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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.
Solution
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
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