When you go out to your car one cold winter morning you discover a 0.70-cm thick layer of ice on the windshield, which has an area of 1.0 m2. If the temperature of the ice is - 4.0 ∘C, and its density is 917 kg/m3, find the heat required to melt all the ice.

Q total = 2204.49 kJ

Explanation:

The mass of ice over the windshield is

mass = density * volume

and

volume = area * width = 1 m² * 0.007 m = 0.007 m³

thus

mass = 917 kg/m³ * 0.007 m³ = 6.419 kg

the heat that must reach the ice in order to melt it is

1) sensible heat until melting temperature (T m = 0°C, assuming that pressure = 1 atm since the windshield is exposed to the atmosphere)

2) Latent heat to melt the ice at its melting temperature

1) Q sen = m ice * c ice * (T final - T initial) = 6.419 kg * 2.108 kJ / Kg °C (0°C - (-4°C)) = 54.125 kJ

2) Q lat = m ice * L ice = 6.419 kg * 335 kJ/kg) = 2150.265 kJ

therefore Q total = Q sen + Q lat = 54.125 kJ + 2150.265 kJ = 2204.49 kJ

this is the minimum amount of heat required, since we did not take into account the heat losses to the surroundings

Note:

- the specific heat of water and ice and also the latent heat were taken from tables.