How to determine the specific heat of aluminum?
If the water and aluminum are regarded as incompressible, then the internal energy is a function only of temperature.  In addition, the heat capacity at constant pressure is equal to the heat capacity at constant volume.  If the pressure is constant, then the change in enthalpy will be equal to the change in internal energy.  So the change in enthalpy of the aluminum is equal to its heat capacity times its temperature change.  The same goes for the water.  So the total change in internal energy and/or enthalpy for the combination of water and aluminum is zero.