20L of water was poured into the aquarium at a temperature of 14C. How much water (by volume)

20L of water was poured into the aquarium at a temperature of 14C. How much water (by volume) at a temperature of 40c should be added to the aquarium so that a temperature of 20c is established in it?

V1 = 20 l = 20 * 10-3 m3.

t1 = 14 ° C.

C = 4200 J / kg * ° C.

t2 = 40 ° C.

t = 20 ° C.

ρ = 1000 kg / m3.

V2 -?

When mixing water of different temperatures, water with a higher temperature will give the water with a lower temperature the amount of heat.

The heat balance equation will take the form: Q1 = Q2.

Q1 = C * m1 * (t – t1).

Q2 = C * m2 * (t2 – t).

We express the mass of water m1 and m2 by the formulas: m1 = ρ * V1 and m2 = ρ * V2.

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

V1 * (t – t1) = V2 * (t2 – t).

V2 = V1 * (t – t1) / (t2 – t).

V2 = 20 * 10-3 m3 * (20 ° C – 14 ° C) / (40 ° C – 20 ° C) = 6 * 10-3 m3.

Answer: V2 = 6 * 10-3 m3 of water was added to the aquarium.