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

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west