Cold water has a temperature of 10 ° C, and hot water -70 ° C. how much hot and cold water should

Cold water has a temperature of 10 ° C, and hot water -70 ° C. how much hot and cold water should be mixed to get 200 liters of water with a temperature of 30 ° C.

Initial data: tх (cold water temperature) = 10 ºС; tg (hot water temperature) = 70 ºС; m (mass of the mixture) = 200 kg (200 l); t (steady-state temperature) = 30 ºС.

1) Ratio of cold and hot water at 30 ° C:

Q1 = Q2: C * mx * (t – tx) = C * mg * (tg – t).

mх * (t – tх) = mg * (tg – t).

mх * (30 – 10) = mg * (70 – 30).

20mx = 40mg and mx = 2mg.

2) Required amounts of water:

mx + mg = 200 = mx + 2mx = 3mx.

mх = 200/3 = 66.67 kg (66.67 l).

mg = 200 – 66.67 = 133.33 kg (133.33 l).