3 liters of water taken at a temperature of 20 C was mixed with water at a temperature of 100 C.

3 liters of water taken at a temperature of 20 C was mixed with water at a temperature of 100 C. The temperature of the mixture turned out to be 40 C. What is the mass of hot water? Neglect heat exchange with the environment.

Vх = 3 l = 3 * 10-3 m3.

tx = 20 ° C.

tg = 100 ° C.

t = 40 ° C.

C = 4200 J / kg * ° C.

ρ = 1000 kg / m3.

mg -?

When mixing water of different temperatures, the heat balance equation will have the form: C * mх * (t – tх) = C * mg * (tg – t).

We express the mass of cold water mх by the product of the density of water ρ and the volume of water Vх: mх = ρ * Vх.

ρ * Vх * (t – tх) = mg * (tg – t).

mg = ρ * Vx * (t – tx) / (tg – t).

mg = 1000 kg / m3 * 3 * 10-3 m3 * (40 ° C – 20 ° C) / (100 ° C – 40 ° C) = 1 kg.

Answer: mg = 1 kg of hot water was poured into cold water.