[Lilly5670]

A 67.0g piece of gold at 725K is dropped into 165g of  H2O (l) at 298K in an insulated container  at 1bar pressure.
Calculate the temperature of the system once the equilibrium has been reached. Assume that Cp,m  for Au and H2O is
constant at its value for 298K throughout the temperature range of interest. Given Cp,m  of Au and H2O are 25.42 JK^-1m^-1
respectively

I know I am given some T values but somehow it does not seem logical to me that I use them as T initial and T final. Therefore I am not so sure how to use T in the delta H equation: delta H= (n)(Cp,m)(deltaT)
I think the volume of the system changes when the gold is dropped in water
I can calculate initial V from what is given but what throws me off here is that I have no way of calculating final V when I don't have final T.
I am just confused about this problem. If anyone can point me in the right direction as to how to approach it, I would really appreciate it.

[Enthalpy]

With only solids and liquids, you can usually neglect the effect of volume variations. Volume is a refinement absolutely necessary to gas but unnecessary to liquids. That's why heat capacities don't tell "at constant pressure", because it changes so little.

The units for heat capacity can't be correct.

After getting a final state, please check that water didn't evaporate.

I'd suggest to evaluate the amount of heat above 298K brought by gold, water, and spread this heat among them for even temperature ("equilibrium"). Easy (but imprecise) with constant heat capacities.

One note about volume and system: what do you want to call system? Water alone? Or with the metal?