Final answer:
To find the final temperature, we can use the principle of conservation of energy and the specific heat of gold and water. By setting the heat lost by the gold equal to the heat gained by the water, we can solve for the final temperature. The final temperature in this case is 23.52 °C.
Step-by-step explanation:
To find the final temperature of the system, the principle of conservation of energy can be used. The heat lost by the gold will be equal to the heat gained by the water. Using the equation:
Q(gold) + Q(water) = 0
Where Q(gold) is the heat lost by the gold and Q(water) is the heat gained by the water. The heat in this case can be calculated using the formula:
Q = mcΔT
Let's calculate:
Q(gold) = m(gold) * c(gold) * ΔT(gold)
Q(water) = m(water) * c(water) * ΔT(water)
Substituting the given values:
Q(gold) = (43.12 g) * (0.129 J/g· °C) * (T(final) - 99.22 °C)
Q(water) = (150.0 g) * (4.18 J/g· °C) * (T(final) - 22.91 °C)
Since Q(gold) + Q(water) = 0, we can set the equations equal to each other:
(43.12 g) * (0.129 J/g· °C) * (T(final) - 99.22 °C) + (150.0 g) * (4.18 J/g· °C) * (T(final) - 22.91 °C) = 0
Now we can solve for T(final):
(5.57208 J/°C) * (T(final) - 99.22 °C) + (627 J/°C) * (T(final) - 22.91 °C) = 0
5.57208(T(final)) - 553.2596 °C + 627(T(final)) - 14351.17 °C = 0
632.57208(T(final)) - 14890.4296 °C = 0
T(final) = 23.52 °C