Final answer:
To find the specific heat of an unknown metal, use the calorimetry principle that the heat lost by the metal equals the heat gained by the water, and apply the formula q = mcΔT, where q is heat transferred, m is mass, c is specific heat, and ΔT is the temperature change.
Step-by-step explanation:
The student's question involves calculating the specific heat of an unknown metal using principles of heat transfer and calorimetry. When the metal and water reach thermal equilibrium at a final temperature, energy lost by the metal as it cools is equal to the energy gained by the water as it warms. The specific heat of the metal can be determined using the formula:
q = mcΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Since the heat lost by the metal will be equal to the heat gained by the water, we can set their q values equal to each other:
–(metal mass)(metal specific heat)(change in metal temperature) = (water mass)(water specific heat)(change in water temperature)
Plugging the provided values into this equation and solving for the metal specific heat gives us the answer. It's important to ensure units are consistent, particularly the mass in grams and temperature in degrees Celsius.