Main Answer
The specific heat of the metal is 0.12 J/g°C, and the metal is likely aluminum.The option A is correct.
Explanation
To calculate the specific heat of the metal, we first need to find the amount of heat absorbed by the water during the process. This can be calculated using the specific heat of water (4.18 J/g°C) and the mass and temperature change of the water:
q = mcΔT
q = (100.0 g)(4.18 J/g°C)(27.8°C - 23.7°C)
q = 9670 J
Next, we can use this value for "q" to calculate the specific heat of the metal using the equation:
q = mcΔT
c = q / (mΔT)
where "m" is the mass of the metal and "ΔT" is the change in temperature. However, we don't know the mass or specific heat of the metal, so we'll have to use some additional information to solve for these variables.
To simplify this problem, let's assume that no heat is lost to the environment, which means that the total amount of heat absorbed by both the water and metal must equal the initial heat content of the metal plus the initial heat content of the water:
q(water) + q(metal) = q(initial metal) + q(initial water)
9670 J + q(metal) = (59.047 g)(specific heat of metal)(100.0°C - 23.7°C) + (100.0 mL)(1 g/mL)(4.18 J/g°C)(23.7°C)
q(metal) = (59.047 g)(specific heat of metal)(76.3°C - 23.7°C) + (100.0 mL)(1 g/mL)(4.18 J/g°C)(23.7°C) - 9670 J
We can solve for "specific heat of metal" by isolating it in this equation:
specific heat of metal = [q(metal) - (59.047 g)(76.3°C - 23.7°C)] / [(59.047 g)(76.3°C - 23.7°C)] + [(100.0 mL)(1 g/mL)(4.18 J/g°C)(23.7°C)] / [(59.047 g)(76.3°C - 23.7°C)].The option A is correct..