Question

Find the final temperature when a mass of 80g of water at 100°C is mixed with a mass of 40g of water at 25°C.

Answer 1

Mass of body = m₁ = 80g, Mass of cold body m₂ = 40g

Initial temperature of hot body θ₁ = 100°C,

Initial temperature of cold body θ₂ = 25 °C

Let final temperature of mixture = θ °C

Heat lost by hot body = Heat gained by cold body  ..(Law of calorimetry)

m₁C (θ₁ - θ) = m₂C (θ - θ₂)

80 × 4.2 × (100 - θ) = 40 × 4.2 × (θ - 25)

100 - θ = `40/80` (θ - 25) = `(θ - 25)/2`

200 - 2θ = θ - 25

3θ = 225

θ = `225/3 = 75^circ "C"`

Final temperature is 75°C