Answer:
The final temperature is approximately 23.55°C
Step-by-step explanation:
The given parameters are;
The mass of the ice block, m₁ = 20 g
The initial temperature of the block, T₁ = -65°C
The mass of the water to which the block is added, m₂ = 570 g
The mass of the copper container containing the water, m₃ = 76 g
The initial temperature of the water and the copper, T₂ = 26°C
The specific heat capacity of copper, c₃ = 387 J/(kg·°C)
The specific heat capacity of ice, c₄ = 2,090 J/(kg·°C)
The latent heat of fusion of ice, l = 3.33 × 10⁵ J/kg
The specific heat capacity of water, c₁ = 4,186 J/(kg·°C)
We have;
ΔQ = m₁·c₁·ΔT + m₁·l = m₂·c₂·ΔT + m₃·c₃·ΔT
Therefore, we get;
20 × 2,090 × -65 + 20 × 3.33 × 10⁵ + 20 × T × 4,186 = 570 × 4,186 × (26 - T) + 76 × 387 × (26 - T)
Using a graphing calculator, we get;
83720·T + 3943000 = 62801232 - 2415432·T
The final temperature, T ≈ 23.55 °C