Answer
Aluminum
Work Step by Step
We can identify the required metal as follows:
$c_m=\frac{(c_w m_w+c_{Al}m_{Al})\Delta T}{m_m \Delta T_m}$
We plug in the known values to obtain:
$c_m=\frac{(4190\times0.325+900\times 0.1)(98-78)}{0.512(78-15)}$
$\implies c_m=900J/KgK$
This is the specific heat of aluminum, thus, the required metal is aluminum.
