Final answer:
The specific heat capacity of the unknown metal is calculated using the heat transfer equation by setting the heat lost by the metal equal to the heat gained by the water. By performing the calculations with the given masses and temperature changes, the specific heat capacity of the metal is found to be approximately 0.89 J/g°C.
Step-by-step explanation:
To calculate the specific heat capacity of the unknown metal, we can use the principle of conservation of energy, which states that the heat lost by the metal must equal the heat gained by the water. Assuming no heat is lost to the surroundings, the equation for heat transfer is:
Qmetal = -Qwater
The specific heat formula is:
Q = m × c × ΔT
Where m is mass, c is specific heat capacity, and ΔT is the change in temperature. For the water, this is:
Qwater = (100.0 g) × (4.18 J/g°C) × (27.4°C - 20.0°C)
We can now calculate the heat absorbed by the water:
Qwater = 3092 J (to maintain significant figures)
Since the heat lost by the metal is the negative of this (by the conservation of energy), we have:
Qmetal = -Qwater = -3092 J
The metal's temperature change is from 200.0°C to 27.4°C, so ΔT for the metal is:
ΔTmetal = 27.4°C - 200.0°C = -172.6°C
Now we use the heat equation for the metal, solving for c:
cmetal = Qmetal / (mmetal × ΔTmetal)
= -3092 J / (20.0 g × -172.6°C)
Calculating gives us:
cmetal = 3092 J / (20.0 g × 172.6°C) ≈ 0.89 J/g°C
Therefore, the specific heat capacity of the metal is approximately 0.89 J/g°C.