Ice has a specific heat of 2090 J / (kg C) and water has a specific heat of 4186 J / (kg C). Water has a latent heat of fusion of 3.3x10^5 J/K and a latent heat of vaporization of 2.26x10^6 J/K. A 10 kg block of ice begins at - 60 degrees C and is slowly heated until the entire mass is boiled to steam. How much energy is required to bring the ice to steam with a temperature of 100 degrees C?

3.1 * 10⁷ J

Explanation:

The total heat required is the sum of the heats required in each stage.

1) Solid: from - 60°C to 0°C.

Q₁ = c (s) * m * ΔT = (2090 J/kg.°C) * 10 kg * (0°C - (-60°C)) = 1.3 * 10⁶ J

where,

c (s) : specific heat of the solid

m: mass

ΔT: change in the temperature

2) Solid to liquid at 0°C

Q₂ = Qf * m = (3.3 * 10⁵ J/kg) * 10 kg = 3.3 * 10⁶ J

where,

Qf: latent heat of fusion

3) Liquid: from 0°C to 100°C

Q₃ = c (l) * m * ΔT = (4186J/kg.°C) * 10 kg * (100°C - 0°C) = 4.2 * 10⁶ J

where,

c (l) : specific heat of the liquid

4) Liquid to gas at 100 °C

Q₄ = Qv * m = (2.26 * 10⁶ J/kg) * 10 kg = 2.26 * 10⁷ J

where,

Qv: latent heat of vaporization

Total heat

Q₁ + Q₂ + Q₃ + Q₄

1.3 * 10⁶ J + 3.3 * 10⁶ J + 4.2 * 10⁶ J + 2.26 * 10⁷ J = 3.1 * 10⁷ J