A copper calorimeter of mass 0.18 kg holds 0.25 kg of water at 16 °C…

Step 1. Water equivalent. $\dfrac{0.18\ \text{kg} \times 385\ \text{J kg}^{-1}\text{K}^{-1}}{4186\ \text{J kg}^{-1}\text{K}^{-1}} = 0.0166\ \text{kg} = 16.6\ \text{g}$.

Step 2. Heat gained. $0.2666\ \text{kg} \times 4186\ \text{J kg}^{-1}\text{K}^{-1} \times 3.5\ \text{K} = 3905\ \text{J}$.

Step 3. Specific heat. $\dfrac{3905\ \text{J}}{0.10\ \text{kg} \times 78.5\ \text{K}} = 497\ \text{J kg}^{-1}\text{K}^{-1}$.