An unknown metal with a mass of 8.5 g was heated in boiling water to a temperature of 100°C. The metal was immediately transferred to an insulated cup containing 50.0 g of water at 22°C. At equilibrium (when the temperature became constant) the temperature of the system was 23.2°C. Calculate the specific heat of the metal and determine its identity. Explain how you arrived at your conclusion. You must show your work to receive credit for your answer.

The specific heat of the metal : 0.384 J/g° C,

and a metal with a specific heat of 0.384 is copper

The law of conservation of energy can be applied to heat changes, i.e. the heat received / absorbed is the same as the heat released  

Q in = Q out  

Q lost(metal) = Q gained(water)

Heat can be calculated using the formula:  

Q = mc∆T  

Q = heat, J  

m = mass, g  

c = specific heat, joules / g ° C  

∆T = temperature difference, ° C / K  

the answer your looking for is c).