Answer: [tex]T = 302.060 K[/tex]
Explanation:
The gold piece is cooled by water, meaning that gold is heating the water in the meantime, such that thermal equilibrium is reached. By First Law of Thermodynamics the following relation is found:
[tex]\dot Q_{net,out,gold} = \dot Q_{net,in,water}\\ m_{gold} \cdot c_{p, gold} \cdot (650 K - T) = m_{water} \cdot c_{p, water} \cdot (T - 298 K)[/tex]
Specific heats for gold and water are [tex]129 \frac{J}{kg \cdot K}[/tex] and [tex]4186 \frac{J}{kg \dot K}[/tex]. Last expression is simplified by substituting known variables:
[tex]5240 J - 8.063 \cdot T = 690.690 \cdot T - 205825.62 J\\698.753 \cdot T = 211065.62 J\\T = 302.060 K[/tex]
