Question

A 5.10 kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -25.0 ∘C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 0.90 kg of ice and 1.10 kg of liquid water.

Part A

What was the initial temperature of the piece of copper?

Express your answer to three significant figures and include the appropriate units.

Answer 1

Mass of the solid copper metal = m₁ = 5.1 kg

Mass of ice used = m₂ = 2 kg

Mass of ice at the end = m₃ = 0.9 kg

Mass of water at the end = m₄ = 1.1 kg

Initial temperature of the copper metal = T

Initial temperature of the ice = T₁ = -25 ^oC

At equilibrium we have a mixture of ice and water therefore the final equilibrium temperature of the mixture is 0^oC

Final temperature = T₂ = 0 ^oC

Specific heat of Copper = C_c = 387 J/(kg.^oC)

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

Latent heat of fusion of water = L = 334000 J/kg

The heat gained by the ice is equal to the heat lost by the copper.

m₂C_i(T₂ - T₁) + m₄L = m₁C_c(T - T₂)

(2)(2090)(0 - (-25)) + (1.1)(334000) = (5.1)(387)(T - 0)

471900 = 1963.5T

T = 239.094 ^oC

Initial temperature of the piece of copper = 239.094 ^oC