In the bathroom, 5 buckets of water were mixed, 10 liters in each, at a temperature of 10 degrees

In the bathroom, 5 buckets of water were mixed, 10 liters in each, at a temperature of 10 degrees Celsius and 6 of the same buckets of water at a temperature of 90 degrees Celsius. Find the temperature of the resulting mixture?

n1 = 5.V = 10 l. t1 = 10 “C. n2 = 6.t2 = 90” C. ρ = 1000 kg / m ^ 3. c = 4183 J / kg * “C. t -? Let us write the heat balance equation when mixing water: c * m1 * (t -t1) + c * m2 * (t2 -t) = 0, where c is the specific heat capacity of water, m1 is the mass of water with a temperature t1 = 10 “С, m2 is the mass of water with a temperature t2 = 90” С, t is the temperature that will be established after mixing. The mass of water is determined by the formula: m1 = n1 * ρ * V, m2 = n2 * ρ * V. c * n1 * ρ * V * (t -t1) = c * n2 * ρ * V * (t -t2). n1 * (t -t1) = n2 * (t -t2). n1 * t – n1 * t1 = n2 * t – n2 * t2. n2 * t2 – n1 * t1 = n2 * t – n1 * t. t = (n2 * t2 – n1 * t1) / (n2 – n1). t = (6 * 90 “C – 5 * 10” C) / (6 – 5) = 40 “C. Answer: after mixing, the water temperature will be set t = 40 “C.