How much hot water, the temperature of which is 90 C, must be added to cold water weighing 5 kg

How much hot water, the temperature of which is 90 C, must be added to cold water weighing 5 kg at a temperature of 10 C, so that the temperature is equal to 40 C

Initial data: t1 (hot water temperature) = 90 ºС; m2 (mass of cold water) = 5 kg; t2 (cold water temperature = 10 ºС; tр (equilibrium temperature) = 40 ºС.

Let’s compose expressions for finding the mass of hot water:

C * m1 * (t1 – tp) = C * m2 * (tp – t2), whence m1 = C * m2 * (tp – t2) / (C * (t1 – tp)) = m2 * (tp – t2) / (t1 – tp).

Let’s do the calculation:

m1 = 5 * (40 – 10) / (90 – 40) = 5 * 30/50 = 3 kg or 3 liters.

Answer: Add 3 kg (3 L) of hot water to cold water.