Answer :
The final temperature of the iron block and water, when a metal block of iron with a mass of 9.10 g at 73.6°C is added to 99.3 g of water at 13.9°C, is approximately 33.6°C.
Determine how to find the final temperature?
To calculate the final temperature, we can use the principle of conservation of energy, assuming no heat is lost to the surroundings.
First, let's calculate the heat gained or lost by the iron block using the formula: Q₁ = m₁ * cp₁ * ΔT₁, where m₁ is the mass of the iron block, cp₁ is the specific heat capacity of iron, and ΔT₁ is the change in temperature of the iron block.
Q₁ = (9.10 g) * (0.450 J/g°C) * (T - 73.6°C)
Next, let's calculate the heat gained or lost by the water using the formula: Q₂ = m₂ * cp₂ * ΔT₂, where m₂ is the mass of the water, cp₂ is the specific heat capacity of water, and ΔT₂ is the change in temperature of the water.
Q₂ = (99.3 g) * (4.184 J/g°C) * (T - 13.9°C)
Since the total heat gained by the water and the iron block is zero, we have Q₁ + Q₂ = 0.
Substituting the values and solving the equation, we find that T ≈ 33.6°C, which is the final temperature of both the block and water.
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