Final answer:
To determine the specific heat and identity of a metal, we can use the formula Q = m * C * ΔT, where Q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature. By equating the heat transferred in the metal and water, we can solve for the specific heat capacity of the metal and identify it.
Step-by-step explanation:
The specific heat capacity (C) of a substance is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius. In this case, we are given the mass and initial and final temperatures of the metal and water. We can use the formula Q = m * C * ΔT, where Q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
For the metal, we have m = 92.9 g, ΔT = 29.7 °C - 178.0 °C = -148.3 °C, and Q = C * m * ΔT. For the water, we have m = 75.0 g, ΔT = 29.7 °C - 24.0 °C = 5.7 °C, and Q = C * m * ΔT. By setting the amount of heat transferred in the metal equal to the amount of heat transferred in the water, we can solve for the specific heat capacity of the metal and determine its identity.