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How much heat is required to melt an ice cube of mass 2.0 g that is at a temperature of -4.0°C? (Specific heat capacity of ice = 2.0x103 Jkg-1K-1, latent heat of fusion of ice = 33.4x104 Jkg-1)

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The total heat required is the sum of the heat needed to raise the ice to its freezing point, 0ºC, and the heat needed to melt it. It's calculated as follows:

Heat needed to warm ice to 0ºC:

q1 = mc `Delta` T (c = specific heat capacity)

q1 = (2.0g)(2.0x10^3J/kg-ºC)(1 kg/1000 g)(4ºC) = 16 J

Heat needed to melt ice:

q2 = (m)(heat of fusion)

q2 = (2.0g)(3.34x10^4 J/kg)(1 kg/1000g) = 668 J

q(total) = q1 + q2 = 16 J + 668 J = 684 J

Since the two constants are stated per kilogram and the mass of ice is in grams, the additional term (1 kg/1000 g) was used to convert to consistent units.

The specific heat capacity of ice was stated in terms of Kelvin temperature, but is consistent with a  `Delta` T in ºC. The size of the Celsius degree and Kelvin are the same so the  `Delta` T is the same in both units.

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