Final answer:
The change in temperature for the metal can be calculated using the formula: ΔT = Q / (m * c), where ΔT is the change in temperature, Q is the energy input, m is the mass of the metal, and c is the specific heat capacity of the metal. Using the given values, we can calculate the specific heat capacity of the metal to be 1.7 J/g.°C.
Step-by-step explanation:
The change in temperature for the metal can be calculated using the formula:
ΔT = Q / (m * c)
Where ΔT is the change in temperature, Q is the energy input, m is the mass of the metal, and c is the specific heat capacity of the metal.
In this case, we are given the mass of the metal (25.0 g), the initial temperature (16.0 °C), the final temperature (22.1 °C), and the energy input (259 J). We can plug in these values into the formula to calculate the change in temperature:
ΔT = 259 J / (25.0 g * c)
Since we are trying to find the change in temperature, we rearrange the formula to solve for c:
c = 259 J / (25.0 g * ΔT)
Now we can substitute the known values and calculate the specific heat capacity:
c = 259 J / (25.0 g * (22.1 °C - 16.0 °C))
c = 259 J / (25.0 g * 6.1 °C)
c = 259 J / 152.5 g °C
c = 1.7 J/g.°C
Therefore, the specific heat capacity of the metal is 1.7 J/g.°C.