How many kilograms of hot-water (70C) must be mixed with cold-water?
How many kilograms of hot water at 70°C must be mixed with cold water at 20°C to achieve a final temperature of 30°C? The total mass of the water mixture (hot and cold) is 200 kg. Please assume that no heat is lost to the surroundings.
1 Answers
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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