Question

A bucket contains 8 kg of water at 20 °C. When 4 kg of hot water is mixed with it, the temperature of the mixture becomes 40 °C. Calculate the temperature of the hot water. (Ignore the heat absorbed by the bucket.)

Answer 1

Data: m₁ = 8 kg, T₁ = 20 °C, m₂ = 4 kg, T = 40 °C,

T₂ = ?

Heat lost by the hot water = heat gained by the cold water (ignoring the heat absorbed by the bucket)

∴ m₂ c (T₂ – T) = m₁ c (T – T₁ ) 

∴ 4 kg × c × (T₂ – 40°C) 

= 8 kg × c × (40°C – 20°C) 

∴ T₂ – 40°C = 2 × 20°C = 40°C 

∴ T₂ = 40 °C + 40 °C = 80 °C 

Temperature of the hot water = 80 °C.