Hi, I have 2 questions and an exam tomorrow, and I have no idea how my teacher answered these 2 problems, if someone can guide me through how to solve these problems i would really appreciate it. I am not looking for an answer just a step by step how to solve it and im not really sure how to start.

For this one, i think my teacher would convert the ice to a liquid and then to a solid, and then taking taking some equation at each part, lol im not really sure

For the roof, I think you need to know the thermal resistance or thermal conductivity of the material of the roof. With that you can calculate the heat flow per square meter [Joules per sec per square meter] then scale it up for the room size and the time period.

For the ice to steam.

Heat the ice - what is the specific heat for ice? [it is 1 for water]
melt the ice - what is the latent heat for melting ice?
Heat the water
evaportate the water - what is the latent heat of evaportation?
heat the steam - what is the specific heat for steam?

NOTE: Suppose the latent heat for melting ice was 50 times the specific heat for water -it's NOT - the getting from ice at -10 to water at +10 would be the same as heating water from +5 to +75, ie 70 degrees.

You could convert each section to a "heating water" equivalent and do the final calculation in one go.

***Saying latent heat is 50 times specific heat I mean suppose you need X Joules to heat a mass of water by 1 degree but need 50X Joules to melt the same mass of ice.

If you don't immediately understand the conversions, ignore them and work it out the "standard" way.

There is a conductance [or its inverse resistance] which tells you the number of joules per second per square metre per degree difference each side. You need to cram that stuff now.

[You may have seen ceiling insulation bats. They can be R2, R3, R4 etc bats - that is referring to their thermal resistance.