# Determine the largest mass of ice that you need to put in water with a mass of 0.5 K at a temperature of 10 C

Determine the largest mass of ice that you need to put in water with a mass of 0.5 K at a temperature of 10 C so that it melts completely. Ice temperature 0 C. specific heat capacity of water – 4200 J / kg * C, specific heat of melting of ice 3.4 * 10 ^ 5 J / kg ..

Data: m1 (mass of water) = 0.5 kg; t0 (water temperature before ice immersion) = 10 ºС; t (temperature of taken ice, beginning of melting) = 0 ºС.

Constants: by condition С (specific heat capacity of water) = 4200 J / (kg * ºС); λ (specific heat of melting of ice) = 3.4 * 10 ^ 5 J / kg.

The largest ice mass is determined from the equality: С * m1 * (t0 – t) = λ * m2, whence m2 = С * m1 * (t0 – t) / λ.

Let’s calculate: m2 = 4200 * 0.5 * (10 – 0) / (3.4 * 10 ^ 5) ≈ 0.062 kg (62 g).

Answer: The largest mass of ice is 62 grams.

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