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25 October, 19:20

Determine the final temperature after 52.5 g of copper (c = 0.385 J/g  C) at 93.6  C is placed into 225 g of water at 21.3  C.

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  1. 25 October, 19:47
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    22.82°C

    Explanation:

    Concept tested: Quantity of heat

    We are given;

    Mass of copper = 52.5 g Specific heat capacity of copper = 0.385 J/g°C Initial temperature of copper = 93.6 °C Mass of water = 225 g Initial temperature of water = 21.3°C

    We are required to calculate the final temperature of the mixture.

    To answer the question we are going to assume the final temperature is X°C. Then we can use the following simple steps; Step 1: Calculate the amount of heat released by copper;

    Q = m * c * ΔT

    Since the final temperature is X°C then the change in temperature, ΔT will be (93.6 - X) °C

    Quantity of heat released by copper, Q will be;

    = 52.5 g * 0.385 J/g°C * (93.6 - X) °C

    = 1891.89 - 20.2125X joules

    Step 2: Amount of heat gained by water

    Specific heat capacity of water = 4.184 J/g°C

    Change in temperature = (X-21.3) °C

    Therefore;

    Q = 225 g * 4.184 J/g°C * (X-21.3) °C

    = 941.4X-20051.82 Joules

    Step 3: Calculate the final temperature

    We know that the quantity of heat released is equivalent to the amount of heat absorbed.

    Therefore;

    1891.89 - 20.2125X Joules = 941.4X-20051.82 Joules

    961.6125X = 21943.71

    X = 22.82°C

    Therefore, the final temperature is 22.82°C
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