How much coal must be burned in order to convert 5 tons of water taken at 30C into steam? Boiler efficiency is 60%. The thermal conductivity of coal is 30MJ / kg.
Data: m1 (mass of water) = 5 t = 5000 kg; t0 (initial water temperature) = 30 ºС; η (boiler efficiency) = 60% = 0.6.
Constants: t (boiling point of water) = 100 ºС; C (specific heat of water) = 4200 J / (kg * K); L (specific heat of vaporization of water) = 2.3 * 10 ^ 6 J / kg; according to the condition q (specific heat of combustion of coal) = 30 MJ / kg = 30 * 106 J / kg.
Boiler efficiency: η = m1 * (C * (t – t0) + L) / (q * m2).
m2 = m1 * (C * (t – t0) + L) / (q * η) = 5000 * (4200 * (100 – 30) + 2.3 * 10 ^ 6) / (30 * 10 ^ 6 * 0 , 6) ≈ 721 kg.
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