. If you don't want to compute individual data points, then you need to look for a different charting application.

Most of the other questions will depend on exactly how automated you need this to be. When I do this kind of phase diagram, I tend not to automate everything into great big formulas. If I were doing something like water, my spreadsheet would look something like

Coefficient table -- A -- B -- C -- D -- E
solid -- Asolid -- B solid -- Csolid -- Dsolid -- Esolid
liquid -- Aliquid --etc.
vapor -- Avapor -- etc.

Main table
T, K -- H, J/g
250 -- formula for Hsolid
270 -- copy of formula for Hsolid
273.15 -- copy of formula for Hsolid
273.15 -- formula for Hliquid
290 -- copy of formula for Hliquid
310 -- copy of formula for Hliquid
etc. to boiling point
373.15 -- copy of formula for Hliquid
373.15 -- formula for Hvapor
and so on to T=473.15

I would use my heats of fusion and vaporization to get the correct E parameter for the respective H functions (remember that you need to get an antiderivative for the Cp function to get H. Excel does not do antiderivatives, so you will need to do this outside of Excel).

If you are stuck at the very beginning, I would suggest that you get your antiderivative function for H solid and fill in the parts of the table for Hsolid up to the melting point. You will then have H(ice) at 273.15. From your heat of fusion, you can compute H(water) at 273.15 and use that value to get E liquid. Continue down the table.