The heat energy associated with a change in temperature that does not involve a change in phase is given by

q=msΔT

where q is heat in joules, m is mass in grams, s is specific heat in joules per gram-degree Celsius, J/(g⋅∘C), and ΔT is the temperature change in degrees Celsius. The heat energy associated with a change in phase at constant temperature is given by

q=mΔH

where q is heat in joules, m is mass in grams, and ΔH is the enthalpy in joules per gram.

Physical constants

The constants for H2O are shown here:
Specific heat of ice: sice=2.09 J/(g⋅∘C)
Specific heat of liquid water: swater=4.18 J/(g⋅∘C)
Enthalpy of fusion (H2O(s)→H2O(l)): ΔHfus=334 J/g
Enthalpy of vaporization (H2O(l)→H2O(g)): ΔHvap=2250 J/g

(a) How much heat must be transferred for this to happen, including the energy needed for phase changes? Your answer should be in terms of the variables in the introduction and the specific heats of ice (ci), water (cw), and steam (cs). The latent heats are Lf = 334 kJ/kg and Lv = 2256 kJ/kg