Question

A bucket contains 10 liters of water at 80°C. Cold water at 25°C is run from a tap into the bucket of hot water for 20 seconds and the temp. Of the water in the bucket falls to 50°C.
(a) Calculate the rate at which cold water came out of the tap.
(b) State an assumption made in the above calculation.

Answer 1

(a) Mass of water in the bucket = Density x Volume
= 1000 kg/m³ x 0.01 m³ = 10 kg
Let the mass of water chat came out from the tap be m.
Heat lost by hot water =  Heat gained by cold water
10 x 4200 x (80 - 50) = m x 4200 x (50 - 25)
300 = 25m
m=12 kg
12 kg of water came out of tap in 20 sec.
So, the rate at which cold water came out of the tap is `12/20` = 0.6 kg/s = 600 g /s
(b) In the above calculation we assumed chat there is no loss of heat to the surroundings