A 48.6 g sample of copper at 99.8 ∘C is carefully placed into an insulated container containing 185 g of water at 18.5 ∘C. Calculate the final temperature when thermal equilibrium is reached. Assume there is no energy transferred to or from the container.

Specific heat capacities:
- Copper (Cu): 0.385 J/g⁻¹∘C⁻¹
- Water (H₂O): 4.184 J/g⁻¹∘C⁻¹

To calculate the final equilibrium temperature between copper and water, the heat lost by the copper must equal the heat gained by the water, following the conservation of energy. By substituting the known values into the heat transfer equation and solving for the final temperature (Tfinal), we can find the temperature at which both substances reach thermal equilibrium.

Explanation:

The student's question pertains to the concept of heat transfer and the eventual thermal equilibrium between copper and water. To find the final equilibrium temperature, we can set up the following equation based on the principle of conservation of energy:

Heat lost by copper = Heat gained by water

(mcu imes Ccu imes (Tinitial_copper - Tfinal)) = (mH2O imes CH2O imes (Tfinal - Tinitial_water))

Where:

mcu = mass of copper = 48.6 g
Ccu = specific heat capacity of copper = 0.385 J/g°C
mH2O = mass of water = 185 g
CH2O = specific heat capacity of water = 4.184 J/g°C
Tinitial_copper = initial temperature of copper = 99.8°C
Tinitial_water = initial temperature of water = 18.5°C
Tfinal = final temperature of both substances

By solving the equation for Tfinal, we can determine the final equilibrium temperature when both substances have reached thermal balance.