A sample of frozen water requires 3.6kcal to be heated from −35◦C to 0◦C. What must the mass be?

Question

How much energy will it take to completely melt the sample above? Don’t account for the 3.6kcal above that brought the sample up to the melting point. Express your answer in calories (or kcal).

Answer 1

Q = mCΔT where Q is the heat (energy) required to heat mass "m" of a substance having specific heat of "C" by a certain number of degrees (ΔT). For ice, C = 0.50 kcal/(kg °C) so:

3.6 kcal = m(0.50 kcal/(kg °C))(35 °C)

m = 3.6/0.50/35 = 0.21 kg

The energy require to accomplish the phase transition from solid to liquid is the heat of fusion and for ice to water, it is 80 kcal/kg so, since the mass is 0.21 the energy will be 80(0.21) = 16 kcal