How many kilograms of hot-water (70C) must be mixed with cold-water?

How many kilograms of hot-water (70C) must be mixed with cold-water (20C) so that the

temperature of the water mixer is 30C? The total mass of water (hot + cold) is 200kg.

(Assume no heat flows to the surroundings)

1 Answer

  • energy needed to cool the hot water equals that to heat the cold water.

    U = c·m·∆T

    U is energy in Joules to heat the material by ∆T

    c is specific heat of the material in J/kg·K

    m is mass in kg, ∆T is temperature change in ºC

    let SH be specific heat of water

    let M be the mass of not water

    SH x M x (70–30) = SH x (200–M) x (30–20)

    40M = 10(200–M)

    40M = 2000 – 10M

    50M = 2000

    M = 40 kg

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