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Answer :
The specific heat of the unknown metal in the problem is calculated to be 0.898 J/g°C. This corresponds to option B. The calculation follows the principle of conservation of energy.
To solve this, we use the principle of conservation of energy which states that the heat lost by the metal will be equal to the heat gained by the water:
Heat gained by water, Q = mass of water * specific heat of water * change in temperature.
Q = 50.0 g * 4.18 J/g°C * (23.00°C - 21.00°C)
Q = 50.0 g * 4.18 J/g°C * 2.00°C
Q = 418 J
Next, we calculate the specific heat of the metal (cmetal) using the formula:
Q = m * cmetal * ΔT
418 J = 28.4 g * cmetal * (23.00°C - 39.4°C)
418 J = 28.4 g * cmetal * (-16.4°C)
cmetal = 418 J / (28.4 g * -16.4°C)
cmetal ≈ 0.898 J/g°C
Therefore, the specific heat of the metal in this problem is 0.898 J/g°C, which corresponds to option B.
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