Question

20 g of hot water at 80°C is poured into 60 g of cold water, when the temperature of cold water rises by 20°C. Calculate the initial temperature of cold water. [Zero degree celsius]

Answer 1

Let the initial temperature of the cold water be x°C.

Rise in temperature of the cold water = 20°C

Final mixture temperature θ = (x + 20)°C

Heat lost by hot water = mc(80 − θ)

= 20 × 4.2 × [80 − (x + 20)]

= 20 × 4.2 × (60 − x) J

Heat gained by cold water = mc(θ − x)

= 60 × 4.2 × 20 J

By the principle of calorimetry,

20 × 4.2 × (60 − x) = 60 × 4.2 × 20

20(60 − x) = 1200

1200 − 20x = 1200

x = 0°C

Thus, the initial temperature of the cold water is 0°C.