My question concerns the heat of capacity, heat of fusion, and heat of vaporization.

Question

How much heat is required to melt 22.0 kg of ice at 0 degrees Celsius and then warm the water to 20.0 C?

Answer 1

The heat required to melt the ice is determined by:

Q = mH_F where "Q" is the heat, "m" is the mass of the ice, and HF is the heat of fusion which you look up in a reference (the value for ice is 333.55 J/g).

Since this is in unit of grams, we would use m = 22000 grams

So:

Q = (22000)(33.55) = 7.34 x 10⁶ joules

The heat required to warm the water to 20°C is dertmiend by:

Q = mC_PΔT where Q is the heat, "m" is the mass of the water, C_P is the specific heat, which you look up in a reference (the value is 4.186 J/(g°C)) and ΔT is the temperature difference (T_final - T_initial) so:

Q = (22000)(4.186)(20 - 0) = 1.84 x 10⁶ joules

So the total heat required is:

7.34 x 10⁶ + 1.84 x 10⁶ = 9.18 x 10⁶ joules