60 liters of water were poured into the bath at a temperature of 10 degrees. How many liters

60 liters of water were poured into the bath at a temperature of 10 degrees. How many liters of water at a temperature of 100 degrees must be added to the bath so that the temperature of the mixture is 26 degrees.

Initial data: V1 (volume of cold water) = 60 l (0.06 m3); t1 (cold water temperature) = 10 ºС; t2 (temperature of hot water (boiling water)) = 100 ºС; t (steady-state mixture temperature) = 26 ºС.

The volume of boiling water added to the bath is determined from the equality:

C * m1 * (t – t1) = C * m2 * (t2 – t).

ρ * V1 * (t – t1) = ρ * V2 * (t2 – t).

V1 * (t – t1) = V2 * (t2 – t).

V2 = V1 * (t – t1) / (t2 – t).

Calculation: V2 = 0.06 * (26 – 10) / (100 – 26) ≈ 0.013 m3 (13 l).

Answer: You need to add 13 liters of boiling water.