What mass of cold water at a temperature of t1 = 15 ° C must be poured into hot water with a volume

What mass of cold water at a temperature of t1 = 15 ° C must be poured into hot water with a volume of V2 = 4.0 liters at a temperature of t2 = 95 ° C in order to obtain water at a temperature of t = 35 ° C?

1) To draw up the heat balance equation, it is necessary to calculate how much heat cold water will receive in order to heat up from t1 = 15 ° C to a temperature of t = 35 ° C according to the formula: Q = m • c • Δt. Specific heat capacity of water c = 4200 J / (kg • deg), temperature change Δt = 35 ° C – 15 ° C; Δt = 20 ° C. We get Q = m • 4200 • 20.
2) Now we will compose an expression for the amount of heat that will be lost by hot water with a volume of V2 = 4.0 liters at a temperature of t2 = 95 ° C, cooling down to a temperature of t = 35 ° C. The mass of hot water can be found by the formula: m = ρV, where the density of water is ρ = 1000 kg / cubic meter, and the volume V = 4 l = 4 cubic dm = 0.004 cubic meters. We get the mass m = 4 kg (1 kg of water takes up a volume of 1 liter). The temperature change will be Δt = 35 ° C – 95 ° C; Δt = – 60 ° C. We get Q = 4 • 4200 • (- 60).
3) We compose the heat balance equation: m • 4200 • 20 + 4 • 4200 • (- 60) = 0; then m = (4 • 60): 20; m = 12 (kg).
Answer: m = 12 kg of cold water.