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10 January, 06:38

Water enters a baseboard radiator at 180 °F and at a flow rate of 2.0 gpm. Assuming the radiator releases heat into the room at a rate of 20,000 Btu / hr., what is the temperature of the water leaving the radiator?

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  1. 10 January, 10:18
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    Temperature of water leaving the radiator = 160°F

    Explanation:

    Heat released = (ṁcΔT)

    Heat released = 20000 btu/hr = 5861.42 W

    ṁ = mass flowrate = density * volumetric flow rate

    Volumetric flowrate = 2 gallons/min = 0.000126 m³/s; density of water = 1000 kg/m³

    ṁ = 1000 * 0.000126 = 0.126 kg/s

    c = specific heat capacity for water = 4200 J/kg. K

    H = ṁcΔT = 5861.42

    ΔT = 5861.42 / (0.126 * 4200) = 11.08 K = 11.08°C

    And in change in temperature terms,

    10°C = 18°F

    11.08°C = 11.08 * 18/10 = 20°F

    ΔT = T₁ - T₂

    20 = 180 - T₂

    T₂ = 160°F
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