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)
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