Question

Describe the process that ice on Mount Everest goes through when being heated from 10 degrees Fahrenheit to 305 kelvin

Answer 1

I think the ice is warmed from 10 degrees Fahrenheit to 32 degrees Fahrenheit. The ice then melts (I believe 333kj/kg K) and then it warms up to 305 K. For that this occurs the heat capacity of the water is 4.19 kj/kg K.
A.K.A Sublimation

Answer 2

First you want to convert the units to something common.
10 F = -12.2 Celsius
305 K = 31.9 Celsius

I chose celsius because the next step is to use the phase diagram for water, because you have to account for the reduced atmospheric pressure on Mount Everest. Google says that at the summit of M. Everest, the atmospheric pressure is 33.7 kPa, which is 0.3325 atm.

Note that I'm using these units of Celsius (for temp) and atm (for pressure) because the phase diagram i found uses these. The phase diagram (attached) is from here http://chemwiki.ucdavis.edu/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chem1_(Lower)/07%3A_Solids_and_Liquids/7.05%3A_Changes_of_State

Now if you look at the diagram, you notice that below 0.6 atm, heating ice will result in sublimation (i.e. skipping melting into water). The pressure on M. Everest is 0.33 atm, well below this threshold, and thus heating ice on M. everest will result in ice sublimating into gas at around 0\(^o\) celsius.