The bath contains water weighing 100 kg at a temperature of 80 degrees. Ice was put in the bath at a temperature

| February 8, 2021 | education

The bath contains water weighing 100 kg at a temperature of 80 degrees. Ice was put in the bath at a temperature of 0 degrees. As a result, during some time the water temperature dropped to 47 degrees. Find a mass of ice.

To calculate the mass of ice placed in a bath with water, it is necessary to use the equality (thermal equilibrium): Cw * mw * (tw – tp) = (λl + Sv * tp) * ml, from where you can express: ml = Cw * mw * ( tv – tp) / (λl + Sv * tp).

Data: Cv – beats. heat capacity of water (Sv = 4.2 * 10 ^ 3 J / (kg * ºС)); mw is the mass of water (mw = 100 k); tv – initial water temperature (tv = 80 ºС); tр – temperature of thermal equilibrium (tр = 47 ºС); λl – beats heat of melting of ice (λl = 340 * 10 ^ 3 J / kg).

Calculation: ml = Cw * mw * (tw – tp) / (λl + Sv * tp) = 4.2 * 10 ^ 3 * 100 * (80 – 47) / (340 * 10 ^ 3 + 4.2 * 10 ^ 3 * 47) = 25.79 kg.

Answer: You need to put 25.79 kg of ice in a water bath.



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