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22 March, 12:51

230 cm3 of hot tea at 96 °C are poured into a very thin paper cup with 100 g of crushed ice at 0 °C. Calculate the final temperature of the "ice tea.

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  1. 22 March, 13:30
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    Final temperature of the ice tea, x = 42.73°C

    Explanation:

    230 cm^3 = 230 g of liquid (taking the density of tea as the same the density of water)

    In cooling from 96°C to 0°

    C (before freezing) the available energy is

    96 * 230 = 22080 cal

    The latent heat (the heat required to melt the crushed ice per gram) of fusion for water = 79.7 cal/g

    Melting 100 g of crushed ice at 0°C will absorb

    100 * 79.7 = 7970 cal

    The retain heat of the iced Tea = (22080 - 7970) cal of heat raising the mixture temperature as follows

    (22080 - 7970) = 14110 cal

    The mass of the final solution 230 + 100 = 330 g solution

    Final temperature = 14110 / 330 = 42.76°C

    Or where specific heat of water = 4.186J/Kg°C

    and the latent heat of the ice = 334J/Kg

    We have

    230 * (specific heat capacity of water) * (96 - x) = 100 * (specific heat capacity of water) * (0-x) + (latent heat) * 100 =

    230 * 4.186 * (96 - x) = 100 * 4.186 * (x-0) + 100*334

    1381.38*x = 59026.88

    Final temperature of the ice tea, x = 42.73°C
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