Question

You are required to make a water bath of 50 kg at 45°C, by mixing hot water at 90°C, with cold water at 20°C. Calculate the amount of hot water required.

[Hint: Let the amount of hot water = x

∴ Amount of cold water = (50 − x) kg]

Answer 1

Let the amount of hot water required be x kg. Then the amount of cold water used is (50 − x) kg.

Heat lost by hot water:

x × c × (90 − 45)

= 45cx

Heat gained by cold water:

(50 − x) × c × (45 − 20)

= 25c(50 − x)

Heat lost = Heat gained

45cx = 25c(50 − x)

45x = 1250 − 25x

70x = 1250

$$x = \frac{1250}{70}$$

x = 17.857 kg

Therefore, the amount of hot water required is approximately 17.86 kg.