A bath with a volume of 100 liters must be filled with water at a temperature of 30C, using water

| May 5, 2021 | education

A bath with a volume of 100 liters must be filled with water at a temperature of 30C, using water at a temperature of 80C and ice at a temperature of -20C. Find the mass of ice to put in the bath. The capacity of the bath and the heat loss are negligible.

To find the mass of ice placed in the specified bath, we use the equality: Cw * (m – ml) * (tв – t) = (Сl * (-tl) + λ + Sv * t) * ml.

Data: Cv – beats. heat capacity of water (Sv = 4.2 * 10 ^ 3 J / (kg * ºС)); m is the mass of water in the specified bath (m = 100 kg (V = 100 l)); tv is the temperature of the water used (tv = 80 ºС); t – required temperature (t = 30 ºС); Sl – beats. heat capacity of ice (Сl = 2.1 * 103 J / (kg * ºС)); tl – initial ice temperature (t2 = -20 ºС); λ – beats heat of melting of ice (λ = 340 * 10 ^ 3 J / kg).

Calculation: 4.2 * 10 ^ 3 * (100 – ml) * (80 – 30) = (2.1 * 10 ^ 3 * (-20) + 340 * 10 ^ 3 + 4.2 * 10 ^ 3 * 30) * ml.

21000 * 10 ^ 3 – 210 * 10 ^ 3 ml = 508 * 10 ^ 3 ml.

718ml = 21000.

ml = 21000/718 = 29.25 kg.

Answer: The specified bath requires 29.25 kg of ice.



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