Refer to the diagrams shown below.
Goal:
We want to determine the amount of heat required to convert 59 g of ice at -35 °C to liquid water at 55 °C.
Given:
c = 2.09 J/(g-°C), the specific heat of ice
= 4.18 J/(g-°C), the specific heat of water
= 2.03 J/(g-°C), the specific heat of steam
L = 334 J/g, the latent heat of fusion of water
= 2260 J/g, the latent heat of vaporization of water
Stage 1: Convert ice at -35 °C to ice at 0 °C.
The heat required is
Q₁ = (59 g)*(2.09 J/(g-°C))*(0-(-35) °C) = 4,315.85 J
Stage 2: Convert ice at 0 °C to water at 0 °C.
The heat required is
Q₂ = (59 g)*(334 J/g) = 19,706 J
Stage 3: Raise the temperature of the water from 0 °C to 55 °C.
The heat required is
Q₃ = (59 g)*(4.18 J/(g-°C))*(55 °C) = 13,564.10 J
The total heat required is
Q = Q₁ + Q₂ + Q₃ = 37,585.95 J = 37.586 kJ
Answer: 37.6 kJ
