How much heat is needed to transform 5 kg ice from -20 C into water with a temperature of 40 C?

univerkov | January 16, 2021 | education

Given: m (mass) = 5 kg; t0 (ice temperature) = -20 ºС; t (final temp.) = 40 ºС.

Constants: Cl (ice heat capacity) = 2100 J / (kg * ºС); tmelt (melting temperature) = 0 ºС; λ (heat of melting of ice) = 34 * 104 J / kg; Cw (heat capacity of water) = 4200 J / (kg * ºС).

1) Ice heating: Q1 = Сl * m * (tmelt – t0) = 2100 * 5 * (0 – (-20)) = 210,000 J.

2) Melting: Q2 = λ * m = 34 * 104 * 5 = 1,700,000 J.

3) Heating water: Q3 = Sv * m * (t – tmelt) = 4200 * 5 * (40 – 0) = 840000 J.

4) Q = Q1 + Q2 + Q3 = 2.75 MJ.

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