Final answer:
To calculate the final temperature of the system, we can use the principle of conservation of energy. The heat lost by the copper will be equal to the heat gained by the water. By rearranging the equation and solving for the final temperature, we find that the final temperature of the system is 364.62 °C.
Step-by-step explanation:
To calculate the final temperature of the system, we can use the principle of conservation of energy. The heat lost by the copper will be equal to the heat gained by the water. We can use the formula q = m * c * ΔT, 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.
For the copper, the initial temperature is unknown, the final temperature is the same as the system's final temperature, the mass is 4.67 g, and the specific heat capacity is 0.39 J/g°C. For the water, the initial temperature is 32.5 °C, the final temperature is unknown, the mass is 64 mL (which is equivalent to 64 g), and the specific heat capacity is 4.18 J/g°C.
Using the equation q(copper) = q(water), we can solve for the final temperature of the system. Plugging in the values, we get:
(4.67 g) * (0.39 J/g°C) * (final temperature - initial temperature of copper) = (64 g) * (4.18 J/g°C) * (final temperature - 32.5 °C)
Rearranging the equation and solving for the final temperature:
(0.39 J/g°C) * (4.67 g - final temperature of copper) = (4.18 J/g°C) * (64 g - 32.5 °C)
0.39 J/g°C * 4.67 g - 0.39 J/g°C * final temperature of copper = 277.52 J - 135.47 J
0.39 J/g°C * final temperature of copper = 142.05 J
final temperature of copper = 142.05 J / (0.39 J/g°C) = 364.62 °C
Therefore, the final temperature of the system is 364.62 °C.