Question

A 31 g block of ice is cooled to −66◦C. It is added to 577 g of water in an 84 g copper calorimeter at a temperature of 29◦C.

Find the final temperature. The specific heat of copper is 387 J/kg ·◦C and of ice is 2090 J/kg ·◦C . The latent heat of fusion of water is 3.33 × 105 J/kg and its specific heat is4186J/kg·◦C.

Answer in units of ◦C.

Answer 1

Specific heat of ice = C₁ = 2090 J/(kg.^oC)

Specific heat of water = C₂ = 4186 J/(kg.^oC)

Specific heat of copper = C₃ = 387 J/(kg.^oC)

Latent heat of fusion of water = L = 3.33 x 10^5 J/kg

Mass of the block of ice = m₁ = 31 g = 0.031 kg

Mass of the water = m₂ = 577 g = 0.577 kg

Mass of the copper calorimeter = m₃ = 84 g = 0.084 kg

Initial temperature of ice = T₁ = -66 ^oC

Melting point of ice = T₂ = 0 ^oC

Initial temperature of water and copper calorimeter = T₃ = 29 ^oC

Final equilibrium temperature = T₄

Heat energy gained by the block of ice = Q₁

Heat energy lost by water = Q₂

Heat energy lost by the copper calorimeter = Q₃

The heat energy gained by the ice is equal to the heat energy lost by the water and the copper calorimeter.

T₄ = 21.88 ^oC

Final temperature of the mixture = 21.88 ^oC