Final answer:
The specific heat capacity of an unknown metal is calculated using the heat transfer between the metal and water until thermal equilibrium, following the formula q = mcΔT and conservation of energy. By plugging in the known values into the equation and solving for the metal's specific heat, the identity of the metal can be determined through comparison with known values.
Step-by-step explanation:
To calculate the specific heat capacity of the unknown metal used in the experiment, you would apply the principle of conservation of energy. When the hot metal is placed into cooler water, the metal loses heat, which the water absorbs till both reach thermal equilibrium.
The formula to calculate the heat gained or lost is q = mcΔT, where q is the heat gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Since energy is conserved, the heat lost by the metal will equal the heat gained by the water, leading to the equation qwater = -qmetal.
To solve for the specific heat capacity of the metal (cmetal), you rearrange the equation to cmetal = (mwater × cwater × ΔTwater) / (mmetal × ΔTmetal). By plugging in the given values: mass of water (mwater = 100.0 g), specific heat of water (cwater = 4.184 J/g°C), change in water temperature (ΔTwater = 60.15°C - 50.0°C), mass of the metal (mmetal = 40.0 g) and change in metal temperature (ΔTmetal = 130.0°C - 60.15°C), you can find the specific heat capacity of the metal. Once you have the specific heat capacity, you can compare it to known values to identify the metal.