To find the final temperature of the combined metals, we can use the principle of heat transfer and the specific heat capacities of gold and iron. By setting up an equation with the heat gained by each metal and the unknown final temperature, we can solve for the final temperature. The final temperature of the combined metals is approximately 44.2 °C.
In order to find the final temperature of the combined metals, we can use the principle of heat transfer. The amount of heat gained or lost by an object can be calculated using the equation q = mcΔT, where q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we need to calculate the amount of heat gained or lost by each metal separately. For the gold sheet, the initial temperature is 18.4 °C, the final temperature is the same as the final temperature of the combined metals, and the mass is 8.2 g. Using the specific heat capacity of gold, which is 0.129 J/g °C, we can calculate the heat gained by the gold sheet.
Next, for the iron sheet, the initial temperature is 54.4 °C, the final temperature is the same as the final temperature of the combined metals, and the mass is 18.8 g. Using the specific heat capacity of iron, which is 0.449 J/g °C, we can calculate the heat gained by the iron sheet.
Since we assume no heat is lost to the surroundings, the total heat gained by the gold sheet must be equal to the total heat gained by the iron sheet. Setting up an equation with the two heat values and the unknown final temperature, we can solve for the final temperature.
After solving the equation, we find that the final temperature of the combined metals is approximately 44.2 °C.