Into a copper saucepan weighing 500 g was poured 1 kg of water at a temperature of 20 ° C. how much boiling water needs to be added so that the temperature of the mixture is equal to 50 ° С?
Equilibrium: Q1 = Q2 + Q3.
Q1 (boiling water cooling) = Sv * m1 * (t1 – t2); Sv = 4200 J / (kg * K); t1 = 100 ºС; t2 = 50 ºС.
Q2 (water heating) = Sv * m2 * (t2 – t3); m1 = 1 kg; t3 = 20 ºС.
Q3 (heating a copper pot) = cm * m3 * (t2 – t3); Cm = 400 J / (kg * K); m3 = 500 g = 0.5 kg.
Sv * m1 * (t1 – t2) = Sv * m2 * (t2 – t3) + Cm * m3 * (t2 – t3).
m1 = (Sv * m2 * (t2 – t3) + Cm * m3 * (t2 – t3)) / (Sv * (t1 – t2)) = (4200 * 1 * (50 – 20) + 400 * 0.5 * (50 – 20)) / (4200 * (100 – 50)) = 0.629 kg = 629 g.
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