50 liters of water were poured into the bathtub at a temperature of 15 degrees and 30 liters of water at a temperature

50 liters of water were poured into the bathtub at a temperature of 15 degrees and 30 liters of water at a temperature of 75 degrees. What will be the temperature of the water in the bathroom?

Vх = 50 l = 0.05 m3.

tx = 15 ° C.

Vg = 30 l = 0.03 m3.

tg = 75 ° C.

t -?

When mixing water of different temperatures, due to heat transfer, cold water will receive a certain amount of heat from hot water. In this case, hot water will cool down, and cold water will be heated to the same temperature t.

Qg = C * Vg * ρ * (tg – t).

Qx = C * Vx * ρ * (t – tx).

C * Vg * ρ * (tg – t) = C * Vх * ρ * (t – tх).

Vg * (tg – t) = Vx * (t – tx).

Vg * tg – Vg * t = Vx * t – Vx * tx.

Vx * t + Vg * t = Vg * tg + Vx * tx.

t = (Vg * tg + Vx * tx) / (Vx + Vg).

t = (0.03 m3 * 75 ° C + 0.05 m3 * 15 ° C) / (0.05 m3 + 0.03 m3) = 37.5 ° C.

Answer: the temperature in the bathroom will be t = 37.5 ° C.