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8 December, 07:32

A metal sample weighing 43.5 g and at a temperature of 100.0 °c was placed in 39.9 g of water in a calorimeter at 25.1 °c. at equilibrium, the temperature of the water and metal was 33.5 °c. determine the specific heat capacity of the metal.

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  1. 8 December, 09:11
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    The initial state of the system is comprised of

    (a) A metal sample

    m₁ = 43.5 g, mass

    T₁ = 100°C, temperature

    c₁ (unknown) specific heat, J / (g-C)

    (b) Water

    m₂ = 39.9 g, mass

    T₂ = 25.1°C, temperature

    c₂ = 4.184 J / (g-C), specific heat

    The final state of the system is

    M = m₁ + m₂, total mass

    T = 33.5°C, equilibrium temperature

    Work in SI units. Note that changes in °C are equal to changes in °K.

    Equate change in total thermal energy to zero because the energy is conserved.

    m₁c₁ (T-T₁) + m₂c₂ (T-T₂) = 0

    (43.5) * (c₁) (33.5 - 100) + (39.9) * (4.184) * (33.5 - 25.1) = 0

    -2892.8c₁ + 1402.3 = 0

    c₁ = 1402.3/2892.8

    = 0.4848 J / (g-C)

    Answer: The specific heat capacity of the metal is 0.485 J / (g-°C)
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