Answer:
The total heat required to melt the ice is approximately 3.473 MJ
Step-by-step explanation:
The given parameters for the layer of ice are;
The thickness of the layer of ice, t = 0.80 cm = 0.008 m
The area of the wind shield, A = 1.4 m²
The initial temperature of the ice, T₁ = -2.0 °C = 271.15 K
The density of the ice, ρ = 917 kg/m
The temperature at which ice melts, T₂ = 0 °C = 273.15 K
We have;
The mass of the ice, m = ρ × t × A
∴ m = 917 kg/m³ × 0.008 m × 1.4 m² = 10.2704 kg
The specific heat capacity of ice, c = 2,090 J/(kg·K)
∴ The equation for the heat capacity of the ice to melt, is given as follows;
ΔQ = m·c·ΔT
Where;
ΔT = T₂ - T₁
∴ ΔT = T₂ - T₁ = 273.15 K - 271.15 K = 2 K
ΔQ = 10.2704 kg × 2,090 J/(kg·K) × 2 K = 42.930272 kJ
The latent heat to melt the ice, Q = The latent heat of fusion of ice, L × Mass of ice, m
The latent heat of fusion of ice, L = 334 kJ/kg
∴ Q = 334 kJ/kg × 10.2704 kg = 3,430.3136 kJ
The total heat required to melt the ice, H = ΔQ + Q
∴ H = 42.930272 kJ + 3,430.3136 kJ = 3,473.243872 kJ ≈ 3.473 MJ.