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24 January, 15:29

If 8.20 kJ of heat is needed to raise the temperature of a sample of metal from 12°C to 29°C, how many kilojoules of heat will be required to raise the temperature of the same sample of metal from 34°C to 57°C?

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  1. 24 January, 17:12
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    The heat needed is 11.1 kJ

    Explanation:

    Step 1: Data given

    8.20 kJ of heat is needed

    Initial temperature of metal = 12°C

    Final temeprature of metal = 29 °C

    Mass of the metal = unknown BUT the sample of metal has the same mass in both cases

    Step 2: Define the formulas

    Q1 = m*c * ΔT1

    Q2 = m*c*ΔT2

    The mass and the heat capacity are constant

    Q1/Q2 = (m*c * ΔT1) / (m*c*ΔT2)

    Q1/Q2 = ΔT1/ΔT2

    Step 2: Calculate heat needed to raise from 34 to 57 °C

    Q2 = (ΔT2 / ΔT1) * Q1

    ⇒ with Q2 = the heat need to raise the metal from 34 to 57 °C

    ⇒ with Q1 = the heat need to raise the metal from 12 to 29 °C = 8200 J

    ⇒ with ΔT2 = the change in temperature = 57° - 34 = 23 °C

    ⇒ with ΔT1 = the change in temperature = 29° - 12 = 17 °C

    Q2 = (23/17) * 8200

    Q2 = 11094 J = 11.1 kJ

    The heat needed is 11.1 kJ
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