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45 votes
45 votes
A 20 g block of ice is cooled to −65 ◦C. It

is added to 570 g of water in an 76 g copper

calorimeter at a temperature of 26◦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 × 10^5

J/kg and its specific heat

is 4186 J/kg ·

◦C .

Answer in units of ◦C.

User Andy Meissner
by
2.7k points

1 Answer

12 votes
12 votes

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

User EFOE
by
3.2k points