Final answer:
To find the specific heat capacity of the metal, we can use the equation Q = mcΔT. By applying this equation and using the given information, we can calculate the specific heat capacity of the metal to be approximately -1.55 J/g°C.
Step-by-step explanation:
To calculate the specific heat capacity of the metal, we can use the equation Q = mcΔT, where Q represents the heat transferred, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature. Using the given information, we can calculate the heat transferred to the water: Qwater = mwater * cwater * ΔTwater. Next, we can calculate the heat transferred from the water to the metal: Qmetal = mmetal * cmetal * ΔTmetal (where the change in temperature is the same for both). Since the system is isolated, the heat transferred from the water to the metal is equal to the heat transferred from the metal to the water: Qwater = Qmetal. By substituting the known values and solving for cmetal, we can find the specific heat capacity of the metal.
Using the given temperatures and specific heat capacity of water, we can substitute those values into the equation Qwater = Qmetal to solve for cmetal:
mwater * cwater * ΔTwater = mmetal * cmetal * ΔTmetal.
Substituting the values: 100g * 4.1 J/g°C * (25°C - 20°C) = 50g * cmetal * (25°C - 90°C).
Simplifying the equation: 100g * 4.1 J/g°C * 5°C = 50g * cmetal * (-65°C).
Now solve for cmetal:
cmetal = (100g * 4.1 J/g°C * 5°C) / (50g * -65°C).
After performing the calculations, the specific heat capacity of the metal is approximately -1.55 J/g°C.