The tank contains 20 kg of water with a temperature of 20 degrees C. A certain amount of water with a temperature

The tank contains 20 kg of water with a temperature of 20 degrees C. A certain amount of water with a temperature of 80 degrees is added to the tank, after mixing the water temperature became 30 degrees. What is the weight of the added water?

mх = 20 kg.

tx = 20 ° C.

tg = 80 ° C.

t = 30 ° C.

mg -?

When mixing water with different temperatures, as a result of heat exchange, water with a higher temperature will give a certain amount of thermal energy to water with a lower temperature: Qg = Qx.

Qg = C * mg * (tg – t), Qx = C * mx * (t – tx), where C is the specific heat capacity of water.

C * mg * (tg – t) = C * mх * (t – tх) – heat balance equation.

mg * (tg – t) = mх * (t – tх).

mg = mx * (t – tx) / (tg – t).

mg = 20 kg * (30 ° C – 20 ° C) / (80 ° C – 30 ° C) = 4 kg.

Answer: hot water was added to the tank mg = 4 kg.