A 65.0  g piece of gold at 650  K is dropped into 162  g of  H2O(l)  at 298  K  in an insulated container at 1  bar  pressure.  CP,m  for  Au  and  H2O at 298  K  are 25.4 and 75.3  J⋅K−1⋅mol−1, respectively. Calculate the temperature of the system once equilibrium has been reached. Assume that CP,m for Au and H2O are constant at their values for 298 K throughout the temperature range of interest.

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A 65.0  g piece of gold at 650  K is dropped into 162  g of  H2O(l)  at 298  K  in an insulated container at 1  bar  pressure.  CP,m  for  Au  and  H2O at 298  K  are 25.4 and 75.3  J⋅K−1⋅mol−1, respectively.

Calculate the temperature of the system once equilibrium has been reached. Assume that CP,m for Au and H2O are constant at their values for 298 K throughout the temperature range of interest.

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The gold piece is cooled by water, meaning that gold is heating the water in the meantime, such that thermal equilibrium is reached. By Law of Thermodynamics the following relation is found 

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