Question

40 g of water at 60°C is poured into vessel of 200 g mass containing 50 g of water at 20°C. The final temperature of mixture is 30°C. Calculate the specific heat of vessel.

Answer 1

Mass of hot water at 60°C = 40 g Mass of cold water at 20°C = 50 g Mass of vessel = 200 g Suppose the specific heat of vessel is S_v

Heat energy given by hot water = mS_w∆T

= 40 × 1 × (60 – 30) [∵ T₁ = 60°C, T₂ = 30°C]

= 40 × 30 = 1200 cal Heat energy taken by cold water = mS_w∆T

= 50 × 1 × (30 – 20) = 50 × 10 = 500 cal 

Heat energy taken by vessel = mS_v∆T = 

200 × S_v × (30 – 20) = 2000 S_v

According to the principle of method of mixtures, 

Heat lost by hot water = heat gained by cold water + heat gained by vessel 1200 = 500 + 2000 S_v