A piece of metal weighing \(100 \mathrm{~g}\) is heated to \(80^{\circ} \mathrm{C}\) and dropped into \(1 \mathrm{~kg}\) of cold water in an insulated container at \(15^{\circ} \mathrm{C}\). If the final temperature of the water in the container is \(15.69^{\circ} \mathrm{C}\), the specific heat of the metal in \(\mathrm{J} / \mathrm{g}^{\circ} \cdot \mathrm{C}\) is:

Heat exchanged is given by, \(\mathrm{Q}=\mathrm{m} \times \mathbf{s} \times\left(\mathrm{T}_2-\mathrm{T}_1\right)\) where \(\mathbf{s}=\) specific heat
So, when heated metal is dropped into the cold water, we can write:
\(\mathrm{m}_{\text {metal }} \times \mathrm{s}_{\text {metal }} \times\left(\mathrm{T}_2-\mathrm{T}_1\right)_{\text {metal }}=\mathrm{m}_{\text {water }} \times \mathrm{s}_{\text {water }} \times\left(\mathrm{T}_2-\mathrm{T}_1\right)_{\text {water }} \)
\( 0.1 \times \mathrm{s}_{\text {metal }} \times(80-15.69)=1 \times 4.18 \times(15.69-15) \)
\( \mathrm{s}_{\text {metal }}=0.45 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}\)