Final answer:
To find the specific heat of the unknown metal, the heat lost by the metal is set equal to the heat gained by the water. Using the provided masses and temperatures, and the specific heat capacity of water, the specific heat of the metal is calculated to be approximately 0.897 J/g°C, corresponding to option A).
Step-by-step explanation:
The student wants to find the specific heat of an unknown metal by using a constant-pressure calorimeter with water. The specific heat capacity of water, which we know as 4.184 J/g°C, allows us to determine the heat absorbed by it. When two substances at different temperatures reach thermal equilibrium, the heat lost by the hotter substance is equal to the heat gained by the cooler substance.
The formula to calculate the heat absorbed or lost is q = mcΔT, where 'q' is the heat, 'm' is the mass, 'c' is the specific heat capacity, and 'ΔT' is the change in temperature. Since the final temperature of the system is 28.4°C, the change in temperature for water (ΔTw) is 28.4°C - 24.0°C, and for the metal (ΔTm) is 99.0°C - 28.4°C.
Set up the equation based on the concept that the heat lost by the metal is equal to the heat gained by the water:
-q_metal = q_water
-m_metal · c_metal · ΔT_metal = m_water · c_water · ΔT_water
Plugging in the known values and solving for c_metal gives us:
-44.0 g · c_metal · (99.0°C - 28.4°C) = 80.0 g · 4.184 J/g°C · (28.4°C - 24.0°C)
After calculations, the specific heat capacity of the unknown metal turns out to be approximately 0.897 J/g°C, which corresponds to option A).