Consider a small but known volume of metal that has a large thermal conductivity.

(a) Since the thermal conductivity is large, spatial temperature gradients that develop within the metal in response to mild heating are small. Neglecting spatial temperature gradients, derive a differential equation that could be solved for the temperature of the metal versus time T(t) if the metal is subjected to a fixed surface heat rate q supplied by an electric heater.

(b) A student proposes to identify the unknown metal by comparing measured and predicted thermal responses. Once a match is made, relevant thermal physical properties might be determined, and, in turn, the metal may be identified by comparison to published property data. Will this approach work? Consider aluminum, gold, and silver as the candidate metals.