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24 March, 10:56

A 200 g sample of water with a temperature of 32◦C is added to 50 g water at 55◦C in an insulated container. What is the final temperature after thermal equilibrium is reached? The specific heat of water in the liquid state is 4.18 J/g◦C, in the solid state is 2.09 J/g◦C, and in the gaseous state is 2.03 J/g◦C. The heat of fusion is 334 J/g and the heat of vaporization is 2260 J/g. 1. 49.2◦C 2. 36.6◦C 3. 52.6◦C 4. 38.4◦C 5. 50.4◦C 6. 43.5◦C 7. 34.1◦C

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  1. 24 March, 11:12
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    2. 36.6°C.

    Explanation:

    ∵ The amount of heat released by hot water = amount of heat absorbed by cold water.

    • The amount of heat released by hot water = Q hot water = - m. c.ΔT.

    where, m is the mass of hot water = 50 g.

    c is the specific heat capacity of liquid water = 4.18 J/g°C.

    ΔT is the temperature difference = (final T - initial T = final T - 55°C).

    • The amount of heat absorbed by cold water = Q cold water = m. c.ΔT.

    where, m is the mass of cold water = 200 g.

    c is the specific heat capacity of liquid water = 4.18 J/g°C.

    ΔT is the temperature difference = (final T - initial T = final T - 32°C).

    ∵ Q hot water = Q cold water

    ∴ ( - m. c.ΔT) hot water = (m. c.ΔT) cold water

    ∴ ( - m.ΔT) hot water = (m.ΔT) cold water

    - (50 g) (final T - 55°C) = (200 g) (final T - 32°C)

    -50 final T + 2750 = 200 final T - 6400

    250 final T = 2750 + 6400 = 9150

    ∴ final T = 9150/250 = 36.6°C.
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