Changes of state and latent heat

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Homework Statement

A 0.2 kg block of ice at -15*C is placed into a pan on a stove, heated to a liquid, and then to vapour with a final temperature of 115*C. Calculate the total amount of heat required for this process.

Homework Equations

Eh = mc(t2 - t1)
Lf (or Lv) = Eh / m

The Attempt at a Solution

Etotal = Emelting + Evapourization

Emelting = mct
= (0.2kg)(4.2x10^3)(0+15*C)
= 12 600 J

Evapourization = mct
= (0.2kg)(4.2x10^3)(115-0*C)
= 96 600 J

Etotal = 12600 + 96 600J
= 109 200 J or 1.1 x 10^5

What am i doing wrong? The answer is 6.2 x 10^5 J.

 

[Mapes]

1) You need to use the correct specific heat capacity for ice, water, and steam.
2) You need to incorporate the latent heat of the phase transformations that occur at 0°C and 100°C.

 

[Moetasim]

Your calculations for the latent heat of fusion and vaporization are correct, but you are missing the energy required to heat the ice from -15*C to its melting point of 0*C. This would be calculated as:

Eheating = mc(t2 - t1)
= (0.2kg)(4.2x10^3)(0-(-15)*C)
= 12 600 J

Therefore, the total energy required for the entire process would be:

Etotal = Emelting + Eheating + Evapourization
= 12600 + 12600 + 96600 J
= 121 800 J or 1.2 x 10^5 J

This is still slightly lower than the given answer of 6.2 x 10^5 J, so there may be additional factors at play such as the specific heat capacity of the pan and the heat lost to the surroundings during the process. It is also possible that the given answer is incorrect. I would recommend double-checking your calculations and assumptions, and if you are still unsure, consulting with your teacher or a fellow classmate.