Question

You have a styrofoam container with 751 g of tomato juice (specific heat of 3,980 J/(kg · °C)) at 39.0° and you add a 62 g chunk of ice at 0°C. Assume the liquid and water mix uniformly as the ice melts and determine the final temperature of the mixture (in °C).

Answer 1

The temperature of the mixture in degrees centigrade is 36.5°C.

The heat lost by the melting ice is equal to the heat gained by the tomato juice and water.

Where;

Heat lost by ice = mL = 0.062 Kg × 33600 J/Kg = 2083.2 J

Heat gained by tomato juice = 0.751 Kg × 3,980 J/kg · °C ( T - 39°C)

Heat gained by water = 0.062 Kg × 4200 J/kg · °C ( T - 0°C)

Hence;

2083.2  = [2988.98T - 116570] + [260.4T - 0]

2083.2 = 2988.98T + 260.4T -  116570

2083.2 =3249.38 T - 116570

2083.2 + 116570 = 3249.38 T

T = 36.5°C

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